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APhO_2025_1_A_1
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents.
Find the values of exponents: (1) $\beta$, (2) $\gamma$, and (3) $\delta$.
[["Award 0.2 pt if the answer correctly expresses the dimension of $G$ as $[G] = L^3 M^{-1} T^{-2}$, where $L$ is the base dimensions length, $M$ is mass, and $T$ is time. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly sets up the exponent equation $0 = 2 - \\beta$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly sets up the exponent equation $0 = \\gamma + 1$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly sets up the exponent equation $1 = \\delta - 3$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct value $\\beta = 2$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct value $\\gamma = -1$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct value $\\delta = 4$. Otherwise, award 0 pt."]]
["\\boxed{$\\beta = 2$}", "\\boxed{$\\gamma = -1$}", "\\boxed{$\\delta = 4$}"]
["Numerical Value", "Numerical Value", "Numerical Value"]
[null, null, null]
[0.3, 0.3, 0.2]
text+illustration figure
Mechanics
APhO_2025
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
None.
1
APhO_2025_1_A_2
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$.
Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1.
[["Award 0.1 pt if the answer correctly calculates $\\omega = \\frac{2\\pi}{24 h} = 7.27 \\times 10^{-5} s^{-1}$, where $\\omega$ is the angular speed of the Earth's rotation. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly gives $h_{\\max} = 21.9 \\mathrm{km}$ from the relation $h_{\\max} \\propto \\frac{\\omega^2 R^4}{G M_E}$, where $R$ is the Earth's radius and $M_E$ is the Earth's mass. Otherwise, award 0 pt."]]
["\\boxed{21.9}"]
["Numerical Value"]
["km"]
[0.2]
text+illustration figure
Mechanics
APhO_2025
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
None.
2
APhO_2025_1_B_1
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis.
Find (1) the direction and (2) magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$.
[["Award 0.2 pt if the answer correctly expresses the magnitude of $U(z) = -G \\frac{M_S}{\\sqrt{z^2 + d_{SE}^2}}$, where $M_S$ is the Sun's mass, $z$ is the axis coordinate, $d_{SE}$ is the Earth-Sun distance, $G$ is the gravitational constant. Otherwise, award 0 pt.", "Award 0.1 pt if the answer includes the correct negative sign in $U(z) = -G \\frac{M_S}{\\sqrt{z^2 + d_{SE}^2}}$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer expresses $g_z(z)$ as a derivative $g_z(z) = - \\frac{dU}{dz}$. Partial points: award 0.1 pt if the answer does not include the negative sign. Otherwise, award 0 pt.", "Award 0.2 pt if the derivative is calculated correctly as $g_z(z) = -G M_S \\frac{z}{(z^2 + d_{SE}^2)^{3/2}}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly obtains the approximate form for small $z$, $g_z(z) \\approx - \\frac{G M_S}{d_{SE}^3} z$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer indicates that the negative sign means $g_z$ points towards the center of the Sun ring (correct direction in figure). Otherwise, award 0 pt."], ["Award 0.2 pt if the answer correctly writes the gravitational field of an element of the ring as $\\mathrm{d}g = G \\frac{\\mathrm{d}M}{z^2 + d_{SE}^2}$, where $\\mathrm{d}M$ is the ring element mass, $z$ is the axis coordinate, $d_{SE}$ is the Earth\u2013Sun distance, and $G$ is the gravitational constant. Otherwise, award 0 pt.", "Award 0.1 pt if the answer includes a figure with correct geometry showing $\\mathrm{d}g$, $\\mathrm{d}g_z$, angle $\\theta$, $z$, and $d_{SE}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer takes only the $z$ component for symmetry reasons, writing $\\mathrm{d}g_z = - \\mathrm{d}g \\cos \\theta$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer sums or integrates over the whole ring to obtain the total field. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly calculates $g_z$ at arbitrary $z$ as $g_z = -G M_S \\frac{z}{(z^2 + d_{SE}^2)^{3/2}}$. Otherwise, award 0 pt.", "Award 0.1 pt if the approximate form for small $z$, $g_z \\approx - G M_S \\frac{z}{d_{SE}^3}$, is correctly given. Otherwise, award 0 pt.", "Award 0.2 pt if the answer indicates that the negative sign means $g_z$ points towards the center of the Sun ring (correct direction in figure). Otherwise, award 0 pt."]]
["\\boxed{The direction of the gravitational field is toward the center of the Sun ring.}", "\\boxed{$g_z(z) \\approx -\\frac{G M_S}{d_{SE}^3} z$}"]
["Open-Ended", "Expression"]
[null, null]
[0.2, 0.8]
text+illustration figure
Mechanics
APhO_2025
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None.
3
APhO_2025_1_B_2
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$.
Find (1) the direction and (2) magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$.
[["Award 0.5 pt if the answer presents the idea of using Gauss's law to calculate the gravitational field in the plane of the Sun ring. Otherwise, award 0 pt.", "Award 0.4 pt if the answer correctly identifies a cylindrical Gaussian surface with axis along $z$ near the center of the Sun ring. Otherwise, award 0 pt.", "Award 0.6 pt if the answer writes Gauss's law correctly as $g_r 2z \\times 2\\pi r + g_z \\cdot 2r^2 \\pi = 0$, where $g_r$ is the radial component and $g_z$ the axial component. Partial points: award 0.3 pt if there is a mistake in areas; award 0 pt if the error is dimensional. Otherwise, award 0 pt.", "Award 0.3 pt if the answer correctly obtains the final result that $g_r$ is proportional to $r$, i.e. $g_r(r) \\propto r$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer gives the correct proportionality constant $g_r(r) = \\frac{G M_S}{2 d_{SE}^3} r$. Partial points: award 0.1 pt if the prefactor is wrong but dimensionally consistent; award 0 pt if the error is dimensional. Otherwise, award 0 pt.", "Award 0.2 pt if the answer indicates that the field points radially outwards (correct direction in the figure). Otherwise, award 0 pt."], ["Award 0.2 pt if the answer correctly expresses the distance $s = \\sqrt{d_{SE}^2 + r^2 - 2 d_{SE} r \\cos \\varphi}$ from trigonometry, where $r$ is the distance of point $P$ from the center, $d_{SE}$ is the Earth-Sun distance, and $\\varphi$ is the angle. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly writes the potential generated by a small element of the ring as $\\mathrm{d}U = - G M_S \\frac{\\mathrm{d}\\varphi}{2 \\pi s}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes the total potential $U(r)$ as an integral $U(r) = - \\frac{G M_S}{2 \\pi} \\int_0^{2\\pi} (d_{SE}^2 + r^2 - 2 d_{SE} r \\cos \\varphi)^{-1/2} \\mathrm{d}\\varphi$. Otherwise, award 0 pt.", "Award 0.6 pt if the answer expands the integrand to second order and obtains $(1 + \\varepsilon)^{-1/2} \\approx 1 - \\frac{r^{2}}{2 d_{SE}^{2}} + \\frac{r \\cos \\varphi}{d_{SE}} + \\frac{3 r^{2} \\cos^{2}\\varphi}{2 d_{SE}^{2}}.$, where $\\varepsilon = \\frac{r^2}{d_{SE}^2} - \\frac{2r \\cos \\varphi}{d_{SE}}$ and $(1+\\varepsilon)^{-1/2} \\approx 1 - \\varepsilon/2 + 3\\varepsilon^2/8$. Partial points: award 0.1 pt if only first order is calculated; award 0.4 pt if the $\\cos^2 \\varphi$ term is missing. Otherwise, award 0 pt.", "Award 0.2 pt if the answer integrates over $\\varphi$ correctly: $U(r) = -\\frac{G M_{S}}{2\\pi d_{SE}} \\int_{0}^{2\\pi} \\left( 1 - \\frac{r^{2}}{2 d_{SE}^{2}} + \\frac{3 r^{2} \\cos^{2} \\varphi}{2 d_{SE}^{2}} \\right) \\mathrm{d}\\varphi$. Partial points: award 0.1 pt if the $\\cos^2 \\varphi$ term is missing. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly expresses $g_z$ as the derivative of $U(z)$: $g_r(r) = - \\frac{dU}{dr}$. Partial points: aAward 0.1 pt if the negative sign is omitted. Otherwise, award 0 pt.", "Award 0.1 pt if the derivative $\\frac{dU}{dr}$ is calculated correctly, yielding $g_r(r) = \\frac{G M_S}{2 d_{SE}^3} r$. Otherwise, award 0 pt.", "Award 0.3 pt if the final result shows $g_r \\propto r$. Otherwise, award 0 pt.", "Award 0.2 pt if the proportionality constant is correct, $g_r(r) = \\frac{G M_S}{2 d_{SE}^3} r$. Partial points: award 0.1 pt if only the prefactor is wrong but dimensionally consistent; award 0 pt if dimensional error. Otherwise, award 0 pt.", "Award 0.2 pt if the answer indicates that the field points radially outwards (correct direction in the figure). Otherwise, award 0 pt."]]
["\\boxed{The direction of the gravitational field is outward along the radial direction.}", "\\boxed{$g_r(r) = \\frac{G M_S}{2 d_{SE}^3} r$}"]
["Open-Ended", "Expression"]
[null, null]
[0.2, 2.0]
text+illustration figure
Mechanics
APhO_2025
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tOUALa20cX5KAa8a8N3kXjP8AaOv9UhIks9Lt2SJxyDtGzI+pZjWrs6yt01+SM46Um+/5s7n4x6zJonwz1KWCVop5ylvG6NhgWYZwR7A1wnhbwt4n+JHhPTTqWt3mk6FbwLHBFExaW7Yfelck9M5xnP8AU3fj/O9+/hjw1CT5l9ebyo/BF/8AQz+Vex2NnDp2n29lboEht41iRR2AGBWcVdOT7/l/w5UnZpLt+f8AwxyF5d2Pwm+GmZJpLtbJCkRlPzzyMSQD+J/IVwmg/D7xB8SbBfEfjDxFqFqt2PMtLK0bYsaHocHIAPpjOOSaX9omWa5TwzpEbhEurl2JPTd8qgn6bjWivwx8fajbrZat8QpI7AKEMVlDtyoGNvG3j86FeV5P+u437tooq/BfUtTt/FniXwxLqkup6Zp7HyJ5GLbSH28HnAI7dOK9qrnfB3grR/BGlGx0mJsyENNPKcySt6k/0HFdFVPZIlbthXzePGWiWH7Qmsa7rl00VrZh7eArG0mXUBOig/7Rr6Iv7tLDTrm8kOEgiaVj7KCf6V4n8CNAstb07Xde1awtrt7u92obiFZMYyzEZB7v+lTH47rovz0HK3JZ9X/wTd1X42aNqFpJp/hK1vtY1e4QpBFHbMqqSPvNnnA68D8q1Pg/4HvPBfhiYantGo30vnTRqc+WAMKuR1PUn61h/Gbwb4esvBFzrljYW2nalZPG0M9ogiZiXAwduM9c+vFdt8N9WvNc+HujahqDF7qWDEjnq+CV3H6gZpwtaTW+36hK90uh1NFFec+PviS2i3SeHPDUH9peJrn5EhjG5YM/xN798fieOqbGkUPjV4qig0D/AIRLTwbrWtXKxLbx8siEjkj3xgfie1dl4D8Ot4U8E6Zo8hDTQRZlI6b2JZsfiSK574ffDX/hHriTX9fn/tHxNdZaW4c7hDnqq+/Yn8BxXolUlyprq/6sS3zNdl/VwooopDCiiigDN8Rf8izqv/XnN/6Aa8x/Zz/5EK+/7CL/APoCV6d4i/5FnVf+vOb/ANANeY/s5/8AIhX3/YRf/wBASiHxT9F+YT2j6v8AI9Q15mTw9qbKxVltJSCDgg7DXnH7P97d3/gS7lvLqa4kF+6h5pC5xsTjJr0bxB/yLeqf9ekv/oBrzL9nX/kn93/2EH/9ASiHxS9F+YT2j6v8jnvGuteJbb47nTNAvHjnvbWO3jV2Jji3rzJt6ZABPStbWvgneJplzqVt4x1mbWo42lEksuFdgM44OVz9TioL5Q37VNlkZxagj/vy1e03n/Hjcf8AXNv5VD0pXW+v5srepbpp+R4B4HvvGPxZ00aTea7Pp+m6aoW6urfie6Yk7VJ9gOf1zmmeNfCWr/CJLHxJ4e8R6hPb/aBFPBcvkHOSMgcMpwRyK6D9nED/AIRvXD3+3D/0AVq/tBf8kz/7fYv/AGarqPks1vp+NiYK909tfwO6uvElrZ+DW8STgi2WzF2VHXBXcB9ecV4/4Z8K658XrebxL4l1+/s9OllZbOysn2qFBxnnIxnjoScda6fxmksn7OxEWcjTLUnH90bCf0rk/h94E8T634H02+0v4i32nWkisFtIoCVhIYgjIkHfnp3ptLnlpsKLfs4+ZLLLrXwY8baVaSaxdan4Z1NthS6bLRHIBI9CMg8YBHaveuteLap8ENf1xrf+1/iFc3ywPvjE9mW2nvjMvHSvZ0XZGq5zgAZo+zrv+gfa02HVieLdJ1PW/D01jpGryaVeSMu26jHKjPzD16Z6EVt15n8S/iDqug6xpnhjw3bxS63qWNskwysQLbRx6kg9eAB3qXrZdylpr2Mub4DQyWrynxdrj6njK3Dyjbu9SPvf+PU/4NeINU8Q6NrvhzXrmS5uNOfyPPZyXKNuUgt1JBU4PXmrkPgH4gXaebqfxKuYZW5aOztFCj6HK/yrm/gDG0XiLxlG87XDJOimZushDyfMfr1qkrtxfb/ImWiUl3Re+DerahpninxH4L1i7mnuLWUywPPIWYqDtOCexG0/ia7P4q+JD4Y+HupXcUhS6mX7NbkHBDvxkfQZP4VwnxMjbwX8V/DvjWEFba6YW94R04+U5+qH/wAdo+KDN41+J3hrwXbtutYiLq729MHk/wDjgP8A31U6zjFdXo/l/wAAq6hJvpv/AF8zV8PancfDr4IDXdUlmutQnTz1W4kZiXk4jXJOcAYJ/Gsbw78M9W8f6RF4k8XeJtUSe+HmwW9s4VYkP3eCCBnrgAVsftBwOvw1t1gXbDFfRbgvQLtYD9cVQ8P/AA68Xah4c028svifqENtNbRvFElu2I1KjCj9726fhTvzOUrdUvwJtyqK+ZF4a1XXPhz8ToPBWr6pNqekagoNlNOSXjJzt5PTkFSOnQiuj+O15c2Pw3ea0uJbeUXcQ3xOUbHPcVlwfBjWZPE+l65q/jifU5bCZJEE9oclVbdtDGQ4zV79oD/kmL/9fkP9amb9xX3v+qsVBe+7bW/Q5/SfC/ib4saZbavrGu3Wk6N5apZ2dtktIFGDI/IHJB65/CvTbXwxc6V4C/4R7TdWnjuo7do4b9xlw5JIY9e5qfwQip4E0BVAAGnw8D/cFc98U/iBN4G0q0TT7ZLjVNQkMdusnKrjGWIHXqAB71pVsm4ruRT1SkYI+BSXcRm1fxjrt3qBGTMsoChvo24/rVb4S61rem+Ntd8C6xqEl+lgpe3mlYswAYDGTzghgcdq0bTwV8StViW51j4gvYSuNxtrK0UhM9sgr0/H61y3w0sp9O+PviCzutRl1GeG1dHu5RhpDmPk/wAvwoh8dvJjl8F/NG78VfFeuXfijTfAXhi5a2vb4Brm4RirIpzgAjkDALEjnGKWH4H3Omwi70vxprEOsINwmZv3bP7r1x9SfxrMYiD9qsG44Elv+5z/ANcO35Gvc6iK9xPqxyfvW6Kx4R8KNe17WPi5ri67M/2mG0MUsCsfLV0ZEJC9BnBPHrWn+0Df3lhpnh9rO7nty94wYwyFNwwODjrVPwA0bftDeMTGQV2SDj13pn9c1J+0X/yC/Dn/AF+t/wCgimneNN+n5glac16/kd18TJ5rf4W61PBLJFKtqCsiMVYHK9CK8z8DeH/E3xN8KWkmr+I73T9FtV+zwxWrESXLL1d2PXrjnPT8/Sfil/ySbXP+vQf+hLVb4LqF+FGi4GMiQn/v41CXvSv5fqK9oxt5/kjzTxd4e1v4NXGna/ofiG+u9PknEU9tdPkE9cEDgggHnAIr3HU/ENtpnhOfxBKD9nitftO3uRtyB+OQK88/aI/5J3b/APYQj/8AQXq/4/SST4BziLORp9sTj0BQn9Klyfs5eT/NFqK9pHz/AMzifCvhLXvi9HP4m8Sa/fWlhJKyWtraNgAA84B4AHToScGq3xG0nxR8NfDL2dj4ivb/AELUGWLNw5861kB3DawPQgEcYHtXqPwckik+FOh+UR8sbq2P729s1jftAtGPhkwcjcbyIJ9ef6Zp1VyaLyJpvm1fmdx4OkeXwVockjs7tYwlmY5JOwck1t1heCv+RG0H/sHwf+gCt2tKnxv1Ip/AvQ80+Ot3c2Xw2kmtLiW3lF1EN8TlGxk9xU+peI77w78DLfWrUmS+j02Da7/NhmCruOeuM5ql8f8A/kmEv/X3D/M11fhaxtdT+G2j2N7Ak9tPpkKSRuMhlKDIrJJuE0u6/I0bSnBvs/zPL/CfwuTx14atfEWs+MNYuby8UyHyJxtiOfunIPI9OK9D8C+B73wbLerP4kvtVtJQot4bknEOM56kjJ46Yri7z4O654ZupdQ+HviSeyYncbG4fKN7Z5B/4EPxrb+GnxF1PxBqt/4Z8S2K2mu2ClnKDCyAEA5HY8jpwc8Vomm/d08iWml72vmemUUU1wTGwHXBxUN2Vxnh93e658XfHmpaJp+rT6X4a0o7JpLY4adskde+SDjPAAzjNVvFfgfWPhXpq+KPC3iPUporaRftVrduGV1JAyQMAjOBgjPOc1zPws8La74gutfi0zxfdaDPbzjz4oYixlyW5OHXoQR+NegX/wAH/FmqWMtlf/Ey+ubWUYkiltWZWHXkebRZqKtv+Y3Zyaex3dp40sp/h4ni91K2/wBjNy8YPIYDlf8AvoYrybwv4e8UfF5bjxFrfiO903TGlZLW1s2KjjrgZwAOmSCSQa6bxb4Xl8Jfs+6hoSXZu2tYgTMI9m5TMGPy5OOD61v/AAceJ/hToflYwI3DY/veY2arRyk102+ZN2oxT63/AAPM/iFaeMPhp4ZktLbxJeajo1+yxJNM7LPaSAhsK4OcEAj+nr7R4Omln8CaJNNI8kr6fEzu7EsxKDJJPU1xf7QDRj4YyB8bjeRbM+vP9M12Pgn/AJJ9oP8A2Dof/QBUp3pzv3X5DatKNuz/ADPOvgDqF7fR+Jvtl3PceXdIE86QvtHz8DJ4r0D4iTS2/wAO/EE0MjxypZSFXRiGU46gjpXm37O/3PFQ7/a4/wD2evQ/idKkXwz8Qs5ABsnX8TwP1NKr8HyX5FU/4nzf5mT8FLq4vPhhYT3U8s8rSy5klcsx+c9zXNfA2/vL3WfGC3d3POsd0oQSyFgo3ScDJ4roPgX/AMkp0/8A66zf+hmuX+Af/Ib8Z/8AX2v/AKFJWsv4j9P8jJfw/n/mP8H3994S+N+r+F7+8uJbLUFMll58pYL/ABqBk8cFl/CvU/FeuR+G/CupavIR/osDOoPd+ij8SRXmXx002fTJtB8bWC4udMuVSUjuudy59sgj/gVV/jHr58S6V4X8OaQ+59ekjuMD+4cbc/ic/wDAay1lTUVve3+X4fka6Kbk9t/8zb+BdjqLeE7jXNVu7m4n1KctH50jNtjUkcAnjJ3fpTbz4PXuvand3fiDxprFxE8rGCC3fYI0z8o5yM49FFdfquoWPw88APcCIvbaXarHHGvBcjCqPxJHNefeHY/iX8RdNj1uTxPD4f024JNvBa2wdyoOM84Pbu34VcrOT5ehEbqOvUyI4dX+EvxS0TSYNau7/QtXZU8m6fdty23p0BBIORjNdZ+0B/yTF/8Ar8h/rXAeNNA1PQPiZ4Lh1TxLda3LJdRurXCBTEPNUYAyev8ASu//AGgP+SYv/wBfkP8AWonrST8/1RcdKjXl+jOy8IzR2/w/0WeVgscemwuzHsBGCTXkmkW2ufG7WNR1C61m80vwzay+Tb21q20yHrz2JxgknPXAr0SFJZPgkqQZ81tBwmOufJryL4T+DvEHiLwnLc6P46u9GiS5ZHtIYSwDYB3ZDjqCO3atJ61Z36f5mcNKUbdf8jV8R6VrfwUvNP1vR9bvtQ0SaYQ3NnePu9/pyAcEAEEd69K+IupGb4S6tqVjM8fmWazRSIxVgGKkEEdODXHar8FvE2uWf2TVfiPeXlvuD+VPaFl3DocGWuk8d6adG+B2oaYZvONpp0cHm7du/btGcZOOnrWc3+7lf5Fx/iRt/Wpwfgbw/wCJvib4UtJNX8R3un6Lar9nhitWIkuWXq7sevXHOen51PF3h7W/g1cadr+h+Ib670+ScRT210+QT1wQOCCAecAivS/guoX4UaLgYyJCf+/jVhftEf8AJO7f/sIR/wDoL1dV8krruvzJpLnVn5nXeLtHbxh4QTyNXvtNheH7QxtHCmVSmQjH0rxL4Q/D0eL/AA9e3Z8Q6rpvlXXl+XZy7Vb5QckevNe+6f8A8iHa/wDYMX/0UK82/Zw/5E7Vf+v/AP8AZFp8qU5ry/ULt04P+tj1fRNM/sXRLPTftM119mjEfnTnLvjux9av0UUm7u40raHzV8WfCctn8QtAWbXdSu31W4PzyvzbDzFAEfoBu/SvWvCfw0HhXWxqX/CS6xqGI2j8m7l3Jz3x61xXxp/5KN4E/wCvgf8Ao1K9wohpTTXdhPWfyR4t4z8Q+IPGfxF/4QHw1qD6dbW67r+8iJDdAWGRzgZAwCMk80+7+BlzYWrXeg+L9Yj1aMb0eWXCuw7fLgjP1NUvhv8A6P8AHzxnBc8Tyea0eepHmKePwIr3Opiv3cX1auNv32ui0POPhH46vfFmlXmn6yANZ0uTypzjHmDkBiPXIIP/ANevR68M+EZE/wAX/HFzb82pkkGR0yZjj+Rr3OqvzRjLuibWlKPZjX+430NeN/AHUL2+j8TfbLue48u6QJ50hfaPn4GTxXsj/wCrb6GvEv2d/ueKh3+1x/8As9TH4n6fqhy+Fev6M9J+Ik0tv8O/EE0MjxypZSFXRiGU46gjpWH8FLq4vPhhYT3U8s8rSy5klcsx+c9zWt8TpUi+GfiFnIANk6/ieB+prE+Bf/JKdP8A+us3/oZpx+16L82Eto+r/I8x8By+L/F2sa54astdubGwF0891eh2eVEyVEaEnjPtjp+B3/FHwhvfDGhXev8Ah/xXrBvrJDcMJpfvheWwVxg455zU3wBUf2x4ybHP2pBn/gUleq+Mv+RI13/sHz/+gGok+WmpLey/IqPvVGntcyfhh4ouPF3gOx1O8wbsFoZ2AxuZTjdj3GDXE+Cb+8m/aA8WWst3O9tHHJshaQlF+ZOgzgVq/s//APJMk/6/Jf6VheBP+TivGH/XKT/0NK2f8b5P8kZf8uvmvzOf+OXha40yfTNQuPEGpX5vbt1WK4cbIBwcIB06/pXqfg/4bjwtqy6n/wAJHq+oZhKeRdy7kGcc49eK4/8AaK/48PDX/X6/8lr2hQTbADrs4/Ks4vlg2u/6IuWslft+p4de6l4g+Lfj3UdB0rVptK8OaYSs8tuSGmIOOxGckHA6ADNT6z8IdV8K6bNrPhHxVq32+0QymGeQETADJHGB+BBBpn7PRENz4rtZuLtLlC4PXALg/rXtd08cVnNJKQI1jZnJ6YA5pS92Ca3te495tPa9rHJfDHxqfHPhGLUJlVL6FzBdKvA3gA7gPQgg/nXk/wDb/it/i34q8O+H7mT7VqE5iillkJSzRTlnA6Dj0rd/ZxRzpXiGYA+Q92gT0yFOf0IpngNFP7RPjBiASqS4Pp86VbSdVej/ACTJvam/X9WdT4Q+FD+GfEMOuXXiXUNTu1RhIs33HZhjPJJ/OuI8a614ltvjudM0C8eOe9tY7eNXYmOLevMm3pkAE9K9/rw++UN+1TZZGcWoI/78tS3nFPbX8mN6Rk+v/BRPrXwTvE0y51K28Y6zNrUcbSiSWXCuwGccHK5+pxWF4HvvGPxZ00aTea7Pp+m6aoW6urfie6Yk7VJ9gOf1zmvf7z/jxuP+ubfyrx39nED/AIRvXD3+3D/0AUR1ck9kr/jYJaJNb3Of8a+EtX+ESWPiTw94j1Ce3+0CKeC5fIOckZA4ZTgjkV7Zf3q6l4Eur5BhbnTHmA9A0RP9a4j9oL/kmf8A2+xf+zV1Fl/ySWH/ALAg/wDRNRJ3pTv0/wAilpUhbr/meefBfTJNY+Dus6fDcS2809zKsc0TlWR9ibSCOeuK2Pgb4lvdR0XUdC1eeWXU9KuCrGdyzlCT1J5OGDD8qh/Z2/5J9df9hB//AEBKzdXT/hAPj/Y6mvyaZ4hXypeyiQkA/wDj21vxNbP+JbukvnbQyX8Nvs2/x1Oj+OHiefw/4IW1sZ5Ir/UZlhiaJirqo5Ygjn0H411vgrSrrRvB2mWV9cTXF4sIaeSaQuxduSMnngnH4V5draf8J5+0FY6Xjfp2gRiSYdi4wx/Nii/hXuFRH4L9/wAkXL4rdvzYV418V9d1a78daF4LtNXfR7G/UPcXcbbWbLEYzkcfL0zyTzXstcr42+H+ieO7KOHU0eO4hz5F1CcPHnt6EexpPdMa2ZxUnwGt4k83TvF+u214ORM0oYZ9cLtP616BLa3WkeAp7aa/muru209w927He7hDls9eteT39j8SfhNaNfWerJr/AIft+ZIbgEtGmfQnKj3ViPavS7XxHbeLPhlca3ao0cdzYTExsclGCsGHvgg0qj/dysEF78bnj3w2j8ZfETQJNLfxHeafpNlI3n3aOz3FwzchNxOQAPfv37XvFXg/xT8LbRfE3h7xRf31rA6/ara6YsNpOMkZwwzweARmt79nN428CX6KR5i37Fh9UTFdn8UJIo/hj4hMxG02bKM/3jwP1xV1XyarsvyJpe9o+/6ktr4ij8S/DSTXLXMf2nT5ZMA8xuEIIz7EGvFfh43jD4heHV8O22sXGn6ZZyM99qG9nlmLHKxqc54Ge/8AhXc/C1JE+AcvmZw0F2Uz6fN/9eo/2dUUeALxgAC2oPk+vyJTcV7SfovzFzPkj6s39A8NWfwo8Na1qE2qXeoQhPPc3HUbQflH1JrhPDPhXXPi9bzeJfEuv39np0srLZ2Vk+1QoOM85GM8dCTjrXoHxiSWT4U64Is5EaE4/uiRSf0rzr4feBPE+t+B9NvtL+It9p1pIrBbSKAlYSGIIyJB356d6he8230sU9EkutyWWXWvgx420q0k1i61PwzqbbCl02WiOQCR6EZB4wCO1e7TI0tvIkchjZ0IWReqkjgjNeNap8ENf1xrf+1/iFc3ywPvjE9mW2nvjMvHSu7+IPjJPAXhBtT8kXFwWWC3jY4DOQeT7AAmnJ+5739dgS9/Q5BPgjPqe6fxL401q9u2Ocwy7FX2Abd+mKyfBl1rXgX4vnwPd6tcajpd1EXtzOxJT5SwIz0+6QQOD1rV0fQPib4s0+31XU/Go0aK5QSx2tnaKxVSMjJyMHHua5Wy0m90X9o7RbLUNbn1i4WAsbmddrYMb4XGT0/rVRTU0n5/kKTTg2vU7b4yeNtT0C107QtAcpq+rPsWRfvRpkD5fQknGe2DWdYfAuUWqXV54x1ldZI3NPDL8qv+PzH65FZ3xNIh+PHgua44tz5IBPTPmt/iK90qIL3Obq2/wHJ+9y9LL8T5v8NtraftE6fZ+IJkuNQs43t2uFGPPURMVc+5UivRfjrd3Nl8NpJrS4lt5RdRDfE5RsZPcVzF60bftU2YQjItgHx6+S39MV0Px/8A+SYS/wDX3D/M0pO9OL/r4hxX7x+n6HSaZNK3wlt52lczHRQ5kLHdu8nOc+teOfDOz8WfEPw/JpUviK80/RbGQ+dPE5M9w7c7NxPQD+fQ9vX9K/5I7bf9gMf+ia5L9nVQPh/dkDk6g+f++ErSSXtan9dTOL/dw/roc340+Huq/DXSP+Eo8NeKNUY2si+fFPJnIJxnjgjJGQR3r2Xw14hTWvBdhr84ESzWgnlx0UgfN+GQawfjL/ySjXP9yP8A9GLWd4VSST9nqNIc+Y2kThceuHrNyahPy/yZoopzj5/8A4jRrTXvjfruo6heazd6b4ctJfKgt7Zsbj2GOmcYJJz1wKteMPCviL4YeF72/wDD/iO+vdKljNvdWt424xBxtEiEdCCR0A/Gt/8AZ4kib4dzohHmJfybx35VcfpXT/Flo1+FuvmQjBt8DPruGP1p1VyRsu33hTfPK77kPwfuJrr4X6PNcTSTSssm55GLMf3jdSa7muC+DH/JKNF/3ZP/AEY1d7WlT42Z0/hR5z8Y/Dsur+Db6+Gr31rDYWskrWsD4juCORv9RXn/AMM/hgPE3gez1T/hJ9asfMeQeRazbY1wxHA969d+JX/JNfEX/XjJ/KsH4Gf8kq07/rrN/wChmogvi+X5s0m9I+r/ACM/48Q/Z/hQsO9n8u5gTc3U4BGTWJ4X8Ba34+8LadqGveI7+w0/yEjstPsW2KsajaGYngk4z0/HtXQftAf8kxf/AK/If612nghQvgTQFUYA0+Dj/gAohqpt91+QpaOKXZ/meN3kOu/Bzx3osMWu3eo6DqcgjeG5YnHIDcdARuBBGK9J+KnjaTwR4TNzZhW1G6k8i1DDIViMlsd8D9cVxfx+/wCQn4N/6/H/AJx1X/aNjkZPDD+YYoRPKrSAZ2MdmD+QNTdygl52/IaSUr+V/wAy5pvwXvtb02LU/EvizWDrFwglIil+WEnkDnOce2Kn+G3iTXNF8dah8PfEd69+8Cl7O6kJLMoAOCTyQVOeemCKsJ8MfGzxq6fFbUirAEEW7dP+/tS+G/hFqWj+OrXxTqfi2XVbmEMrCW1Ks4KFR83mHpn07VotJdl/ViHrHuz1WiiipKPA/F66p8Mvi5L42TT5L3Rr9ds7R/wZADKT2OVBGeD0r1Hwx8SPC3i4ImmapGLph/x6z/u5R7bT1/DNdTJFHNE0UqK8bDDKwyCPQivJ/iH8HfD15o97q+iwDStTtYmuFNv8sblQWwV6A8dRilfljZ7IduaV1uz1h/uN9DXjfwB1C9vo/E32y7nuPLukCedIX2j5+Bk8V0Pwa8TX3if4erNqUjTXVrK9s0zdZAACCT3ODjPtXK/s7/c8VDv9rj/9nqrWm15fqib3gn5/oz0n4iTS2/w78QTQyPHKllIVdGIZTjqCOlYfwUuri8+GFhPdTyzytLLmSVyzH5z3Na3xOlSL4Z+IWcgA2Tr+J4H6msT4F/8AJKdP/wCus3/oZpR+16L82OW0fV/keY+A5fF/i7WNc8NWWu3NjYC6ee6vQ7PKiZKiNCTxn2x0/A7/AIo+EN74Y0K71/w/4r1g31khuGE0v3wvLYK4wcc85qb4AqP7Y8ZNjn7Ugz/wKSvVfGX/ACJGu/8AYPn/APQDUSfLTUlvZfkVH3qjT2uZPww8UXHi7wHY6neYN2C0M7AY3Mpxux7jBrsa8t/Z/wD+SZJ/1+S/0r1Ktp/EZw2CvKrz4PXuvand3fiDxprFxE8rGCC3fYI0z8o5yM49FFd54s8RQeFPDF/rdxGZEtY9wjBwXYnCjPuSK8x8Ox/Ev4i6bHrcnieHw/ptwSbeC1tg7lQcZ5we3dvwrNav0L2XqZEcOr/CX4paJpMGtXd/oWrsqeTdPu25bb06AgkHIxmvTPix/wAkt8Qf9e3/ALMK8g8aaBqegfEzwXDqniW61uWS6jdWuECmIeaowBk9f6V6/wDFj/klviD/AK9v/ZhSnrRv6hHSrb0KPwfmjt/hDpM8rBY445Xdj2AdiTXBaTH4h+N2tajeTazdaT4ZtJfKhgtTgyHtnsTjBJOcZwBXUeBIpZv2d/Kgz5r6fdKmOucviof2eJYm+Hc8aEeYl/J5g78quP0rSSvVlfov1M4u1ONurMPxJ4A174Z6a3iXwn4l1CeO0Ie5tLttyumeTgYBHqMdOQa9a8HeJYfF3hSx1qFQn2hP3kec7HBww/MVF49lih+H/iB5yBH9gmBz6lSB+uK4/wCAEcqfDGNpAdr3crJn04H8wamLvzJ9LMuStytdbo888By+L/F2sa54astdubGwF0891eh2eVEyVEaEnjPtjp+B3/FHwhvfDGhXev8Ah/xXrBvrJDcMJpfvheWwVxg455zU3wBUf2x4ybHP2pBn/gUleq+Mv+RI13/sHz/+gGok+WmpLey/IqPvVGntcyfhh4ouPF3gOx1O8IN2C0M7AYDMpxux7jBrzW8u9d+MHxB1HRLDVp9N8N6WxWVoCQZSDjJwRkkg4zwAK6f4BAn4XADr9rmx+lYP7PBWObxVBLxdLcxlweuPnH881rJJ1Plf8vyM4tqn87fmWtU+H+t/DjSrjX/CniXULkWiGS5sL1t8c0Y+9jGMEDnpn3rT+AN9dah4Eupry5muJft7jdK5YgbV4ya9C8SNGnhfVmlIEYs5i2fTYa81/Z2/5J9df9hB/wD0BKUHrJeS/Mc1pH1/Q9drmfHXh6XxJ4eltU1e+05Iw0jm0baZQFPysfSumqrqf/IKvP8Arg//AKCazqfCzSHxI+b/AIQ/D0eL/D17dnxDqum+VdeX5dnLtVvlByR6816x480z+xfglqum/aZrr7NZCPzpzl3ww5Y+tc3+zh/yJ2q/9f8A/wCyLXafFj/klviD/r2/9mFXX0i0uy/IilrJPz/U8r+HHhLXvHngu0jvNeu9K0C0LQwW9kdr3DbiWdj6ZOB16fmni7Qdc+DVxp2vaJ4iv7zTpJxFPbXT5BOM4I6EEA84BFek/BdQvwo0XAxkSE/9/GrC/aI/5J3b/wDYQj/9BenVfJK67r8xUkpKz8zsvFvjKDw14Dm8RhA5MKNbxsfvO4G0H88n2BrzXw78M9W8f6RF4k8XeJtUSe+HmwW9s4VYkP3eCCBnrgAVP8ZElb4J6IyZ2K9qZMenlED9SKd4f+HXi7UPDmm3ll8T9QhtpraN4okt2xGpUYUfve3T8KLLmn5OwJvlj5q5F4a1XXPhz8ToPBWr6pNqekagoNlNOSXjJzt5PTkFSOnQivb68fg+DGsyeJ9L1zV/HE+py2EySIJ7Q5Kq27aGMhxmvYKPsq+/9WD7Ttt/VwryT4peMdcbxJpvgbwrN5Gp3+GmuVOGjU5wAe3AJJ646V63XhbEQ/tVg3PAkt8Q5/64cY/EGpSvNRe3+XQq9otovj4DSmETP421f+0cZM4JK7vpuz+tdR40trvQfgxqNt/aFxPd2tgqm8aRvMdgRls5z+td7XHfFb/kl3iD/r1/9mFKo/caHBe+iv8AB+5nu/hdpE9zNJNKwk3SSMWY/vG6k15B4K1Pxj4lv9b8J6PqU1sJrx5rnUZJGdreEErtTnIJPoR+HNetfBf/AJJRo30l/wDRjVxvwBRf7Z8ZPgbvtSDPtukrSaTqtPaz/NGcXandd/8AM7HwZ8OoPAV3e6pLr17f+ZblZDc9FAO4sOT6V5/pg8S/G3XNQuf7audH8M2kvlxRW5IMh7A4IyccknOM8CvZvFySSeDNbSHPmtYThceuw159+zxJE3w7nRCPMS/k8wd+VXH6VMfek79F+bKfupW6v9C54a+EUvhfxJZ6laeLNVmtYiTLaSscS8HGSDjGcHBFc98VP+S0eBf9+P8A9HV7fXiHxU/5LR4F/wB+P/0dRF/vILz/AMxSXuTfkem+OfFMfg7wjfay6CSSJQsMZ6PIxwo+meT7CvLvDvwz1bx/pEXiTxd4m1RJ74ebBb2zhViQ/d4IIGeuABW1+0OkrfDmFkzsS/jMmPTawH6kVneH/h14u1Dw5pt5ZfE/UIbaa2jeKJLdsRqVGFH73t0/ClHXmb6afgVLTlS66kXhrVdc+HPxOg8Favqk2p6RqCg2U05JeMnO3k9OQVI6dCK9vrx+D4MazJ4n0vXNX8cT6nLYTJIgntDkqrbtoYyHGa9gqvsq+/8AViftO239XCvFvGfiHxB4z+Iv/CA+GtQfTra3Xdf3kRIboCwyOcDIGARknmvaa8M+G/8Ao/x88ZwXPE8nmtHnqR5inj8CKlK80ntZv7ht2g2vJfeXbv4GXNhatd6D4v1iPVoxvR5ZcK7Dt8uCM/U1ufCfxxfeL9Ev9M1dvL1vTW8maRQAWByA+Om4EEH6e9elV4Z8IyJ/i/44ubfm1MkgyOmTMcfyNOOsuV7NP8AlpHmW6a/E5n4g+DJrH4m+G9OuPEeq30mouoN1cSAyQ5fb8mOnrXtXgvwGPB093L/bup6n9oVV23sm4JgnkfnXn/xU/wCS0eBf9+P/ANG17fRD+HfzYpfG15IKKKKBhRRRQAUUUUANclY2ZVLEAkAd68r+D3hLWtFv/Eer+ILFrW81C4BRXdWJXLMT8pPdv0r1aihaO4PVWCvK9W8H69rPx103Xp7HGhafCBHOZk5YKx+7u3feb07V6pRQtGn2B6prucd8TvB0njfwbNpls6JeRus9uX4UuueCe2QSK4nQrr4vyaPB4bOjWenGGMQHVp3BKIOAQoYhmx3ArtfHXjHU/B7WFxa+HrnVrGXeLlrYHdDjG08AjByeuOnWuJ1D43Xuq2clj4Y8JaxJqky7I2mi+WMn+LC5zj3xUrrbW/Qb6X+8xfg9oVunxc8RXFvLJcQaZG0AnkOWkkLbWcn1O1z+Ndv8Y/BGq+LtI0+50QK9/psxkSFmC+YDjOCeMgqOtXPhN4IuPBvhqU6kQdVv5PPusHO30XPcjJJ9ya7+rktIq+1vvJi9W+//AAx5JbzfFPxlbLpWo6bbeHLFwEu71HzNIvcRruOCfX9am+D/AIBv/CGoeIbnULE2i3E4js1aVZCYQWIOVJ9R154r1WihOzugtdWPLNf8H67rnxu0bWpbIf2Dp0S4nMqcuAzfdzu+8QOnavU6KKS0XL/Wo3q7nBfFXwDL468PwpZTJDqdlIZbZnOFbI5UntnA59RXMWXif4x21pHp0ng21uLuMeX9sklUK2ONxw+D+BFeyUUkrXG9bGL4VTXk8P2//CTSQPqrFmm8jGxQWO0DA7DA/qa2qKKpu5KOb8f2eqaj4F1ex0a3Nxf3MBhjjDqmQxAbliB0J715N4TtfjJ4N0GLR9M8I6U1vG7PvnnjZ2LHJJInA/SvfaKlKzb7lN3SXY8Qu/AvxH+Il1bx+NL200zSYnDtaWhBLH2AJGfcscelbHxL0/xpYadoOkeAIbiGyiBjkNqwDJjAQMT0XGefzr1ein5fMXW5yXi0eLY/AXk+Hoxc+IHjjiZw6JtOPncFyBnrj61474U8NfFrwfJc3Gn+E9PmvLli0t3dXEUkzZ7bvOHH8+9fR9FHVvuHRLseR6Xq3xrm1W0j1Dw9pUFk0yCeVXjJSPPzEATE9M9jV74uDx7KdJt/Bi3Kxu7faZLZgrBuNoYnovWvTqKHrYFpcr2CXMenWyXjh7pYlEzjoz4G4/nmrFFFNu7uJKysFFFFIZS1i3lu9Dv7aFd0s1tJGgzjLFSBXDfBrwnrHg/wnd2GtW6wXEl40qqsivlSqjOVJ7g16NRQtG33B628ilrEEt1ol/bwrulltpERcgZYqQBzXDfBfwvrPhPwfcWGt2f2W5e8aVU81HypVQDlSR2NejUULRt9weqS7Hllz4Q12T4/23idbHOjpb7GufOTg+UVxt3bup9K9OuUaS1mRRlmRgB74qWik1ePL/WoX97m/rQ8x+CvhLXPCWh6pb65ZfZJZ7vzI181JNy7QM/ITir/AMYvDereKvA39naLafarv7VHJ5fmInyjOTliB39a7+inP3t/L8Bxdvx/ExNL0YSeCLLRdUgBBsEtrmIkH+AKwyOPXkV5Pp3h74jfCy7ubXw3Zw6/oM0hkjidgHjJ9sgg+uMg+1e50U225OXclJKKj2PK9L8QfFfW9Xs0m8NWWj6csyG6llcFzHkbguWPJGf4fxFeqUUUdLB1uFeU/FLwJr2qa/pPizwsY5NV07AMEjBd4ViykE4B6kEEjg16tRU21T7FX0a7nkqar8XPEsX9nHQLHQI5Rsm1B5NzIp6lF3E59OD9RU/wo8A6p4H17xKl3GxsJ3jFncNIrNMql+SAcg8jqBXqdFUnZ3RLV1Y5D4m+FH8YeBr3TbeMPeria1BIH7xegyeBkZH41yXwl8D+IdK1zU/EPi22EWpSxR20AMqSHYAATlWIHCqPwNeuUUo+6211HLVJMyvEvh+z8UeHrzRr4HyLlNu4dUPUMPcHBryPR4Pip8NoDo1no9v4h0mNj9mkV8Mgz06ggexB9jXuNFJaO6HurM838Max8Tda8RWsms6FZaPoqbjMu4NLJ8pwB8xPXHYVa+MHhzVvFPgVtN0a0+1XZuY5PL8xE+UZycsQP1rvqKJJNWEm07mT4Xs7jTvCmk2V1H5dxb2cUUqZB2sFAIyODz6Vx3xd8A3/AIz0uxudHkRdU06QyQo7bRIDjIz0ByARnivR6KcnzO/zCPuqx5Fa+IfjHfW6af8A8Irp9ncbdj388o2L23bQxyfpn6UngT4ca34T+KN9ql3K17ZXFkQ9+7ruknYoz/LncBkNjjpXr1FNOzv1E1pY8y+J3w81LxBf2HiXw1OkGv6fjYGO0SqDkDPQEHPXgg4rPg8R/GLUIhYDwnp9jcEbHv5pRsT/AGgu45/DP0rqPHPjTVvB91ZSWvhq61fT5Ub7RJbBt0LAjHQEYPPXH1rkrj49RS27RaZ4R1qa/IwkUkQC7vfbk/pUra3TsU97mD8JNLk0b40+JNPmumupoLZ1lnYcyOXQsfzJrr/jR4R1zxbYaLFodj9qe2umklHmom1SBz8zDP4VD8H/AAfrWn3mr+K/EkRh1TVmyIWGGRS24kjtk447AV6vVNWUU91b87kp+9JrZ/5WOX8e6Rfa18PNV0vT4POvZ7cJHFvVdzZHGSQB09ah+GWi6h4e+H2l6Xqlv9nvYA4kj3q+3LsRypI6Ed666il38wtol2PO/jN4Y1jxZ4Mh0/RLP7VdLeJKU81E+UKwJyxA7iusttIS68IQaNqUOUexW2njyD/AFYZFbFR3DSJbSvEu+RUJVfU44FLRRa7/AORWrkn2PD9H0T4k/C24utO0PTIPEGhyyGSEGQKyE+2QQfXgisT4qW3jbWfB51zxZFbaXbW0yJa6bbtuJdjgu5yegzjnv0Hfr4/jjcaePJ8QeCdas7peHEUe5SfUbgv9a5zxLq/iT40XdjomkaDeadokcwluLq6UjPbJPTgE4UEkmhpyst9gTSu3oezeCv8AkRtB/wCvCD/0AVu1BY2kVhYW9nCMRW8SxIPZRgfyqerm7ybREFaKTOC+L/hzVfFPgSTTdGtftV2biNxH5ip8ozk5YgfrV1tP8TWPwwsbHRfJg1+2tIEVJipUMoXepPIPAI/rXYUVFrJrvqV1T7HkSeLvjBEn2ebwJZS3A481JwEJ9f8AWY/WtD4ceBNb0zxFqni7xVNCdZ1EbPIgOViUkE5I4zwBgZ4HU16bRVJ2d+omrqwUUUUhnjniPwD4p8M+NJ/F/gEwzNdZN3p0pADk8tjJAIJ56gg9Kf8A8Jh8Xr8fZ7TwNaWkzcGeeT5V9+XH9a9gopJWVug27u/UyE0ybVfCS6Zr+yWe5tBDe+XjaWK4Yj8c4rx/RNO+JHwqnudL0zRU8QaJJIZICj4Kk/jlT0yMEehr3ein9pyXUXSzPnD4pp4117we2t+KLSDSLG1lRbXTon3u7scF3OT0GcdOvSvb/A3/ACIOgf8AYPg/9AFcl8eYpJvhlMkSM7faoflUZPU113gdSvgTQFYEMNPhBB7fIKcPhl6r8hS+KPo/zPKv+ES8d/DbxhqWp+EdPh1fSdQcu9uzgFeSQCMg5GTgjPHWrWtaT8S/iTpFxZatp9roWmpG0gt45A0t1Koyik5OF3Y64/GvaqKm3u8rKvrzHE/CjQdT8NfD6z0zV7b7NeRySFo96vgFyRypI6e9YXwi8Ia74X1TxPNrFj9mjvbhXtz5yPvUM5z8rHHUdcV6nRVN3lzfL+vuJt7vL8zH8VaFF4l8Lajo8oGLqBkUn+Fuqn8CAa8k+F3w48U2Pi+11XxZZiGHSrPyLEGaOTJycfdY4wGbrjqK9zopR0d/66/5jeqt/X9aGD4z8OL4t8I6hojSiJrmPCSEZCuCCpPtkCvLPDM/xa8F6VH4di8KWmpQW5K29wbhQApOeTuGRz3wa9xopJWb8weqPC9U+G/jbVvFPh3xRqssN5qK3sb3dvA6pFZwKylQu45b+LOM/j1rtvjB4c1bxT4FbTdGtPtV2bmOTy/MRPlGcnLED9a76ihq8eXpe/5f5AnZ8xkeGbGax8JaVYXkQSeGziimjJDYYIARkcGvKJPBXjX4beI73UvA0MOp6PeNvk0+VgCntgkZxngg5x1Fe3UVTbcubqJJKPL0PIR4o+MGsMLaz8IWWl7j81zcODsHqAW/oa7fx/pN/rnw+1bTLCHz764twkce5V3NkHqSAOneunoqZJOPKNOzucj8MtF1Dw98PtL0vVLf7PewBxJHvV9uXYjlSR0I71k/GbwxrHizwZDp+iWf2q6W8SUp5qJ8oVgTliB3FeiUU5++7sIe7sZ2lWbxeHbKyuk2ulokUqZBwQgBGRXi2g6F8Rvhbqmo2Wh6HBrek3UvmRN5oXB6A/eBBxgEEY44r3qim23Jy7glaPKZ2gz6ndaHaT6zaR2moumZ4I23LG2egOTnjHetGiih7gjzL4veBNV8VW+l6poBQ6rpcheONmC7wSDwTxkFR1q54N8Q/ELU9WhtvEfha30+yWNvOuhKMs4HGF3HqfrXoNFKOmgPU8t8e/D7WZvFFv4z8G3EUOtwgLNBIQFuABjqeM44IPBHcVmXfiH4x61aPplv4TtdMmlXY96ZhhAepXLHH617LRStpboO+t+pxfw28AxeA9Ae3eYXGoXT+bdzgcM3ZRnnA5+uSa7SiiqbuSlYK8L/AOES8d/DbxhqWp+EdPh1fSdQcu9uzgFeSQCMg5GTgjPHWvdKKnrdD6WZ4rrWk/Ev4k6RcWWrafa6FpqRtILeOQNLdSqMopOThd2OuPxrtPhRoOp+Gvh9Z6Zq9t9mvI5JC0e9XwC5I5UkdPeu2oqlpe3UHra/Q8s+EPhDXfC+o+JZdZsfsyXtwr2585H3qC/PyscdR1xXfeJrOfUPC2rWVrH5lxcWcsUSZA3MyEAZPA59a1aKmSvHl8rDTtLm87nA/B/w5q3hbwKum6zafZbsXMknl+Yj/KcYOVJH61leE/CGu6Z8aPEniC8sfL0u8RxBP5yHeSyEfKG3DoeoFep0VV/e5vKxNvd5fO55d8Z/COueLLTQ00Sx+1NbXTSTDzUTapA5+Zhnp2r0+MFY1B6gAGnUUlorDerueQ+JPAfibw740n8YeAjBLJdZN5p0zBVkJ5OMkAgnnqCD0qlq138XPG1hJon/AAjtroVrcDZc3TzDOw9QPmJwfYE+9e10Uklaz2HfW/U57wT4StPBXhi30e1YyFMvNMRgyyHq39B7AVxvhHwhrul/GXxLr95Y+Vpd6ji3n85G35ZSPlDFhwD1Ar1Oiqu+bm9fxJsuXlCvLLnwhrsnx/tvE62OdHS32Nc+cnB8orjbu3dT6V6nRSWjT7Deqa7kVyjSWsyKMsyMAPfFebfBXwlrnhLQ9Ut9csvsks935ka+akm5doGfkJxXp1FC0bfcHqkjgPjF4b1bxV4G/s7RbT7Vd/ao5PL8xE+UZycsQO/rW9a6ZeR/DyLSnhxerpYtzFuH+s8rbjOcde+cV0NFK3uyj3/ysO/vKXY86+DHhfWPCfg6ew1uz+y3L3jyqnmo+VKqAcqSOxpnxv0WPUvh7Pfh1judLkW6hkJx3wRn3z+YFdvrurLoWh3eqPbzXK20fmGGAZdx6AeteJ+JvE2u/GE2vhrQNCv7DTGmV7y7u02gAHvjgAdcZJJxRNubst9AglDV7anRfAjSJzoeo+KtQ+a+1m5Z95HJQE8/ixb8hXrdUtI0y30XSLTTLRdtvaxLEg9gMZq7VyavpsRFO2u4VwPjS7+Ium65Fd+FbCy1LSzCBLazMquHyckElT0x3PTpXfUVBZ4rrN18WfG+lzaE3hiy0a1uh5dxcyzgnZ3A+Ynn2Bru7Hw3F4R+F0+iQyeaLawmDyYxvcqxY4+pNdfWb4hBPhrVQBkmzm4/4Aamp/DkkOGs0fO/wmt/GWkeHZ/EPhSCDU4ZJ2gvNNmbaTtAKuhyOcMR/Q9uj1+2+JvxQ8nRrzQk8P6R5ge4eR87sHvzlsdgB16mt39nqGSHwBdLLG8bfb3OGUg/dSvWq1mldX12M4N208zBTw/FpXgaTQNMjLLFYvbwqSAWYoRyemST+tcx8GPC+seE/B09hrdn9luXvHlVPNR8qVUA5UkdjXotFK+rl3/4cdlZLsV7+xt9T0+4sbuMSW9xG0UiHupGDXimneHviN8LLu5tfDdnDr+gzSGSOJ2AeMn2yCD64yD7V7nRU7O6K6WZ5XpfiD4r63q9mk3hqy0fTlmQ3UsrguY8jcFyx5Iz/D+Irofif4Lk8c+D5NNtpUjvIpBPbl/ulgCMH0yCea7OiiSTVhJtO54zo2tfGDTNMt9E/wCEQsppbdBCl7LOoXaBgFsPg8en5UzSvhr4osPitovifUbhdRaRHk1K5V1VYpCrKERSQSoBUDAr2miqv73N1Fb3eXocD8U/h8/jjSLeSwmW31ewcyWsjHAbOMqSOnQEHsRXN2HiX4yQW6aZN4Qs57pBs+3STKEP+02Hwfwx9K9ioqUrFPU8S0D4b+K9L+Lmm+I9TddQWWJ5b+7R0VY5WVxsVSQxAG0DArsPi/4c1XxT4Ek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None.
4
APhO_2025_1_C_1
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$.
Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$.
[["Award 0.2 pt if the answer includes the idea of transforming the ellipsoid of revolution into a perfect sphere of radius $R_e$ by stretching uniformly along the polar diameter with factor $R_e/R_p$. Otherwise, award 0 pt.", "Award 0.3 pt if the answer correctly computes the volume of one of the excess regions as $V = \\frac{1}{2} \\left( \\frac{4\\pi}{3} R_e^3 - \\frac{4\\pi}{3} R_e^2 R_p \\right) = \\frac{2\\pi}{3} R_e^2 h_{max}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes the correct expression for the Earth's density as $\\rho = \\frac{3 M_E}{4 \\pi R_e^2 R_p}$, where $M_E$ is the Earth's mass. Otherwise, award 0 pt.", "Award 0.2 pt if the answer obtains the final expression for the mass of one excess region as $m = \\frac{h_{max}}{2 R_p} M_E$. Otherwise, award 0 pt."]]
["\\boxed{$m = \\frac{h_{\\max}}{2 R_p} M_E$}"]
["Expression"]
[null]
[0.8]
text+variable figure
Mechanics
APhO_2025
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tOUALa20cX5KAa8a8N3kXjP8AaOv9UhIks9Lt2SJxyDtGzI+pZjWrs6yt01+SM46Um+/5s7n4x6zJonwz1KWCVop5ylvG6NhgWYZwR7A1wnhbwt4n+JHhPTTqWt3mk6FbwLHBFExaW7Yfelck9M5xnP8AU3fj/O9+/hjw1CT5l9ebyo/BF/8AQz+Vex2NnDp2n29lboEht41iRR2AGBWcVdOT7/l/w5UnZpLt+f8AwxyF5d2Pwm+GmZJpLtbJCkRlPzzyMSQD+J/IVwmg/D7xB8SbBfEfjDxFqFqt2PMtLK0bYsaHocHIAPpjOOSaX9omWa5TwzpEbhEurl2JPTd8qgn6bjWivwx8fajbrZat8QpI7AKEMVlDtyoGNvG3j86FeV5P+u437tooq/BfUtTt/FniXwxLqkup6Zp7HyJ5GLbSH28HnAI7dOK9qrnfB3grR/BGlGx0mJsyENNPKcySt6k/0HFdFVPZIlbthXzePGWiWH7Qmsa7rl00VrZh7eArG0mXUBOig/7Rr6Iv7tLDTrm8kOEgiaVj7KCf6V4n8CNAstb07Xde1awtrt7u92obiFZMYyzEZB7v+lTH47rovz0HK3JZ9X/wTd1X42aNqFpJp/hK1vtY1e4QpBFHbMqqSPvNnnA68D8q1Pg/4HvPBfhiYantGo30vnTRqc+WAMKuR1PUn61h/Gbwb4esvBFzrljYW2nalZPG0M9ogiZiXAwduM9c+vFdt8N9WvNc+HujahqDF7qWDEjnq+CV3H6gZpwtaTW+36hK90uh1NFFec+PviS2i3SeHPDUH9peJrn5EhjG5YM/xN798fieOqbGkUPjV4qig0D/AIRLTwbrWtXKxLbx8siEjkj3xgfie1dl4D8Ot4U8E6Zo8hDTQRZlI6b2JZsfiSK574ffDX/hHriTX9fn/tHxNdZaW4c7hDnqq+/Yn8BxXolUlyprq/6sS3zNdl/VwooopDCiiigDN8Rf8izqv/XnN/6Aa8x/Zz/5EK+/7CL/APoCV6d4i/5FnVf+vOb/ANANeY/s5/8AIhX3/YRf/wBASiHxT9F+YT2j6v8AI9Q15mTw9qbKxVltJSCDgg7DXnH7P97d3/gS7lvLqa4kF+6h5pC5xsTjJr0bxB/yLeqf9ekv/oBrzL9nX/kn93/2EH/9ASiHxS9F+YT2j6v8jnvGuteJbb47nTNAvHjnvbWO3jV2Jji3rzJt6ZABPStbWvgneJplzqVt4x1mbWo42lEksuFdgM44OVz9TioL5Q37VNlkZxagj/vy1e03n/Hjcf8AXNv5VD0pXW+v5srepbpp+R4B4HvvGPxZ00aTea7Pp+m6aoW6urfie6Yk7VJ9gOf1zmmeNfCWr/CJLHxJ4e8R6hPb/aBFPBcvkHOSMgcMpwRyK6D9nED/AIRvXD3+3D/0AVq/tBf8kz/7fYv/AGarqPks1vp+NiYK909tfwO6uvElrZ+DW8STgi2WzF2VHXBXcB9ecV4/4Z8K658XrebxL4l1+/s9OllZbOysn2qFBxnnIxnjoScda6fxmksn7OxEWcjTLUnH90bCf0rk/h94E8T634H02+0v4i32nWkisFtIoCVhIYgjIkHfnp3ptLnlpsKLfs4+ZLLLrXwY8baVaSaxdan4Z1NthS6bLRHIBI9CMg8YBHaveuteLap8ENf1xrf+1/iFc3ywPvjE9mW2nvjMvHSvZ0XZGq5zgAZo+zrv+gfa02HVieLdJ1PW/D01jpGryaVeSMu26jHKjPzD16Z6EVt15n8S/iDqug6xpnhjw3bxS63qWNskwysQLbRx6kg9eAB3qXrZdylpr2Mub4DQyWrynxdrj6njK3Dyjbu9SPvf+PU/4NeINU8Q6NrvhzXrmS5uNOfyPPZyXKNuUgt1JBU4PXmrkPgH4gXaebqfxKuYZW5aOztFCj6HK/yrm/gDG0XiLxlG87XDJOimZushDyfMfr1qkrtxfb/ImWiUl3Re+DerahpninxH4L1i7mnuLWUywPPIWYqDtOCexG0/ia7P4q+JD4Y+HupXcUhS6mX7NbkHBDvxkfQZP4VwnxMjbwX8V/DvjWEFba6YW94R04+U5+qH/wAdo+KDN41+J3hrwXbtutYiLq729MHk/wDjgP8A31U6zjFdXo/l/wAAq6hJvpv/AF8zV8PancfDr4IDXdUlmutQnTz1W4kZiXk4jXJOcAYJ/Gsbw78M9W8f6RF4k8XeJtUSe+HmwW9s4VYkP3eCCBnrgAVsftBwOvw1t1gXbDFfRbgvQLtYD9cVQ8P/AA68Xah4c028svifqENtNbRvFElu2I1KjCj9726fhTvzOUrdUvwJtyqK+ZF4a1XXPhz8ToPBWr6pNqekagoNlNOSXjJzt5PTkFSOnQiuj+O15c2Pw3ea0uJbeUXcQ3xOUbHPcVlwfBjWZPE+l65q/jifU5bCZJEE9oclVbdtDGQ4zV79oD/kmL/9fkP9amb9xX3v+qsVBe+7bW/Q5/SfC/ib4saZbavrGu3Wk6N5apZ2dtktIFGDI/IHJB65/CvTbXwxc6V4C/4R7TdWnjuo7do4b9xlw5JIY9e5qfwQip4E0BVAAGnw8D/cFc98U/iBN4G0q0TT7ZLjVNQkMdusnKrjGWIHXqAB71pVsm4ruRT1SkYI+BSXcRm1fxjrt3qBGTMsoChvo24/rVb4S61rem+Ntd8C6xqEl+lgpe3mlYswAYDGTzghgcdq0bTwV8StViW51j4gvYSuNxtrK0UhM9sgr0/H61y3w0sp9O+PviCzutRl1GeG1dHu5RhpDmPk/wAvwoh8dvJjl8F/NG78VfFeuXfijTfAXhi5a2vb4Brm4RirIpzgAjkDALEjnGKWH4H3Omwi70vxprEOsINwmZv3bP7r1x9SfxrMYiD9qsG44Elv+5z/ANcO35Gvc6iK9xPqxyfvW6Kx4R8KNe17WPi5ri67M/2mG0MUsCsfLV0ZEJC9BnBPHrWn+0Df3lhpnh9rO7nty94wYwyFNwwODjrVPwA0bftDeMTGQV2SDj13pn9c1J+0X/yC/Dn/AF+t/wCgimneNN+n5glac16/kd18TJ5rf4W61PBLJFKtqCsiMVYHK9CK8z8DeH/E3xN8KWkmr+I73T9FtV+zwxWrESXLL1d2PXrjnPT8/Sfil/ySbXP+vQf+hLVb4LqF+FGi4GMiQn/v41CXvSv5fqK9oxt5/kjzTxd4e1v4NXGna/ofiG+u9PknEU9tdPkE9cEDgggHnAIr3HU/ENtpnhOfxBKD9nitftO3uRtyB+OQK88/aI/5J3b/APYQj/8AQXq/4/SST4BziLORp9sTj0BQn9Klyfs5eT/NFqK9pHz/AMzifCvhLXvi9HP4m8Sa/fWlhJKyWtraNgAA84B4AHToScGq3xG0nxR8NfDL2dj4ivb/AELUGWLNw5861kB3DawPQgEcYHtXqPwckik+FOh+UR8sbq2P729s1jftAtGPhkwcjcbyIJ9ef6Zp1VyaLyJpvm1fmdx4OkeXwVockjs7tYwlmY5JOwck1t1heCv+RG0H/sHwf+gCt2tKnxv1Ip/AvQ80+Ot3c2Xw2kmtLiW3lF1EN8TlGxk9xU+peI77w78DLfWrUmS+j02Da7/NhmCruOeuM5ql8f8A/kmEv/X3D/M11fhaxtdT+G2j2N7Ak9tPpkKSRuMhlKDIrJJuE0u6/I0bSnBvs/zPL/CfwuTx14atfEWs+MNYuby8UyHyJxtiOfunIPI9OK9D8C+B73wbLerP4kvtVtJQot4bknEOM56kjJ46Yri7z4O654ZupdQ+HviSeyYncbG4fKN7Z5B/4EPxrb+GnxF1PxBqt/4Z8S2K2mu2ClnKDCyAEA5HY8jpwc8Vomm/d08iWml72vmemUUU1wTGwHXBxUN2Vxnh93e658XfHmpaJp+rT6X4a0o7JpLY4adskde+SDjPAAzjNVvFfgfWPhXpq+KPC3iPUporaRftVrduGV1JAyQMAjOBgjPOc1zPws8La74gutfi0zxfdaDPbzjz4oYixlyW5OHXoQR+NegX/wAH/FmqWMtlf/Ey+ubWUYkiltWZWHXkebRZqKtv+Y3Zyaex3dp40sp/h4ni91K2/wBjNy8YPIYDlf8AvoYrybwv4e8UfF5bjxFrfiO903TGlZLW1s2KjjrgZwAOmSCSQa6bxb4Xl8Jfs+6hoSXZu2tYgTMI9m5TMGPy5OOD61v/AAceJ/hToflYwI3DY/veY2arRyk102+ZN2oxT63/AAPM/iFaeMPhp4ZktLbxJeajo1+yxJNM7LPaSAhsK4OcEAj+nr7R4Omln8CaJNNI8kr6fEzu7EsxKDJJPU1xf7QDRj4YyB8bjeRbM+vP9M12Pgn/AJJ9oP8A2Dof/QBUp3pzv3X5DatKNuz/ADPOvgDqF7fR+Jvtl3PceXdIE86QvtHz8DJ4r0D4iTS2/wAO/EE0MjxypZSFXRiGU46gjpXm37O/3PFQ7/a4/wD2evQ/idKkXwz8Qs5ABsnX8TwP1NKr8HyX5FU/4nzf5mT8FLq4vPhhYT3U8s8rSy5klcsx+c9zXNfA2/vL3WfGC3d3POsd0oQSyFgo3ScDJ4roPgX/AMkp0/8A66zf+hmuX+Af/Ib8Z/8AX2v/AKFJWsv4j9P8jJfw/n/mP8H3994S+N+r+F7+8uJbLUFMll58pYL/ABqBk8cFl/CvU/FeuR+G/CupavIR/osDOoPd+ij8SRXmXx002fTJtB8bWC4udMuVSUjuudy59sgj/gVV/jHr58S6V4X8OaQ+59ekjuMD+4cbc/ic/wDAay1lTUVve3+X4fka6Kbk9t/8zb+BdjqLeE7jXNVu7m4n1KctH50jNtjUkcAnjJ3fpTbz4PXuvand3fiDxprFxE8rGCC3fYI0z8o5yM49FFdfquoWPw88APcCIvbaXarHHGvBcjCqPxJHNefeHY/iX8RdNj1uTxPD4f024JNvBa2wdyoOM84Pbu34VcrOT5ehEbqOvUyI4dX+EvxS0TSYNau7/QtXZU8m6fdty23p0BBIORjNdZ+0B/yTF/8Ar8h/rXAeNNA1PQPiZ4Lh1TxLda3LJdRurXCBTEPNUYAyev8ASu//AGgP+SYv/wBfkP8AWonrST8/1RcdKjXl+jOy8IzR2/w/0WeVgscemwuzHsBGCTXkmkW2ufG7WNR1C61m80vwzay+Tb21q20yHrz2JxgknPXAr0SFJZPgkqQZ81tBwmOufJryL4T+DvEHiLwnLc6P46u9GiS5ZHtIYSwDYB3ZDjqCO3atJ61Z36f5mcNKUbdf8jV8R6VrfwUvNP1vR9bvtQ0SaYQ3NnePu9/pyAcEAEEd69K+IupGb4S6tqVjM8fmWazRSIxVgGKkEEdODXHar8FvE2uWf2TVfiPeXlvuD+VPaFl3DocGWuk8d6adG+B2oaYZvONpp0cHm7du/btGcZOOnrWc3+7lf5Fx/iRt/Wpwfgbw/wCJvib4UtJNX8R3un6Lar9nhitWIkuWXq7sevXHOen51PF3h7W/g1cadr+h+Ib670+ScRT210+QT1wQOCCAecAivS/guoX4UaLgYyJCf+/jVhftEf8AJO7f/sIR/wDoL1dV8krruvzJpLnVn5nXeLtHbxh4QTyNXvtNheH7QxtHCmVSmQjH0rxL4Q/D0eL/AA9e3Z8Q6rpvlXXl+XZy7Vb5QckevNe+6f8A8iHa/wDYMX/0UK82/Zw/5E7Vf+v/AP8AZFp8qU5ry/ULt04P+tj1fRNM/sXRLPTftM119mjEfnTnLvjux9av0UUm7u40raHzV8WfCctn8QtAWbXdSu31W4PzyvzbDzFAEfoBu/SvWvCfw0HhXWxqX/CS6xqGI2j8m7l3Jz3x61xXxp/5KN4E/wCvgf8Ao1K9wohpTTXdhPWfyR4t4z8Q+IPGfxF/4QHw1qD6dbW67r+8iJDdAWGRzgZAwCMk80+7+BlzYWrXeg+L9Yj1aMb0eWXCuw7fLgjP1NUvhv8A6P8AHzxnBc8Tyea0eepHmKePwIr3Opiv3cX1auNv32ui0POPhH46vfFmlXmn6yANZ0uTypzjHmDkBiPXIIP/ANevR68M+EZE/wAX/HFzb82pkkGR0yZjj+Rr3OqvzRjLuibWlKPZjX+430NeN/AHUL2+j8TfbLue48u6QJ50hfaPn4GTxXsj/wCrb6GvEv2d/ueKh3+1x/8As9TH4n6fqhy+Fev6M9J+Ik0tv8O/EE0MjxypZSFXRiGU46gjpWH8FLq4vPhhYT3U8s8rSy5klcsx+c9zWt8TpUi+GfiFnIANk6/ieB+prE+Bf/JKdP8A+us3/oZpx+16L82Eto+r/I8x8By+L/F2sa54astdubGwF0891eh2eVEyVEaEnjPtjp+B3/FHwhvfDGhXev8Ah/xXrBvrJDcMJpfvheWwVxg455zU3wBUf2x4ybHP2pBn/gUleq+Mv+RI13/sHz/+gGok+WmpLey/IqPvVGntcyfhh4ouPF3gOx1O8wbsFoZ2AxuZTjdj3GDXE+Cb+8m/aA8WWst3O9tHHJshaQlF+ZOgzgVq/s//APJMk/6/Jf6VheBP+TivGH/XKT/0NK2f8b5P8kZf8uvmvzOf+OXha40yfTNQuPEGpX5vbt1WK4cbIBwcIB06/pXqfg/4bjwtqy6n/wAJHq+oZhKeRdy7kGcc49eK4/8AaK/48PDX/X6/8lr2hQTbADrs4/Ks4vlg2u/6IuWslft+p4de6l4g+Lfj3UdB0rVptK8OaYSs8tuSGmIOOxGckHA6ADNT6z8IdV8K6bNrPhHxVq32+0QymGeQETADJHGB+BBBpn7PRENz4rtZuLtLlC4PXALg/rXtd08cVnNJKQI1jZnJ6YA5pS92Ca3te495tPa9rHJfDHxqfHPhGLUJlVL6FzBdKvA3gA7gPQgg/nXk/wDb/it/i34q8O+H7mT7VqE5iillkJSzRTlnA6Dj0rd/ZxRzpXiGYA+Q92gT0yFOf0IpngNFP7RPjBiASqS4Pp86VbSdVej/ACTJvam/X9WdT4Q+FD+GfEMOuXXiXUNTu1RhIs33HZhjPJJ/OuI8a614ltvjudM0C8eOe9tY7eNXYmOLevMm3pkAE9K9/rw++UN+1TZZGcWoI/78tS3nFPbX8mN6Rk+v/BRPrXwTvE0y51K28Y6zNrUcbSiSWXCuwGccHK5+pxWF4HvvGPxZ00aTea7Pp+m6aoW6urfie6Yk7VJ9gOf1zmvf7z/jxuP+ubfyrx39nED/AIRvXD3+3D/0AUR1ck9kr/jYJaJNb3Of8a+EtX+ESWPiTw94j1Ce3+0CKeC5fIOckZA4ZTgjkV7Zf3q6l4Eur5BhbnTHmA9A0RP9a4j9oL/kmf8A2+xf+zV1Fl/ySWH/ALAg/wDRNRJ3pTv0/wAilpUhbr/meefBfTJNY+Dus6fDcS2809zKsc0TlWR9ibSCOeuK2Pgb4lvdR0XUdC1eeWXU9KuCrGdyzlCT1J5OGDD8qh/Z2/5J9df9hB//AEBKzdXT/hAPj/Y6mvyaZ4hXypeyiQkA/wDj21vxNbP+JbukvnbQyX8Nvs2/x1Oj+OHiefw/4IW1sZ5Ir/UZlhiaJirqo5Ygjn0H411vgrSrrRvB2mWV9cTXF4sIaeSaQuxduSMnngnH4V5draf8J5+0FY6Xjfp2gRiSYdi4wx/Nii/hXuFRH4L9/wAkXL4rdvzYV418V9d1a78daF4LtNXfR7G/UPcXcbbWbLEYzkcfL0zyTzXstcr42+H+ieO7KOHU0eO4hz5F1CcPHnt6EexpPdMa2ZxUnwGt4k83TvF+u214ORM0oYZ9cLtP616BLa3WkeAp7aa/muru209w927He7hDls9eteT39j8SfhNaNfWerJr/AIft+ZIbgEtGmfQnKj3ViPavS7XxHbeLPhlca3ao0cdzYTExsclGCsGHvgg0qj/dysEF78bnj3w2j8ZfETQJNLfxHeafpNlI3n3aOz3FwzchNxOQAPfv37XvFXg/xT8LbRfE3h7xRf31rA6/ara6YsNpOMkZwwzweARmt79nN428CX6KR5i37Fh9UTFdn8UJIo/hj4hMxG02bKM/3jwP1xV1XyarsvyJpe9o+/6ktr4ij8S/DSTXLXMf2nT5ZMA8xuEIIz7EGvFfh43jD4heHV8O22sXGn6ZZyM99qG9nlmLHKxqc54Ge/8AhXc/C1JE+AcvmZw0F2Uz6fN/9eo/2dUUeALxgAC2oPk+vyJTcV7SfovzFzPkj6s39A8NWfwo8Na1qE2qXeoQhPPc3HUbQflH1JrhPDPhXXPi9bzeJfEuv39np0srLZ2Vk+1QoOM85GM8dCTjrXoHxiSWT4U64Is5EaE4/uiRSf0rzr4feBPE+t+B9NvtL+It9p1pIrBbSKAlYSGIIyJB356d6he8230sU9EkutyWWXWvgx420q0k1i61PwzqbbCl02WiOQCR6EZB4wCO1e7TI0tvIkchjZ0IWReqkjgjNeNap8ENf1xrf+1/iFc3ywPvjE9mW2nvjMvHSu7+IPjJPAXhBtT8kXFwWWC3jY4DOQeT7AAmnJ+5739dgS9/Q5BPgjPqe6fxL401q9u2Ocwy7FX2Abd+mKyfBl1rXgX4vnwPd6tcajpd1EXtzOxJT5SwIz0+6QQOD1rV0fQPib4s0+31XU/Go0aK5QSx2tnaKxVSMjJyMHHua5Wy0m90X9o7RbLUNbn1i4WAsbmddrYMb4XGT0/rVRTU0n5/kKTTg2vU7b4yeNtT0C107QtAcpq+rPsWRfvRpkD5fQknGe2DWdYfAuUWqXV54x1ldZI3NPDL8qv+PzH65FZ3xNIh+PHgua44tz5IBPTPmt/iK90qIL3Obq2/wHJ+9y9LL8T5v8NtraftE6fZ+IJkuNQs43t2uFGPPURMVc+5UivRfjrd3Nl8NpJrS4lt5RdRDfE5RsZPcVzF60bftU2YQjItgHx6+S39MV0Px/8A+SYS/wDX3D/M0pO9OL/r4hxX7x+n6HSaZNK3wlt52lczHRQ5kLHdu8nOc+teOfDOz8WfEPw/JpUviK80/RbGQ+dPE5M9w7c7NxPQD+fQ9vX9K/5I7bf9gMf+ia5L9nVQPh/dkDk6g+f++ErSSXtan9dTOL/dw/roc340+Huq/DXSP+Eo8NeKNUY2si+fFPJnIJxnjgjJGQR3r2Xw14hTWvBdhr84ESzWgnlx0UgfN+GQawfjL/ySjXP9yP8A9GLWd4VSST9nqNIc+Y2kThceuHrNyahPy/yZoopzj5/8A4jRrTXvjfruo6heazd6b4ctJfKgt7Zsbj2GOmcYJJz1wKteMPCviL4YeF72/wDD/iO+vdKljNvdWt424xBxtEiEdCCR0A/Gt/8AZ4kib4dzohHmJfybx35VcfpXT/Flo1+FuvmQjBt8DPruGP1p1VyRsu33hTfPK77kPwfuJrr4X6PNcTSTSssm55GLMf3jdSa7muC+DH/JKNF/3ZP/AEY1d7WlT42Z0/hR5z8Y/Dsur+Db6+Gr31rDYWskrWsD4juCORv9RXn/AMM/hgPE3gez1T/hJ9asfMeQeRazbY1wxHA969d+JX/JNfEX/XjJ/KsH4Gf8kq07/rrN/wChmogvi+X5s0m9I+r/ACM/48Q/Z/hQsO9n8u5gTc3U4BGTWJ4X8Ba34+8LadqGveI7+w0/yEjstPsW2KsajaGYngk4z0/HtXQftAf8kxf/AK/If612nghQvgTQFUYA0+Dj/gAohqpt91+QpaOKXZ/meN3kOu/Bzx3osMWu3eo6DqcgjeG5YnHIDcdARuBBGK9J+KnjaTwR4TNzZhW1G6k8i1DDIViMlsd8D9cVxfx+/wCQn4N/6/H/AJx1X/aNjkZPDD+YYoRPKrSAZ2MdmD+QNTdygl52/IaSUr+V/wAy5pvwXvtb02LU/EvizWDrFwglIil+WEnkDnOce2Kn+G3iTXNF8dah8PfEd69+8Cl7O6kJLMoAOCTyQVOeemCKsJ8MfGzxq6fFbUirAEEW7dP+/tS+G/hFqWj+OrXxTqfi2XVbmEMrCW1Ks4KFR83mHpn07VotJdl/ViHrHuz1WiiipKPA/F66p8Mvi5L42TT5L3Rr9ds7R/wZADKT2OVBGeD0r1Hwx8SPC3i4ImmapGLph/x6z/u5R7bT1/DNdTJFHNE0UqK8bDDKwyCPQivJ/iH8HfD15o97q+iwDStTtYmuFNv8sblQWwV6A8dRilfljZ7IduaV1uz1h/uN9DXjfwB1C9vo/E32y7nuPLukCedIX2j5+Bk8V0Pwa8TX3if4erNqUjTXVrK9s0zdZAACCT3ODjPtXK/s7/c8VDv9rj/9nqrWm15fqib3gn5/oz0n4iTS2/w78QTQyPHKllIVdGIZTjqCOlYfwUuri8+GFhPdTyzytLLmSVyzH5z3Na3xOlSL4Z+IWcgA2Tr+J4H6msT4F/8AJKdP/wCus3/oZpR+16L82OW0fV/keY+A5fF/i7WNc8NWWu3NjYC6ee6vQ7PKiZKiNCTxn2x0/A7/AIo+EN74Y0K71/w/4r1g31khuGE0v3wvLYK4wcc85qb4AqP7Y8ZNjn7Ugz/wKSvVfGX/ACJGu/8AYPn/APQDUSfLTUlvZfkVH3qjT2uZPww8UXHi7wHY6neYN2C0M7AY3Mpxux7jBrsa8t/Z/wD+SZJ/1+S/0r1Ktp/EZw2CvKrz4PXuvand3fiDxprFxE8rGCC3fYI0z8o5yM49FFd54s8RQeFPDF/rdxGZEtY9wjBwXYnCjPuSK8x8Ox/Ev4i6bHrcnieHw/ptwSbeC1tg7lQcZ5we3dvwrNav0L2XqZEcOr/CX4paJpMGtXd/oWrsqeTdPu25bb06AgkHIxmvTPix/wAkt8Qf9e3/ALMK8g8aaBqegfEzwXDqniW61uWS6jdWuECmIeaowBk9f6V6/wDFj/klviD/AK9v/ZhSnrRv6hHSrb0KPwfmjt/hDpM8rBY445Xdj2AdiTXBaTH4h+N2tajeTazdaT4ZtJfKhgtTgyHtnsTjBJOcZwBXUeBIpZv2d/Kgz5r6fdKmOucviof2eJYm+Hc8aEeYl/J5g78quP0rSSvVlfov1M4u1ONurMPxJ4A174Z6a3iXwn4l1CeO0Ie5tLttyumeTgYBHqMdOQa9a8HeJYfF3hSx1qFQn2hP3kec7HBww/MVF49lih+H/iB5yBH9gmBz6lSB+uK4/wCAEcqfDGNpAdr3crJn04H8wamLvzJ9LMuStytdbo888By+L/F2sa54astdubGwF0891eh2eVEyVEaEnjPtjp+B3/FHwhvfDGhXev8Ah/xXrBvrJDcMJpfvheWwVxg455zU3wBUf2x4ybHP2pBn/gUleq+Mv+RI13/sHz/+gGok+WmpLey/IqPvVGntcyfhh4ouPF3gOx1O8IN2C0M7AYDMpxux7jBrzW8u9d+MHxB1HRLDVp9N8N6WxWVoCQZSDjJwRkkg4zwAK6f4BAn4XADr9rmx+lYP7PBWObxVBLxdLcxlweuPnH881rJJ1Plf8vyM4tqn87fmWtU+H+t/DjSrjX/CniXULkWiGS5sL1t8c0Y+9jGMEDnpn3rT+AN9dah4Eupry5muJft7jdK5YgbV4ya9C8SNGnhfVmlIEYs5i2fTYa81/Z2/5J9df9hB/wD0BKUHrJeS/Mc1pH1/Q9drmfHXh6XxJ4eltU1e+05Iw0jm0baZQFPysfSumqrqf/IKvP8Arg//AKCazqfCzSHxI+b/AIQ/D0eL/D17dnxDqum+VdeX5dnLtVvlByR6816x480z+xfglqum/aZrr7NZCPzpzl3ww5Y+tc3+zh/yJ2q/9f8A/wCyLXafFj/klviD/r2/9mFXX0i0uy/IilrJPz/U8r+HHhLXvHngu0jvNeu9K0C0LQwW9kdr3DbiWdj6ZOB16fmni7Qdc+DVxp2vaJ4iv7zTpJxFPbXT5BOM4I6EEA84BFek/BdQvwo0XAxkSE/9/GrC/aI/5J3b/wDYQj/9BenVfJK67r8xUkpKz8zsvFvjKDw14Dm8RhA5MKNbxsfvO4G0H88n2BrzXw78M9W8f6RF4k8XeJtUSe+HmwW9s4VYkP3eCCBnrgAVP8ZElb4J6IyZ2K9qZMenlED9SKd4f+HXi7UPDmm3ll8T9QhtpraN4okt2xGpUYUfve3T8KLLmn5OwJvlj5q5F4a1XXPhz8ToPBWr6pNqekagoNlNOSXjJzt5PTkFSOnQivb68fg+DGsyeJ9L1zV/HE+py2EySIJ7Q5Kq27aGMhxmvYKPsq+/9WD7Ttt/VwryT4peMdcbxJpvgbwrN5Gp3+GmuVOGjU5wAe3AJJ646V63XhbEQ/tVg3PAkt8Q5/64cY/EGpSvNRe3+XQq9otovj4DSmETP421f+0cZM4JK7vpuz+tdR40trvQfgxqNt/aFxPd2tgqm8aRvMdgRls5z+td7XHfFb/kl3iD/r1/9mFKo/caHBe+iv8AB+5nu/hdpE9zNJNKwk3SSMWY/vG6k15B4K1Pxj4lv9b8J6PqU1sJrx5rnUZJGdreEErtTnIJPoR+HNetfBf/AJJRo30l/wDRjVxvwBRf7Z8ZPgbvtSDPtukrSaTqtPaz/NGcXandd/8AM7HwZ8OoPAV3e6pLr17f+ZblZDc9FAO4sOT6V5/pg8S/G3XNQuf7audH8M2kvlxRW5IMh7A4IyccknOM8CvZvFySSeDNbSHPmtYThceuw159+zxJE3w7nRCPMS/k8wd+VXH6VMfek79F+bKfupW6v9C54a+EUvhfxJZ6laeLNVmtYiTLaSscS8HGSDjGcHBFc98VP+S0eBf9+P8A9HV7fXiHxU/5LR4F/wB+P/0dRF/vILz/AMxSXuTfkem+OfFMfg7wjfay6CSSJQsMZ6PIxwo+meT7CvLvDvwz1bx/pEXiTxd4m1RJ74ebBb2zhViQ/d4IIGeuABW1+0OkrfDmFkzsS/jMmPTawH6kVneH/h14u1Dw5pt5ZfE/UIbaa2jeKJLdsRqVGFH73t0/ClHXmb6afgVLTlS66kXhrVdc+HPxOg8Favqk2p6RqCg2U05JeMnO3k9OQVI6dCK9vrx+D4MazJ4n0vXNX8cT6nLYTJIgntDkqrbtoYyHGa9gqvsq+/8AViftO239XCvFvGfiHxB4z+Iv/CA+GtQfTra3Xdf3kRIboCwyOcDIGARknmvaa8M+G/8Ao/x88ZwXPE8nmtHnqR5inj8CKlK80ntZv7ht2g2vJfeXbv4GXNhatd6D4v1iPVoxvR5ZcK7Dt8uCM/U1ufCfxxfeL9Ev9M1dvL1vTW8maRQAWByA+Om4EEH6e9elV4Z8IyJ/i/44ubfm1MkgyOmTMcfyNOOsuV7NP8AlpHmW6a/E5n4g+DJrH4m+G9OuPEeq30mouoN1cSAyQ5fb8mOnrXtXgvwGPB093L/bup6n9oVV23sm4JgnkfnXn/xU/wCS0eBf9+P/ANG17fRD+HfzYpfG15IKKKKBhRRRQAUUUUANclY2ZVLEAkAd68r+D3hLWtFv/Eer+ILFrW81C4BRXdWJXLMT8pPdv0r1aihaO4PVWCvK9W8H69rPx103Xp7HGhafCBHOZk5YKx+7u3feb07V6pRQtGn2B6prucd8TvB0njfwbNpls6JeRus9uX4UuueCe2QSK4nQrr4vyaPB4bOjWenGGMQHVp3BKIOAQoYhmx3ArtfHXjHU/B7WFxa+HrnVrGXeLlrYHdDjG08AjByeuOnWuJ1D43Xuq2clj4Y8JaxJqky7I2mi+WMn+LC5zj3xUrrbW/Qb6X+8xfg9oVunxc8RXFvLJcQaZG0AnkOWkkLbWcn1O1z+Ndv8Y/BGq+LtI0+50QK9/psxkSFmC+YDjOCeMgqOtXPhN4IuPBvhqU6kQdVv5PPusHO30XPcjJJ9ya7+rktIq+1vvJi9W+//AAx5JbzfFPxlbLpWo6bbeHLFwEu71HzNIvcRruOCfX9am+D/AIBv/CGoeIbnULE2i3E4js1aVZCYQWIOVJ9R154r1WihOzugtdWPLNf8H67rnxu0bWpbIf2Dp0S4nMqcuAzfdzu+8QOnavU6KKS0XL/Wo3q7nBfFXwDL468PwpZTJDqdlIZbZnOFbI5UntnA59RXMWXif4x21pHp0ng21uLuMeX9sklUK2ONxw+D+BFeyUUkrXG9bGL4VTXk8P2//CTSQPqrFmm8jGxQWO0DA7DA/qa2qKKpu5KOb8f2eqaj4F1ex0a3Nxf3MBhjjDqmQxAbliB0J715N4TtfjJ4N0GLR9M8I6U1vG7PvnnjZ2LHJJInA/SvfaKlKzb7lN3SXY8Qu/AvxH+Il1bx+NL200zSYnDtaWhBLH2AJGfcscelbHxL0/xpYadoOkeAIbiGyiBjkNqwDJjAQMT0XGefzr1ein5fMXW5yXi0eLY/AXk+Hoxc+IHjjiZw6JtOPncFyBnrj61474U8NfFrwfJc3Gn+E9PmvLli0t3dXEUkzZ7bvOHH8+9fR9FHVvuHRLseR6Xq3xrm1W0j1Dw9pUFk0yCeVXjJSPPzEATE9M9jV74uDx7KdJt/Bi3Kxu7faZLZgrBuNoYnovWvTqKHrYFpcr2CXMenWyXjh7pYlEzjoz4G4/nmrFFFNu7uJKysFFFFIZS1i3lu9Dv7aFd0s1tJGgzjLFSBXDfBrwnrHg/wnd2GtW6wXEl40qqsivlSqjOVJ7g16NRQtG33B628ilrEEt1ol/bwrulltpERcgZYqQBzXDfBfwvrPhPwfcWGt2f2W5e8aVU81HypVQDlSR2NejUULRt9weqS7Hllz4Q12T4/23idbHOjpb7GufOTg+UVxt3bup9K9OuUaS1mRRlmRgB74qWik1ePL/WoX97m/rQ8x+CvhLXPCWh6pb65ZfZJZ7vzI181JNy7QM/ITir/AMYvDereKvA39naLafarv7VHJ5fmInyjOTliB39a7+inP3t/L8Bxdvx/ExNL0YSeCLLRdUgBBsEtrmIkH+AKwyOPXkV5Pp3h74jfCy7ubXw3Zw6/oM0hkjidgHjJ9sgg+uMg+1e50U225OXclJKKj2PK9L8QfFfW9Xs0m8NWWj6csyG6llcFzHkbguWPJGf4fxFeqUUUdLB1uFeU/FLwJr2qa/pPizwsY5NV07AMEjBd4ViykE4B6kEEjg16tRU21T7FX0a7nkqar8XPEsX9nHQLHQI5Rsm1B5NzIp6lF3E59OD9RU/wo8A6p4H17xKl3GxsJ3jFncNIrNMql+SAcg8jqBXqdFUnZ3RLV1Y5D4m+FH8YeBr3TbeMPeria1BIH7xegyeBkZH41yXwl8D+IdK1zU/EPi22EWpSxR20AMqSHYAATlWIHCqPwNeuUUo+6211HLVJMyvEvh+z8UeHrzRr4HyLlNu4dUPUMPcHBryPR4Pip8NoDo1no9v4h0mNj9mkV8Mgz06ggexB9jXuNFJaO6HurM838Max8Tda8RWsms6FZaPoqbjMu4NLJ8pwB8xPXHYVa+MHhzVvFPgVtN0a0+1XZuY5PL8xE+UZycsQP1rvqKJJNWEm07mT4Xs7jTvCmk2V1H5dxb2cUUqZB2sFAIyODz6Vx3xd8A3/AIz0uxudHkRdU06QyQo7bRIDjIz0ByARnivR6KcnzO/zCPuqx5Fa+IfjHfW6af8A8Irp9ncbdj388o2L23bQxyfpn6UngT4ca34T+KN9ql3K17ZXFkQ9+7ruknYoz/LncBkNjjpXr1FNOzv1E1pY8y+J3w81LxBf2HiXw1OkGv6fjYGO0SqDkDPQEHPXgg4rPg8R/GLUIhYDwnp9jcEbHv5pRsT/AGgu45/DP0rqPHPjTVvB91ZSWvhq61fT5Ub7RJbBt0LAjHQEYPPXH1rkrj49RS27RaZ4R1qa/IwkUkQC7vfbk/pUra3TsU97mD8JNLk0b40+JNPmumupoLZ1lnYcyOXQsfzJrr/jR4R1zxbYaLFodj9qe2umklHmom1SBz8zDP4VD8H/AAfrWn3mr+K/EkRh1TVmyIWGGRS24kjtk447AV6vVNWUU91b87kp+9JrZ/5WOX8e6Rfa18PNV0vT4POvZ7cJHFvVdzZHGSQB09ah+GWi6h4e+H2l6Xqlv9nvYA4kj3q+3LsRypI6Ed666il38wtol2PO/jN4Y1jxZ4Mh0/RLP7VdLeJKU81E+UKwJyxA7iusttIS68IQaNqUOUexW2njyD/AFYZFbFR3DSJbSvEu+RUJVfU44FLRRa7/AORWrkn2PD9H0T4k/C24utO0PTIPEGhyyGSEGQKyE+2QQfXgisT4qW3jbWfB51zxZFbaXbW0yJa6bbtuJdjgu5yegzjnv0Hfr4/jjcaePJ8QeCdas7peHEUe5SfUbgv9a5zxLq/iT40XdjomkaDeadokcwluLq6UjPbJPTgE4UEkmhpyst9gTSu3oezeCv8AkRtB/wCvCD/0AVu1BY2kVhYW9nCMRW8SxIPZRgfyqerm7ybREFaKTOC+L/hzVfFPgSTTdGtftV2biNxH5ip8ozk5YgfrV1tP8TWPwwsbHRfJg1+2tIEVJipUMoXepPIPAI/rXYUVFrJrvqV1T7HkSeLvjBEn2ebwJZS3A481JwEJ9f8AWY/WtD4ceBNb0zxFqni7xVNCdZ1EbPIgOViUkE5I4zwBgZ4HU16bRVJ2d+omrqwUUUUhnjniPwD4p8M+NJ/F/gEwzNdZN3p0pADk8tjJAIJ56gg9Kf8A8Jh8Xr8fZ7TwNaWkzcGeeT5V9+XH9a9gopJWVug27u/UyE0ybVfCS6Zr+yWe5tBDe+XjaWK4Yj8c4rx/RNO+JHwqnudL0zRU8QaJJIZICj4Kk/jlT0yMEehr3ein9pyXUXSzPnD4pp4117we2t+KLSDSLG1lRbXTon3u7scF3OT0GcdOvSvb/A3/ACIOgf8AYPg/9AFcl8eYpJvhlMkSM7faoflUZPU113gdSvgTQFYEMNPhBB7fIKcPhl6r8hS+KPo/zPKv+ES8d/DbxhqWp+EdPh1fSdQcu9uzgFeSQCMg5GTgjPHWrWtaT8S/iTpFxZatp9roWmpG0gt45A0t1Koyik5OF3Y64/GvaqKm3u8rKvrzHE/CjQdT8NfD6z0zV7b7NeRySFo96vgFyRypI6e9YXwi8Ia74X1TxPNrFj9mjvbhXtz5yPvUM5z8rHHUdcV6nRVN3lzfL+vuJt7vL8zH8VaFF4l8Lajo8oGLqBkUn+Fuqn8CAa8k+F3w48U2Pi+11XxZZiGHSrPyLEGaOTJycfdY4wGbrjqK9zopR0d/66/5jeqt/X9aGD4z8OL4t8I6hojSiJrmPCSEZCuCCpPtkCvLPDM/xa8F6VH4di8KWmpQW5K29wbhQApOeTuGRz3wa9xopJWb8weqPC9U+G/jbVvFPh3xRqssN5qK3sb3dvA6pFZwKylQu45b+LOM/j1rtvjB4c1bxT4FbTdGtPtV2bmOTy/MRPlGcnLED9a76ihq8eXpe/5f5AnZ8xkeGbGax8JaVYXkQSeGziimjJDYYIARkcGvKJPBXjX4beI73UvA0MOp6PeNvk0+VgCntgkZxngg5x1Fe3UVTbcubqJJKPL0PIR4o+MGsMLaz8IWWl7j81zcODsHqAW/oa7fx/pN/rnw+1bTLCHz764twkce5V3NkHqSAOneunoqZJOPKNOzucj8MtF1Dw98PtL0vVLf7PewBxJHvV9uXYjlSR0I71k/GbwxrHizwZDp+iWf2q6W8SUp5qJ8oVgTliB3FeiUU5++7sIe7sZ2lWbxeHbKyuk2ulokUqZBwQgBGRXi2g6F8Rvhbqmo2Wh6HBrek3UvmRN5oXB6A/eBBxgEEY44r3qim23Jy7glaPKZ2gz6ndaHaT6zaR2moumZ4I23LG2egOTnjHetGiih7gjzL4veBNV8VW+l6poBQ6rpcheONmC7wSDwTxkFR1q54N8Q/ELU9WhtvEfha30+yWNvOuhKMs4HGF3HqfrXoNFKOmgPU8t8e/D7WZvFFv4z8G3EUOtwgLNBIQFuABjqeM44IPBHcVmXfiH4x61aPplv4TtdMmlXY96ZhhAepXLHH617LRStpboO+t+pxfw28AxeA9Ae3eYXGoXT+bdzgcM3ZRnnA5+uSa7SiiqbuSlYK8L/AOES8d/DbxhqWp+EdPh1fSdQcu9uzgFeSQCMg5GTgjPHWvdKKnrdD6WZ4rrWk/Ev4k6RcWWrafa6FpqRtILeOQNLdSqMopOThd2OuPxrtPhRoOp+Gvh9Z6Zq9t9mvI5JC0e9XwC5I5UkdPeu2oqlpe3UHra/Q8s+EPhDXfC+o+JZdZsfsyXtwr2585H3qC/PyscdR1xXfeJrOfUPC2rWVrH5lxcWcsUSZA3MyEAZPA59a1aKmSvHl8rDTtLm87nA/B/w5q3hbwKum6zafZbsXMknl+Yj/KcYOVJH61leE/CGu6Z8aPEniC8sfL0u8RxBP5yHeSyEfKG3DoeoFep0VV/e5vKxNvd5fO55d8Z/COueLLTQ00Sx+1NbXTSTDzUTapA5+Zhnp2r0+MFY1B6gAGnUUlorDerueQ+JPAfibw740n8YeAjBLJdZN5p0zBVkJ5OMkAgnnqCD0qlq138XPG1hJon/AAjtroVrcDZc3TzDOw9QPmJwfYE+9e10Uklaz2HfW/U57wT4StPBXhi30e1YyFMvNMRgyyHq39B7AVxvhHwhrul/GXxLr95Y+Vpd6ji3n85G35ZSPlDFhwD1Ar1Oiqu+bm9fxJsuXlCvLLnwhrsnx/tvE62OdHS32Nc+cnB8orjbu3dT6V6nRSWjT7Deqa7kVyjSWsyKMsyMAPfFebfBXwlrnhLQ9Ut9csvsks935ka+akm5doGfkJxXp1FC0bfcHqkjgPjF4b1bxV4G/s7RbT7Vd/ao5PL8xE+UZycsQO/rW9a6ZeR/DyLSnhxerpYtzFuH+s8rbjOcde+cV0NFK3uyj3/ysO/vKXY86+DHhfWPCfg6ew1uz+y3L3jyqnmo+VKqAcqSOxpnxv0WPUvh7Pfh1judLkW6hkJx3wRn3z+YFdvrurLoWh3eqPbzXK20fmGGAZdx6AeteJ+JvE2u/GE2vhrQNCv7DTGmV7y7u02gAHvjgAdcZJJxRNubst9AglDV7anRfAjSJzoeo+KtQ+a+1m5Z95HJQE8/ixb8hXrdUtI0y30XSLTTLRdtvaxLEg9gMZq7VyavpsRFO2u4VwPjS7+Ium65Fd+FbCy1LSzCBLazMquHyckElT0x3PTpXfUVBZ4rrN18WfG+lzaE3hiy0a1uh5dxcyzgnZ3A+Ynn2Bru7Hw3F4R+F0+iQyeaLawmDyYxvcqxY4+pNdfWb4hBPhrVQBkmzm4/4Aamp/DkkOGs0fO/wmt/GWkeHZ/EPhSCDU4ZJ2gvNNmbaTtAKuhyOcMR/Q9uj1+2+JvxQ8nRrzQk8P6R5ge4eR87sHvzlsdgB16mt39nqGSHwBdLLG8bfb3OGUg/dSvWq1mldX12M4N208zBTw/FpXgaTQNMjLLFYvbwqSAWYoRyemST+tcx8GPC+seE/B09hrdn9luXvHlVPNR8qVUA5UkdjXotFK+rl3/4cdlZLsV7+xt9T0+4sbuMSW9xG0UiHupGDXimneHviN8LLu5tfDdnDr+gzSGSOJ2AeMn2yCD64yD7V7nRU7O6K6WZ5XpfiD4r63q9mk3hqy0fTlmQ3UsrguY8jcFyx5Iz/D+Irofif4Lk8c+D5NNtpUjvIpBPbl/ulgCMH0yCea7OiiSTVhJtO54zo2tfGDTNMt9E/wCEQsppbdBCl7LOoXaBgFsPg8en5UzSvhr4osPitovifUbhdRaRHk1K5V1VYpCrKERSQSoBUDAr2miqv73N1Fb3eXocD8U/h8/jjSLeSwmW31ewcyWsjHAbOMqSOnQEHsRXN2HiX4yQW6aZN4Qs57pBs+3STKEP+02Hwfwx9K9ioqUrFPU8S0D4b+K9L+Lmm+I9TddQWWJ5b+7R0VY5WVxsVSQxAG0DArsPi/4c1XxT4Ek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None.
5
APhO_2025_1_C_2
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$. (C.1) Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$. It can be shown that the torque acting on the excess regions is equivalent to the torque acting on two point masses, each with a mass equal to $2m / 5$, positioned at the endpoints $A$ and $B$ of the polar diameter (see Figure C.1).
Given this idea, find the torque $\tau$ exerted by the Sun ring on the Earth. Express your answer in terms of $M_{E}, M_{S}, d_{SE}, R$ (the average radius), $h_{\max}$ and the angle $\alpha$. You can use that $h_{\max} \ll R$.
[["Award 0.1 pt if the answer mentions that the net torque acting on a perfect sphere of radius $R_e$ is zero due to symmetry. Otherwise, award 0 pt.", "Award 0.2 pt if the answer states the idea that the torque on the ellipsoid-shaped Earth is given by $\\vec{\\tau} = - \\vec{\\tau}'$. Otherwise, award 0 pt.", "Award 0.4 pt if the answer correctly includes the torque contribution from $F_z$, where $F_z = \\frac{2}{5} m |g_z| = \\frac{2}{5} m G M_S \\dfrac{R \\cos \\alpha}{d_{SE}^3}$. Otherwise, award 0 pt.", "Award 0.4 pt if the answer correctly includes the torque contribution from $F_r$, where $F_r = \\frac{2}{5} m |g_r| = \\frac{2}{5} m G M_S \\dfrac{R \\sin \\alpha}{2 d_{SE}^3}$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly adds the two torque contributions with the right sign in $|\\tau'| = 2 F_z R \\sin \\alpha + 2 F_r R \\cos \\alpha$. Otherwise, award 0 pt.", "Award 0.3 pt if the calculation is carried through to obtain the correct net torque $|\\tau'| = \\frac{6}{5} \\dfrac{G m M_S}{d_{SE}^3} R^2 \\sin \\alpha \\cos \\alpha = \\frac{3}{5} \\dfrac{G M_E M_S}{d_{SE}^3} R h_{max} \\sin \\alpha \\cos \\alpha$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer gives the correct direction of $\\vec{\\tau}$: pointing into the plane (opposite to $\\vec{\\tau}'$). Otherwise, award 0 pt."]]
["\\boxed{$|\\tau| = \\frac{3}{5} \\cdot \\frac{G M_E M_S}{d_{SE}^3} \\cdot R h_{\\max} \\sin \\alpha \\cos \\alpha$}"]
["Expression"]
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[1.8]
text+variable figure
Mechanics
APhO_2025
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3UnlSPImJIz7ZyQcZI5IODQul9Lg+ttbHulFRwTR3NvHPCwaKRQ6MO4IyDUlGwLUKKxvFXiO18J+Gr3WrwFo7ZMhAcF2PCqPqSK8n0Ox+JvxIshr0nij/AIR/T5yTa29shyVz14IOPckk0lq9B7LU9xqG8uUs7Ke6k+5DG0jfQDP9K8Xj8VeMfhh4osdM8Y36avod+2yK/wBuHjPAJJ68ZGQc8dDXc/ETTvEmpaFOdD1yDTrRLWVrlWtxI8y7c4DH7oxkfjSm7Q5kEfiszzDwhomv/GCTUvEGq+J9RsLSO4MVtbWjkKvGeBnAABHbJ9a9s8L6HJ4d0C30ybUrrUZIt2bm5Ys7ZJI6k4AGB+FeB/CXwz4x1jwpNcaB4u/sm0W6ZWt/I35bC5bP4j8q+kIEeO3jSR98ioAzf3jjk1o0oqy8iE+Z3fmSVzvinxjY+FJNKju4pZZNSu1tYUjxkE/xHPYZH510VfNfxZ0vxNH8QNAW/wDECTtd3J+weXBsWzHmKBx/EeRz3xUr4oruy/st9j6UrxnwPqN9P8fPFtpNeXEltEknlwvKxRPnTopOBXV+E/C3jTSNbF1rvjH+1bLy2X7N5Gz5j0OfavJbfUtdsvjp4otPDdvFJq1/I8EUk3+rgGVZpG9cBf8A9fSiOlRejFLWD9UfStFeM6n4J+KdhYzana+Pnu7yJTIbXy9qNjkhc5X8CBXVfCfxxceOPCr3N+iLqFpL5FxsGA5xkNjtkdvUU1rfyB6W8zvKK8m8ceNfEOo+NIfAvgt44b8rvvL1wD5IxnA4OMAjJxnkAVla5oPxN8D6XJ4htvGj6ylqPMubS4iOCnfAJOQPbBqU9LvYdtbLc9uorn/BPiqDxl4Vs9agTyzKCssWc+XIOGH+HsRXQVTTTsyU7q4V4Jb+NPid4j8aa9o/hy6sCmnXEihZ4kXCByo5I56V73Xz58Odf0jQPix42l1fUrWxjknkVGuJAgY+aeBmpWs0n2f6FPSDfmjf8v46/wDPfRvyj/wr1nSxejSrQaiVN95KfaCmMeZgbsY7ZzWGPiN4LJwPFGlf+BS/410UpeS1c2zoJGQ+WzDK5xwT6im3ZCtqS0V5Engf4o6zuudV8fDTZGOVgsYsqvoDtK/1qv4I8VeKtC+JUvgTxXfLqPmRl7a7I+b7u4c9SCAevII600ruwPRXPZaK8s+NHivVPCcPh650+9lto5Lwi5EYB8yMYJBz+NZa2nxM+Ia/21Z62vhvSJfmsrZciR4+zNtGeevJ/CpTvsN6bnqviDWrbw5oF7rF4GMFpEZGVeregHuTxTtC1aLXtCsdWgjeOK7hWZUfG5QRnBxXkXxr0rxLB4GSeTX1bS7eKCK4tRF89xLkAuz9SM4OKf4G8I+O5vD2hX1v44MWmtFFItl9nHEfB2Z+nGaqKvf1sJ6W9CT4m6jfWvxf8FW1veXEMEzx+ZFHKyq/73HIBwa9mrwH436i2k/EzwnqCQNO9tGJFiXq7CTIH4muhbwd8U9cjGoXvjZNKuJBuWxtYjsi9FJGP6/U1MH+7+bCXx/JHrtFeR/DTxr4jPjDUfBHi6RLjULRS8VyoALgYyDgDIIIIOM+teuVVtE11F1a7BRRXmXxP+IWpaDf2HhnwzAs+v6jjYWAYRKTgHB4yTnrwAM1LfQpI9NorxoeAPis0Ium+IIW8I3GH5vLB9M4x/47XqWlwarB4ctoL+7jn1ZbcCWfYNrS464GOM/Sm9FcXU06K8iTwP8AFHWd1zqvj4abIxysFjFlV9AdpX+tV/BHirxVoXxKl8CeK75dR8yMvbXZHzfd3DnqQQD15BHWmld2B6K57LRXlXxs8Wat4StdAu9Lu5IA923nomP3qAA7TkfWqsWi/EzxxbJrEnihfDtrcDzLaxtoyWVDyu8jByR7n8OlStb26A9Nz1+ivFfCfivxd4W+JUXgnxdfLqUV2ubW7x83IJU5wCQcEEHkGvaqromg62YV43+0Bf3ljYeHTZ3c9uXvGDGGQpuGBwcda9krxH9o2QRaX4dkYZCXjsQO+FFS3Zp+a/Ma6+j/ACPa4uYU/wB0U+vH4PDvxK8Z2cWsTeLf+EfhuEEltYWsZJjQ8rvYEHOMev8ASovCfjLxR4X8fp4I8a3KXv2kA2V8By2c7ecDIOCOeQaq15We5C0jfoey0VynxD8aQ+BfC0uqNGJrl2EVtCTw8h6Z9gASfpXBad4S+KPiXTo9ZvvHEmlT3CiWKyijIVAeQG2kAfkalO9/It6W8z2iivK/ht461ufxJqHgrxdsbWbIFo7hAB5yjGc44JwQQcDIr1Sqton3J8grhPF8Pj2TxloL+G5Y10RWH28MUH8Xzbg3zEbem3vXd15N8RfE+taR8UPCGmWGoSwWV7IguIVxiQGQDnj0pL44rzG/hk/I9Zorz34za7qfh3wC1/pN5JaXQuo08xMZwc5HNc1pkPxF+JOk2+r2/iFfDumugFvFEhaWbAwXYjB5IOOfw9Utb26A9LX6ns9FfPUXj/x54D8TXXhLV2XXb2dVXT5G6l3ICHPBK9cg85HWuhv/AAR8VpLOTU/+E7/4mAUyfYoUKRZ67QRx7crTvpzdA626nslFeefCDxxe+NPDdx/aoX+0rCbyZnVdvmAjIYgdD1B+laHjjTfG+qXFlbeFdXtdNtGVvtc0iZkU8Y28Hrz0x0605KzsCdzs6K8M8T+H/iR4H0WXxFbeO59UW1w89vNFgbc4JAYsCPyr1TwT4j/4SzwfputGMRyXMf7xF6K4JVse2QaFqm+wno15m/RXieueLvFnjzx5deFPBd6unWNgSLq/A5JBwTnqBngAcnHXFT3tn8R/hzYya1J4iHiTTYRm7tp0KyKndlJyePr+FTf3eZ7FW15Vuey1wmgw+PV+JGsSavLGfDLKfsagp6jbgD5gcZzmqPwT8Q6r4l8G3N7q95Jd3AvXRXfGQu1SBx9TWf4Q8T61f/G7xNot1qEsum2sbmC3bG1CGQDHGe5qkrTS8n+RLd4N+f6nrNFeVfGzxZq3hK10C70u7kgD3beeiY/eoADtOR9aqxaL8TPHFsmsSeKF8O2twPMtrG2jJZUPK7yMHJHufw6VK1vboN6bnr9FeK+E/Ffi7wt8SovBPi6+XUortc2t3j5uQSpzgEg4IIPINdb8UfH0vgvSraDTYVuNZ1F/KtI2GQvQFiO/JAA9TTeya1uC3afQ72ivG18B/FSey/tGTx+8WpFd/wBjCHyg3XaSPl9vu4re+FXj698VwX+la5EsWuaW+yfaNokGSN2OxBGDjjpTS6dRN9eh6NRXlnxT8f6vpOq6f4T8LKra5qGP3hAbylJwMA8ZOCcnoBVOHwL8UtOgF/B4++1XyjebOeMtC5/u5Ofp90fhUp3V+hTVnbqQeCtQvZv2gPFlpLeXEltHHIUhaVii/MnRc4FezV8+fCLU7jWfjR4hv7u1+y3U1q/nw5zskDIGH5g19B1SVoQ9P8yfty9f0QUUVzHje18W3mm28HhG+tbO5eXbPNcKDtjweVyDzn2PXtUspHT0V4vq/gj4l6PpNxq9r8Qrm8ureMzNatGVRgBkgZJB+hUV2Pwv8aTeNPBKaneoi3kEjQ3GwYDMoB3AdsgjinpZ+Qn08zt6K8J0TUfHPxa1DU7vTfEo8P6RaTeTHFAmZD3GcEE8d8/QV1fhzwl8Q9D8SWrXvjJdV0bJ+0JNH+8IxxjIOOcchqEr76A9L2PS6KKKAOE8Xw+PZPGWgv4bljXRFYfbwxQfxfNuDfMRt6be9dreXKWdlPdSfchjaRvoBn+leWfEXxPrWkfFDwhplhqEsFleyILiFcYkBkA549K6X4i6b4l1DQ7j+xNbh021jtpWula3EjygLnAJ+7xkfjUt2pXXd/16FJXqWfkeX+ENE1/4wSal4g1XxPqNhaR3Bitra0chV4zwM4AAI7ZPrXtnhfQ5PDugW+mTaldajJFuzc3LFnbJJHUnAAwPwrwP4S+GfGOseFJrjQPF39k2i3TK1v5G/LYXLZ/EflX0hAjx28aSPvkVAGb+8ccmtGlFWXkZp8zu/MkrnfFPjGx8KSaVHdxSyyaldrawpHjIJ/iOewyPzroq+a/izpfiaP4gaAt/4gSdru5P2Dy4Ni2Y8xQOP4jyOe+KlfFFd2X9lvsfSleM+B9Rvp/j54ttJry4ktokk8uF5WKJ86dFJwK6vwn4W8aaRrYutd8Y/wBq2Xlsv2byNnzHoc+1eS2+pa7ZfHTxRaeG7eKTVr+R4IpJv9XAMqzSN64C/wD6+lEdKi9GKWsH6o+laK8Z1PwT8U7Cxm1O18fPd3kSmQ2vl7UbHJC5yv4ECuq+E/ji48ceFXub9EXULSXyLjYMBzjIbHbI7eoprW/kD0t5neUV5N448a+IdR8aQ+BfBbxw35XfeXrgHyRjOBwcYBGTjPIArK1zQfib4H0uTxDbeNH1lLUeZc2lxEcFO+AScge2DUp6Xew7a2W57dRXP+CfFUHjLwrZ61AnlmUFZYs58uQcMP8AD2IroKppp2ZKd1cKKR2VEZ3ICqMknsK8Rh8QeM/ivr9/D4X1UaF4esX8v7WqZkmbsfXJ64BAAxmp3dkPpdnt9FeF6lrHjn4R6rYXGua2fEPh+6k8qR5ExJGfbOSDjJHJBwa9G8dWuuat4Qa78J6pNa38aCeHysYuFxnbyO46e9DaUeYEteU66iuB+G/xCt/FPhGS61GVLfUNNXbqCv8ALtwP9ZjsDg/Qg1geCfEPiP4heO73Wbe+uLPwlZP5cMCgD7Sw6ZOM+5/AVVve5RX92567RXknj3x74gufGEPgfwSI11Rlzc3bgEQgjOBnIGByTg9cDmq58AfFW2C3Fv8AEITXAILRShtn4ZBB/IUlrr0G9ND2OisPxH4gg8I+FLnV9Qcyi1iGcYBlfoAPTJryzRNM+JfxEsB4gm8WNoFncEtaWttGfudicEHHuSSaOrS6B0TfU9vorx/wj4x8S+HfHw8DeM7lL1513WV+owXzkgHgZBwRzyCO9W/iX4w8QReLdH8F+GZ4rK91FQ73koB2AkgAZBx90npnpijtbW4d79D1WivIJPh18S7VPPsviTNPcjny7iNhGT6clh/47XYa/wCINS8GfDSXV9TaO91W1tkEhVdqPMxA6DHGT+lJtJXYJNtJHX0V4joPhv4j+NdEtvEE/j+TTheL5sVvbRHaqnoDtKgfrXd+BdG8Z6PLew+KNeh1W2wv2RlTD99xY4B9OMmqt0Yr9UdnRRRSGFFeJeMfiJ4m0D4vvoumA3sM9skdrYFVC+c68MTjOAeTzVu88I/F94H1BPGtub0DeLOKMLHn+6Dtx7cj8aSd1zdB21sexUV5v8KfiHd+L4L3S9ahWDXNObbOFXaJFzjOOxBGCPpWr4403xvqlxZW3hXV7XTbRlb7XNImZFPGNvB689MdOtN6W8xLU7OivDPE/h/4keB9Fl8RW3jufVFtcPPbzRYG3OCQGLAj8q9U8E+I/wDhLPB2na0YxHJcx/vEXorglWx7ZBo3TfYHo15m/RXzx4a+IfjfW59V8NaRKbvWZbx/Ku7gDy7O3Xgnp64xkH8a9B8MeEfHekDUpdS8Yi+nntilt5is6QS5+9tPBH5ULVX/AK/roD0djpF8Y2L+PG8JJFK14lp9qeUY2KM/d9c8g/jXRV8waPoHi27+NGsabB4qMOtRQkzaj5OfMXCfLt7DkflXrM114i+HHgDWtV17WRr13EVa3LR7ApOFAOO2Tmi6UFJ9v1HZubiv60PRqK8R0Hw38R/GuiW3iCfx/JpwvF82K3tojtVT0B2lQP1ru/AujeM9HlvYfFGvQ6rbYX7Iyph++4scA+nGTTt0ZN+qOzoopsqGSJ0DFCykBh1HvSYx1FeT/B/xTrWpar4k0DxDfSXd9p1x8jSAA7QSpHA6ZA/Oq3xn8Ya7peo6Vofhm8kt7+SKW6nMWM+Wqkgcg/3WP4Um7JPuNK7a7HsNFcr8OPET+KfAel6nNJ5ly0fl3DdzIp2kn64z+Ncf4X8Ta34l+Nmu2sWoS/2Dpisn2dcbGcYT0z13Hr2qmrT5PX8CU/d5j1qivG9a8WeKvHPji78KeC71NNstPyL3USuSWBwQD254AHJwecVn6+nxF+FsEWuyeJj4h0pZFS6huUIKgn3JIHbIPXHFSmrJvRMprWy3R7pRVDRNXttf0Oy1azJNvdxLKmeoyOh9x0rwfw18Q/G+tz6r4a0iU3esy3j+Vd3AHl2duvBPT1xjIP403dS5eolZrm6H0PRXBeCPDHi3w/f3d54m8VtqsDw4WIs22Ns5Lc8dBXGw+IPGfxX1+/h8L6qNC8PWL+X9rVMyTN2Prk9cAgAYzR1sg6XZ7fRXhepax45+Eeq2FxrmtnxD4fupPKkeRMSRn2zkg4yRyQcGvcIJo7m3jnhYNFIodGHcEZBp7q6DZ2ZJRRRSAKKKKAIL25Sysbi6kOEhjaRj7AZP8q+avhv8MbP4lWmra9q17e25e9YJ9nKjcT8zE7gf7wr2/wCJs93D8OtaWxt57i6mg8iOOCMux3kKcAc9Cap/CDRJdC+GumW9xC8NzLvnljkUqylmOAQeQcYpRSbk32Q5OySXcyPDfwM0Dwz4hs9Zg1HUZ5rV96RzMm0nBHOFB75rn5/+Kk/aehT70OjW2T6Aqmf/AEKQflXuBOBmvHvhJouqt438W+JNX028snupisAuoGjLKzljjcBkYC1UX767K7+exMl7j87Iy/i+p1/4reEPDMhJtWZZJF7Hc+D/AOOp+te5gJDFjhI0X6AAV478XfD2uWvizQ/G+hWEl++nbVngjUs2FYsDgc4IJBx0qPWPGnijxt4cvYbPQbzw9pEdu8moaheEh/LC5ZIgQMk9M+/aoTtTfdNltXmu1kZ/wraLxL8ZvFfiWIbrePcsLf7zYU/98ofzqf4hf8VF8ePCmhD5orMLPIv4lz+iCtD9nXSvsvgm91Erhr27IU+qoAB+pas3xva674Q+MkHja20W51XTpYRGwt1LFDs2EHAOD3BPBq7KEoLt/kR8am11/wAz2rUb6DS9Nub+5cJBbxNK7HsAMmvH/gBA9+PE3iSZT5l/e7QT+Ln9XH5VF4q1Dxl8RvCmoeRoF9o2iwwGTynUtdX0g+6ioBkLnBPHOK7X4Q6FP4f+G+nW13byW91KXnmilQq6szHAIPIOAKIqzk32/P8A4YcndJLv+RwWvW0XjD9pOx06YCS00qBXkU8jKjfg/wDAmUV7tXj3wt0TVZPiP4u8S6tpl3Z/aJDHbG5gaPerOT8u4DIwq17DSjpCK+fzYS+OX3fcfOvjiTXtc+P8dvoUFtc3ulQo1vFdHEYwu8k8ju2fwFdPeeD/AIpeNITY+Jde0/S9Lc4mgsVy8g9OByPq2PY1D8QfDviLw38R7b4geG9PfUk2BLu1jBLcLtPA5wVxyAcEVcHxd8S6sottC+HuqNeNxvugyxR+5O0fqRSgvdS6jl8V/Q9I8OeH7DwvoVto+mxlLa3XALHLMTyWJ9Sa1abGXMSGQAPtG4Dse9Oqm23qSttDiPi80ifCvXjHnJhUHHoXXP6VU+CIiHwo0nysZLSl8f3vMb/61dprOlW+uaNeaXdgmC7haJ8dQCMZHvXgug6h4z+C93daTe6DcavoUkpeKa3BwD/eVgDjIxlTUxdnJPrYcldK3Rn0RRXk2m/F/Wde1S0s9K8C6mI5ZkWa4n3bYkJGWOFxwPUin+P/ABl4z0vx/o+ieHdOL2k4RpJDblxLliGG7ooAH61VtUu+gX0b7Hq1ZviHUl0fw3qeoscC2tpJfxCkj9a0q4T4wDUpvhxf2elWN1eXV2yQ+XawtIwUtljhQTjA/Ws6nwtIqHxK5zn7PWmtB4KvdUkH7y/vGO491UY/mWr16uY+HejPoHw/0XTpomimjtg0qMMFXb5mBHrk1zHxc8X+K/DR0m38L2LSyXbt5kwtzNgjGEA6DOT+Va1GlKy9DOCbV/menUVXsHuJNOtnvECXLRIZkXor4G4D8c1YpNWdhp3VwooopDCvDfi3/wAli8C/9dYv/Rwr3KvHviboGr6n8VPB19Y6bdXFpayRmeaKIskYEoJ3EdOOaI/xIeoS/hy9D2GvDfizGsvxk8DI4ypePIP/AF2r3KvHviVouq3/AMW/Bl7Z6ZeXFpbuhmnhgZ0i/e5+ZgMDjnmiP8SHqEv4cvQ9hrxG14/apu/+vP8A9orXt1eP22jaov7Slzqp028GnG12i7MDeST5SjG/GM5460R/iL0f5A/gfy/NHJ+KIvEN3+0dPFoF1aW2prAv2aS8GUC+SM/wtz97tXZnSPjcRg+IfDn/AH7P/wAZp3xR8Ea1Pr2neNfCah9YsMCSDvKozgj1OCQR3BqpF8bdUjiEN58P9ZW/HDxxq20t7ZTI/I0o25VHqhy+K/TQ1fhJ8P8AW/Azaw2sXFjKb543QWjswBG7OcquOor02ua8Fa3rfiDSJr3XNEbR5TMRDbOTv8vAwWzg5znsOnSulqnfqSurGvkRsR1wcV8w/Cu08d3txr8vhPUtLtJPtC/axerlmOWxj5G4+9X1BXhuqaB4o+GHjq+8S+GdLfVtE1ElrqziBLoSckYAJ4OSCAeDg1K0ld9UU9Y2Xcta34P+MHiLR7jStS13w7LaXACyIFZScEHqIsjkCvQfh94evfCvgjT9F1GWGS5tg4ZoWLJy5IwSAeh9K4b/AIXVq14PI0v4fazNeNwFkDBQfchOn5V6npM95c6PZz6hbi3vZIUaeFekbkcr1PQ1WyZL3R478Af+Qt4y/wCvtP8A0KSi8/5Ops/+vQf+iWq98EdF1XSdU8VvqWmXlms9yrRG5gaMSDc/K7gM9R09aLvRdVb9pS11VdMvDpy2wU3YgbyQfKYY34x1460o7w9P/bQltU9f1RU/aL/5Bfhz/r9b/wBBFdv8Uv8Akk2uf9eg/wDQlrlvj1o2qaxpugppmm3l80V2zSC2gaUoMDk7QcCup+KQI+E+ugjBFoP/AEJaiX8KXq/yRa/iR/rqU/gmsa/CjSPLxyZS2PXzGqn8e0ib4W3RkxuW5hMef727H8s1wvw48U+IvAng21ln0C61jQL3dNBPZDc9u2SGVhjpkZ7detS+Ib7xR8adRsdIsdCvNJ0GGUSXFxdKRk9Mk4AJAzhRnk1pVXPKy7r5EU3yq78z0zwppNt4j+D+kaXqsZkt7rTY45BnBxgYIPqMAiuFXwT8R/hxvbwfqqaxpKksNPuR8wHXhT/7KQT6V6drral4b8G48M6ct7dWUcccFq38aKQCOo525/8Ar1wifGfWETyrn4c68t4ODGiMQT9Smf0ok05ylEIq0Emb/wAOviZD42e60+7sX07WrMZntmzgjOCRnkYPUHp71xXw2G749+NGuP8Aj4HnbM9dvmr/AExWx8MvC+vzeNdZ8c+IbAabNfqUhsz94AkZJHbhQOeTycVF438JeIfD/jyPx94QtPtsrLtvrEfekGMEgd8gDpyCM80fDKMn2d/JsLXjKK7q3yPYK8M+EmE+MPjiO3/49fMk6dM+ccf1q9d/F/xNqdo9jongHV49VkXYGnRikR9fujOPfFdH8J/AVz4M0a5udVdZNY1FxLckHdsHOFz3OSST6miKtLm8n+ISd48vmvwOSv8A/k6ix/69B/6Jam/tEZZ/Cscn/Hu1zJv9P4P6ZrQvdF1V/wBpOy1VdMvDpy2wVrsQMYQfKYYL4x14611HxV8ESeOPCRtbQquoWz+faljgM2MFSe2R+uKm9oxfZ/qVvNruv0O3jCrGgTG0AAY9K8P+KyRj40eBnGPMMkYb6Cbj+ZqbRPir4p0PT4dH17wNrFzqVuoiEsEbYmxwCflPPuCQaw9Y0TxtrnxH8L+KdX0aeGOa7jC2kEbS/YoUdSDIwGATuJ5x0/AUl+9i1tch/wAOSe9j1j4h+P7TwDo0VzJbtdXly5jtrZTjew6knsBx+YrmrST4y63Et2D4e0aKQblhlV3kUHpnhufxFHxt8H6v4h07S9U0SA3N3pcrObdeWdTg5A7kFRx71Xtfi34m1C3S0svh5qp1Vl2nzQyQq3qSVGB9cfWpjrfuXLS3Y574ax6nD8ffEEes3EFxqK2jieWBdqM2Y+g49qv/ABU/5LR4F/34/wD0dTvh54T8S6H8Y9TvtchlmN1YtLJepEwhMrlGKK3Tg5H4Vc+JWi6rf/FvwZe2emXlxaW7oZp4YGdIv3ufmYDA455qo70vL/gky2qef/APYaKKKQzk/HvgLTvHujx2d3LJb3EDF7a5jGTGx68dweOPavOZb34qfDGDfeLD4l0KAfNLkmSNB6n7w+p3AV6B468TeJPDL2NxovhyTWrNt/2tIc+YmMbSMZP97+E9O1cdffFrX9Y0+fT9I+H2s/bp42jBnjby0yMZPy8/jipu0m4/cVo7cx6J4O8Xaf418PRavp4dEYlJIn+9G46qfzHPvXlnwBjX+3PGUuPn+0oufbdJXa/CTwbeeC/Bv2TUSovrmY3E0anIjJAAXPc4HNc38EdF1XSdU8VvqWmXlms9yrRG5gaMSDc/K7gM9R09a0slUdu3+RnduGvdfqei+M+fBGvf9g+f/wBANcR+z+cfDFM/8/kv9K7vxZDLc+D9aggieWaSxmVI0UszMUIAAHU1xvwS0q/0z4cCz1OxubKc3MpMVxE0b4OOcMAaiN7z9F+ZUto+r/Iy3+Jnijxd4gvdJ8AaTaSW9m22bUb5jszkjIAIxnBx1J9K5z4p2XxFh8B3EviXV9FmsPNjDwWcTB927jBKjoaj8Mz+Jfg5rmr2Fz4XvtV0y8lDw3NmhbOM4OQCOQeQcEVb8cv43+Jnha5kh8OXWk6XZ7Zo7WZWa5vZM4AC4BAAJPT8+yfwprXYpaTafyPRdC/5ItZ/9gMf+ia5P9nNYx4EvmXHmHUG3+v3ExXYaXbT2fwfgtrmGSGeLRdkkcilWRhFyCD0NeKfCXWvEfhDQLnWLPRptZ0O5nMdxDa5MtvIoGGxg5BDfp276tr2tT+upkk/Zw/roe3/ABQSJ/hj4hE2Nos2Iz/eHI/XFcX8O5bkfs7XbIW8xLW88r/x7GPxzWF4r8X+J/inaJ4Z8O+GNQsrWd1N1c3alRtBzgnGFGeepJxXsfhvw3a+HvCVnoCYlhgg8pyR/rCfvH8STWbi3Cfnp/wTTmSlHy1PB/hPp/xGuPCUknhLVtGtbA3Th47pCZPMwuSf3bcYx3rovE3gD4s+L9LGm6zrXh6a2EglCruQhhnByIvc1VsbPxZ8F9dv0sNFn1zwxdyeYv2cEvF6ZwDtIHByMHA5rdHxi1/VWFtoPw/1WS4Y433IYInucL/UVTtO1vISTjc9L8O2E+leGtM0+6dHuLW1jhkZCSpZVAOCQOOK06ahYopYYYjke9Ook7ttiikkkjyb9oYyj4cRBM7Dfx+Z9NrY/XFd/wCD1iXwXoYgx5X2CHbj/cFN8YeGrfxd4WvdFuG2CdPkkxnY45VvzFeUeH/F/jD4a6cnh3xB4Sv9St7XKWt5ZAsrJ2GQCD7dCPSpi7cyfVp/hYclfla6XRpftGLEfAlgzY80aguz1+4+f6V3m6Rvhlumz5p0fL59fJ5ry250zxT8Y/EunTatos+ieGLF/M8u4yHm9eCASTjGcYAz1r2XW4Gfw1qNvBGWY2cqRxoMknYQABUyTVKV+v8AlYpO9SNun+Z5r+zt/wAk9uf+v+T/ANBSvXK8u+A+lajo/gW4t9TsLqynN67CO5haNiu1ecMAccV6jW1Tf5L8jKG3zf5hXh/xp/5KN4E/6+B/6NSvcK8k+NfhbWtSOieIdCtXu7rSZSzQRruYjKsCB1OCvIHPNQnyzjJ7JmlrxlFdUet14b4DjVv2i/F7kZZEl2n0y6V2Pg34k6h4p1aHT5/CGqacPLZprmdWESMB0BKjqfXFc/4J0XVbT47eK9RudMvIbGdJBFcyQMscmXT7rEYPQ9KcVaovRkyd4P1R6/J/q2+hrxX9nbiw8Sj/AKfV/ka9qfmNgPQ15H8B9G1TR7PxAup6beWRlu1aMXMDR7xg8jcBkUo/FL0/UcvhXr+jOG0W38X3vxn8XHwvfWFpqKyzeY18uQYvMAwvyt/s13F74d+NGoWNxZ3Ov+HHgnjaKRdhGVYYI/1Xoah8b+EvEfhrx6vj3wfafbmkXF9YqMs3GDgDkggDpyCM1Kvxu1KRBFF8Ptbe9PHlYbG767M/pUxS5FF9FYcr87l31Ol+FHg3VPA/hafS9VntZZnummU2zsyhSqj+JRzkGu7rG8LahquqeHra91rThp1/LuL2vP7sbjtznvjFbNaSvfUmNraBXzn4F8JaH4t+K3jS31ywF3FBcSPGpkdNpMpGflIr6Mr5v0m+8XeB/iJ4o1Kz8D6vqcV9cyKjLbSqu3zCQwIQ5BqFb2iv2f6FO/I7d0eqD4MfD4EEeHUyP+nqb/4utrxh4rsPA3hiTVbtGeOPbHDCh5kc9FBP06+grzv/AIW745/6JXq//fE//wAarc+JnhvVPHvwytvsto0Opp5d59jc4bdtO6PnHI3HrjkUS5uXQI25rMztL1j4ueLrSLUtPttC0WwnXfCLre8jIeh79foK5Ozg1+3/AGjdEj8SXtpd6h5BJktU2pt8uTAxgc9a3tB+KniSw0e00ef4e6zNqltEsHyRsqOVGATlfl6e4qhpnhjxh/wuvQ/EmvWTsbuN5Zzbxs0VmNjqsTPyM42/iatWVRW21/JkNt03fexa/aNUPpnhxG6NeOD+Qr2m1jSG0hijUKiIqqo6AAcV5L8edG1TWLHw+umabeXzRXbNILaBpSgwOTtBwK9ciBESA8HaKmPwv1/RFS+Jen6nnPx3/wCSVX//AF2h/wDQxXRfDr/knHh7/rxi/wDQah+Jfhu58WeAtR0qzwbpgskKk4DMrBsZ98Yrz3wT8RPEOhaRp/hjUfA2sS3lrtthLHEwXZnAJ+U4wO4yOKIfaj1bX5BP7Mu1xnxZjWX4yeBkcZUvHkH/AK7V7lXj3xK0XVb/AOLfgy9s9MvLi0t3QzTwwM6Rfvc/MwGBxzzXsNEP4a9WEv4j9EeI2vH7VN3/ANef/tFa9urx+20bVF/aUudVOm3g042u0XZgbySfKUY34xnPHWvYKI/w4+n6sH8b+X5IK8MbEv7VYFzyEt/3Of8Arh2/M17nXknxS8Fa4/iLTvG/hSPztVsMCW3HWRRnBA78EgjqR0pJ2mpPb/MdrxaR63XP+M/Ftj4K8OTaxfK0iqQkcSHBkc9FHp359BXnifG/VfJEDfD/AFg6jjBhUMF3f98Z/StT4h+Hdb+IHwqtCtj9m1lCl2bInB3YIKc98Hv6UTvy3QRtezKel6x8XPF1pFqWn22haLYTrvhF1veRkPQ9+v0FcnZwa/b/ALRuiR+JL20u9Q8gkyWqbU2+XJgYwOetb2g/FTxJYaPaaPP8PdZm1S2iWD5I2VHKjAJyvy9PcVQ0zwx4w/4XXofiTXrJ2N3G8s5t42aKzGx1WJn5GcbfxNWrKorba/kyG26bvvYt/tGKH0zw4p6G8cH8hXtNuoS2iVRhVQAAdhivJPjzo2qaxY+H10zTby+aK7ZpBbQNKUGBydoOBXrkQIiQHg7RUx+F+v6IqXxL0/U8U8f/APJwvgw/9M4//Q3r26vH/G+japd/HTwlqFtpt5NYwIgmuY4GaOP53+8wGB1HWvYKIfw16v8AMJfH8kFeI/tHbTpfh3d937W+fptFe3V5H8dPDmqeJrbw5ZaZZ3E7NeMsjxRM6whgBucgcD3NJ7q3dfmNdfR/ker2wUWsITGwIu3HpivEPjR8vxM8DvB/x8+cvTrjzVx/WtO2+IXivwVZRaL4i8HahfzWqiKK+sctHcKOAehwcY759hVLwx4f8SeP/iPB418TaZJpen2IH2K0lBDEjJXg4OATuJIGTjFWtaiktk7kbU3F72sQ/tGmdl8MRRsqo08vL/dDfJjP5mtpdI+NoQbfEPhzbjjEZ6f9+a6b4neB/wDhOvCjWULrHf27+dau3TcBgqfYjj8q4bSfin4q8LWEWkeKfBeqXF3bKI1ubdSRKBwCeCCfcHmojomn3LlrZoteG/hz43h+J9t4v8R6jpM7KrJMbVmDMPLKjC+WB6V7HXB+C/G/iDxZrMoufCd1pGkJCWS4ut2+STIwBkDjGex6da7yqeiSJ6thXiHxX/5LJ4E/66x/+jhXt9ePfEzRdVv/AIr+C7yz0y8ubW3kQzTwwM6RfvQfmYDA455pR/iQ9Ry/hy9C/wDtAf8AJMX/AOvyH+tdn4GjWLwFoCIMKLCHj/gArlvjhpl/q3w7e102xub24+1xN5VtE0j4GcnCgnFdf4RgltvBuiwTxPFNHYwq8cilWVggyCD0NEPhl6r8gn8UfR/meT+MEV/2lvC4YAjyEP4jzMV7gehrx/xRouq3H7QnhzU4dMvJLCKBRJdJAxiQ/vOC4GB1HfvXsB6Ghfwvmxy/ifJHif7P3/H34vH/AE+J/N62df8Aibrd54xn8JeB9Igvr+2yLm6umIiiI68AjpnGSevGDVP4H6Nqmk3Xik6lpt5ZCe7VojcwNH5gy/K7gMjkdKw57bxH8LvijrGuweH7rWNH1Usxe1Usy7m3YOAcEHI54IpdYp7W/GyF/M1vf9TQ8Z2PxTHgjV59a1fQBYC2YzwW0TFyvcAlev411HwTz/wqTS8dczY/7+NXM+INY8ZfE7w/e6Zpvhq70XTPJaSee9B8y42jKxIuB1IAzz/j2Hwf0690r4Z6ZZ6haT2lyjS74Z4yjrmRiMg89KpLSS9P1FL7Pq/yOH/Z3CtL4qkkx9qNzHvJ64+f+ua9f8SJHJ4X1ZJQDG1nMGz6bDXjt/o/iX4VeP8AUPEGg6PNq+g6kS09vbgloyTnGACRgk4OCMHFXtZ8ceKfHOg32l6P4UvtJtZIH+16hf5VY4wCWCjAySMjr3/Gon71PTt9xcdKl/Mtfs7f8k+uv+wg/wD6AlZvgT/k4rxh/wBcpP8A0NK0v2dv+SfXX/YQf/0FKj8GaLqtr8efFWo3GmXkNjPG4iuZIGWKT5k+6xGD0PT0rV/xV/hf5IyX8N+v6sp/tGKH0zw4p6G8cH8hXtNuoS2iVRhVQAAdhivJPjzo2qaxY+H10zTby+aK7ZpBbQNKUGBydoOBXrkQIiQHg7RUR+F+v6IuXxL0/U8U8f8A/Jwvgw/9M4//AEN6zPjGupz/ABh8LQabNBDdGKP7JJcDMaymRsE8HuB2NdD430bVLv46eEtQttNvJrGBEE1zHAzRx/O/3mAwOo61sfFrwFe+LLCy1PRHCa3pj+ZACdvmDIO0HsQQCM/1qY6Ri30kxy1lJd0jP/sn43f9DD4c/wC/Z/8AjNHw6+Hninw7451PxF4gvNNna/hcSfZHbJkZlbOCigDg1RtPjNr+nW62mveBNW/tGMbXaCNgsh9QCvGfYmu18DeKdf8AFJvbjVfDc2i2abPsonJ8yXOdxOQPbt371a0d0S9rM88IEn7Vn+kchLf9zn/rh2/WvdK8i+Kfg3XR4k03xx4UhM+pWOFmt1GWkUZwQP4uCQR1x0pLf4veJNSiFnYfD3Vf7VYbcShlhRvUkqMD64+tTH4FHqhyXvX6Oxl+AUjT9ojxgseNvlynj1LoT+ua9yrw74X+FvEeg/FvWrjXLad2ntC73ohYQySOyOQrkYOCSPwr3GqStCC8v8xPWcn5/ogrzbxt8TL3SfE1v4T8MaUup69MASJGxHFkZGcEZ45PIAFek14f410jxF4P+LSeO9K0ebV7GaMLPFACzJ8mxgQASOACDjFT9pJ7FdHbc2buy+ME+l3M15q3hy1i8py8UcTMwXByOVI/Wqf7OXPgbUc/9BBv/RaVNP4y8XeP7OTRdD8KXujw3SmO51LUAVWJCMNtGBubHv8A41Z+B2h6r4f8IapaajY3FrcC/cxrPEU3jYoDDPUEjrVR05r9v1Jlry27/oUNW+E+v+Htaudc+Hmt/YpJ23y6fMf3bc5wCQQR1wGHHrVnwr8VtVj8TQ+FfHGj/wBm6pMQkM8YxHIx6ZGT17EEjPpUafFvxRpbG21/4e6oLhTjzbNWKP7jKkfkxrLSw8S/FL4haJrd74en0PRtJcSK11kSS4YNgAgE5IHbAGeaIbpdPyQ57N9fzPcqKKKQHiHxX/5LJ4E/66x/+jhXrviL/kWNW/685v8A0A15h8TNF1W/+K/gu8s9MvLm1t5EM08MDOkX70H5mAwOOea9R16N5vDupxRIzyPaSqqKMliUOAB3NRL+A15yKX8ZeiPM/wBnb/kntz/1/wAn/oKV65Xl3wH0rUdH8C3FvqdhdWU5vXYR3MLRsV2rzhgDjivUa2qb/JfkZQ2+b/MK8P8AjT/yUbwJ/wBfA/8ARqV7hXknxr8La1qR0TxDoVq93daTKWaCNdzEZVgQOpwV5A55qE+WcZPZM0teMorqj1uvDfAcat+0X4vcjLIku0+mXSux8G/EnUPFOrQ6fP4Q1TTh5bNNczqwiRgOgJUdT64rn/BOi6rafHbxXqNzpl5DYzpIIrmSBljky6fdYjB6HpTirVF6MmTvB+qPX5P9W30NeK/s7cWHiUf9Pq/yNe1PzGwHoa8j+A+japo9n4gXU9NvLIy3atGLmBo94weRuAyKUfil6fqOXwr1/RnDaLb+L734z+Lj4XvrC01FZZvMa+XIMXmAYX5W/wBmu4vfDvxo1CxuLO51/wAOPBPG0Ui7CMqwwR/qvQ1D438JeI/DXj1fHvg+0+3NIuL6xUZZuMHAHJBAHTkEZqVfjdqUiCKL4fa296ePKw2N312Z/SpilyKL6Kw5X53LvqdL8KPBuqeB/C0+l6rPayzPdNMptnZlClVH8SjnINd3WN4W1DVdU8PW17rWnDTr+XcXtef3Y3HbnPfGK2a0le+pMbW0MXxe0qeC9caHPmiwnK49dhrwb4T6f8RrjwlJJ4S1bRrWwN04eO6QmTzMLkn923GMd6+kJYknheGVQ0cilWU9weCK8HsbPxZ8F9dv0sNFn1zwxdyeYv2cEvF6ZwDtIHByMHA5qI6Sd+q/Up6xVujLXibwB8WfF+ljTdZ1rw9NbCQShV3IQwzg5EXua9e8O2E+leGtM0+6dHuLW1jhkZCSpZVAOCQOOK80Hxi1/VWFtoPw/wBVkuGON9yGCJ7nC/1FdX8Rtf1rRfCrJoOlX19q12PKj+y2zyiDI5dioOMds9/pTbcYuy3EknJHg3xX+yR+P9aHhdroQtAP7ZFt/qwdw3dO2duc8Zr6J8BLoi+CdKHh7B03yR5Z/iJ/i3f7Wc596wvhv8O7fwz4Slt9UiS41HVFLag0nzZ3D/V57gZOfUk1zPg/Tte+Gnj+68PLp+oX3hXUH8y3uYYHlW2Y9NxAIHoc+xpxXL+7/q/b/IUnze//AFbv/mUvhriX49+NJLjmdfOCZ6481R/LFe514v438LeI/CvxBHj7wnZHUElXF7ZICWPGG4HJBAB4yQRmpv8AhdmrXai3074f6xJfNwEcNtU++Ezj8qmPwRj1SsOS9+T6PUsftDtKvw5hCZ2Nfxh8em1sfriqGgaT8YT4d006br/h5LE2sZt1aM5Ee0bQf3XXGK9F8WeGk8aeC7jSLzEEtxErK2M+VKOQfwPH0ry3w9408Y/DbT08O+I/Cd9qFva5S2vLQFgU7DIBBHpyCB1FEfdck+//AAAeqi0WG+G3xE1fxvoviDxDquiTnTpoyTAzo3lq+4gARgE9etdp8Qvhra+OPs15DeyadrFmP9Hu4+eM5AIGD15BByKo+GPiL4h8VeIrW2h8GXun6Sd32i9u9wx8pICjAHXHc9ateNPGfibwrrkX2Lwncazozwhnltd3mRyZOQcBuMY6gfWm9EkC3bOLl8W/Ev4ZhP8AhKbGLXdGVgpvoT86jPdgOP8AgS8+tepI+i/EPwVnDT6XqcGCD8rD/BgR+YrzDxH4/wDEvjjQbrw9ongPVYpL1PKknu0KpGp68kAZ9yRXYaZpOufD/wCE9vZaRaR6nq9oodoBnbIWfLgcg8AnH06UPWL5gXxLlOOXwT8R/hxvbwfqqaxpKksNPuR8wHXhT/7KQT6V2Xw6+JkPjZ7rT7uxfTtasxme2bOCM4JGeRg9QenvWAnxn1hE8q5+HOvLeDgxojEE/Upn9Kd8MvC+vzeNdZ8c+IbAabNfqUhsz94AkZJHbhQOeTycU43bs9rf8MKVrXW/9XPW6KKKQzwzUljb9qmw8zHFupXPr5LYr3OvnPx7bavcftCRtoJjOqQW8c8CSHAkKJuKfiARXVXfxq1aC3e0/wCED1hNZxtEToxjD+uQuSPw/GlF+4vn+YNe+/l+RmeEcRftM+JEtuImikMgHTPyE/8Aj1dDr/xN1u88Yz+EvA+kQX1/bZFzdXTERREdeAR0zjJPXjBpvwg8E6vpNxqfinxIhTWNUYnym+9GpO4lvQk447AVzM9t4j+F3xR1jXYPD91rGj6qWYvaqWZdzbsHAOCDkc8EU7W5IS6L8Qvfmkur/A0PGdj8Ux4I1efWtX0AWAtmM8FtExcr3AJXr+NdT8EP+ST6T/vTf+jGrmPEGseMvid4fvdM03w1d6LpnktJPPeg+ZcbRlYkXA6kAZ5/x7D4P6de6V8M9Ms9QtJ7S5Rpd8M8ZR1zIxGQeelOO0r+X6il9n1f5HDfAKGM694xn2jzBcKgbuBuc4/QV7nXj3wR0XVdJ1TxW+paZeWaz3KtEbmBoxINz8ruAz1HT1r2Gkvhj6L8hv4perPD/C//ACc54k/692/9Bjr2HW9GsvEGjXWlahGZLW5QpIoOD7EHsQcGvGfFNl4h8B/GCbxnp+i3GraZfR7Zlt1LFcqAwOAcHKggkYPSu0tvHfiHW/CWp6rpHhG9gvbWSMQWt8pBuVJG/aOOgz0zzSVnTin0Vn943dVG11en3HIL4J+I/wAON7eD9VTWNJUlhp9yPmA68Kf/AGUgn0rsvh18TIfGz3Wn3di+na1ZjM9s2cEZwSM8jB6g9PesBPjPrCJ5Vz8OdeW8HBjRGIJ+pTP6U74ZeF9fm8a6z458Q2A02a/UpDZn7wBIySO3Cgc8nk4qo3bs9rf8MTK1rrf+rnrdFFFIZ4lKv/CJ/tLRSfctdet8H0LEY/8AQ0H50/wjEvjX42+JtdmHmWOnRGxhz0Ocp/IOf+BVofG3QdVuU0DX9CsLm81HTbv/AFdtE0j7ThgcKCcAr+tbHwa8N3Ph7wKj6hbyQajfzPc3CSoVdcnABB5BwM/jRBXWvS6+/b8Gwnvp1t+G/wCKRxvww1f/AIQoeOfDt42Bo7SXkIY9VAIP54Q/jWr8AtMkj8I6nr04zc6pdM249Sq5/wDZi1c38ZPC/iCLxnNqXh7Sr68i1ew+z3RtLd5NpBAOdoOMhV6+9ez+DtGHh7wdpOlbdrW9siuP9sjLfqTRG7g297Jfnr+CCWkrLa9/y/Vs+e/hXaeO7241+XwnqWl2kn2hftYvVyzHLYx8jcferuNb8H/GDxFo9xpWpa74dltLgBZECspOCD1EWRyBVXVNA8UfDDx1feJfDOlvq2iaiS11ZxAl0JOSMAE8HJBAPBwa0v8AhdWrXg8jS/h9rM143AWQMFB9yE6flS0cV+Q3dSbO5+H3h698K+CNP0XUZYZLm2DhmhYsnLkjBIB6H0rzP4BQxnXvGM+0eYLhUDdwNznH6CvZtJnvLnR7OfULcW97JCjTwr0jcjlep6GvK/gjouq6Tqnit9S0y8s1nuVaI3MDRiQbn5XcBnqOnrV3ftG32f5ojT2at3X6no/i9pU8F640OfNFhOVx67DXg3wn0/4jXHhKSTwlq2jWtgbpw8d0hMnmYXJP7tuMY719ISxJPC8Mqho5FKsp7g8EV4PY2fiz4L67fpYaLPrnhi7k8xfs4JeL0zgHaQODkYOBzUR0k79V+pb1irdGWvE3gD4s+L9LGm6zrXh6a2EglCruQhhnByIvc1694ds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None.
6
APhO_2025_1_D_1
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$. (C.1) Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$. It can be shown that the torque acting on the excess regions is equivalent to the torque acting on two point masses, each with a mass equal to $2m / 5$, positioned at the endpoints $A$ and $B$ of the polar diameter (see Figure C.1). (C.2) Given this idea, find the torque $\tau$ exerted by the Sun ring on the Earth. Express your answer in terms of $M_{E}, M_{S}, d_{SE}, R$ (the average radius), $h_{\max}$ and the angle $\alpha$. You can use that $h_{\max} \ll R$. [Part D: Angular speed of the precession of the Earth's axis] The Earth's axis of rotation moves very slowly around the $z$ axis in a conical motion. That is, it precesses.
Give an expression for the period $T_{1}$ of precession of the Earth's axis. Express your answer in terms of $M_{S}, d_{SE}$, the angular speed $\omega$ of the Earth's rotation, $h_{\text{max}}, R$ and $\alpha$.
[["Award 0.2 pt if the answer applies Newton's second law for rotational motion, $\\vec{\\tau} = \\dfrac{d \\vec{L}}{dt}$, where $\\tau$ is torque and $\\vec{L}$ is angular momentum. Otherwise, award 0 pt.", "Award 0.2 pt if the answer expresses angular momentum as $|\\vec{L}| = I \\omega$, where $I$ is the moment of inertia and $\\omega$ is the angular velocity of Earth's rotation. Otherwise, award 0 pt.", "Award 0.2 pt if the answer writes the correct moment of inertia for a uniform sphere as $I = \\frac{2}{5} M_E R^2$. Partial points: award 0.1 pt if the prefactor is wrong but dimensions are correct; award 0 pt if there is a dimensional error. Otherwise, award 0 pt.", "Award 0.8 pt if the answer correctly relates the time derivative of angular momentum to precession angular speed: $| \\frac{d \\vec{L}}{dt} | = \\Omega_1 |\\vec{L}| \\sin \\alpha$, where $\\Omega_1$ is the angular speed of precession and $\\alpha$ is the half-apex angle. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses the relation $\\Omega_1 = \\dfrac{2\\pi}{T_1}$ between precession angular velocity and precession period. Otherwise, award 0 pt.", "Award 0.3 pt if the answer finds the correct precession period $T_1 = \\dfrac{4 \\pi}{3} \\dfrac{d_{SE}^3 R \\omega}{G M_S h_{\\max} \\cos \\alpha}$. Otherwise, award 0 pt."]]
["\\boxed{$T_1 = \\frac{4 \\pi}{3} \\cdot \\frac{d_{SE}^3 R \\omega}{G M_S h_{\\max} \\cos \\alpha}$}"]
["Expression"]
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[1.8]
text+variable figure
Mechanics
APhO_2025
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None.
7
APhO_2025_1_D_2
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$. (C.1) Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$. It can be shown that the torque acting on the excess regions is equivalent to the torque acting on two point masses, each with a mass equal to $2m / 5$, positioned at the endpoints $A$ and $B$ of the polar diameter (see Figure C.1). (C.2) Given this idea, find the torque $\tau$ exerted by the Sun ring on the Earth. Express your answer in terms of $M_{E}, M_{S}, d_{SE}, R$ (the average radius), $h_{\max}$ and the angle $\alpha$. You can use that $h_{\max} \ll R$. [Part D: Angular speed of the precession of the Earth's axis] The Earth's axis of rotation moves very slowly around the $z$ axis in a conical motion. That is, it precesses. (D.1) Give an expression for the period $T_{1}$ of precession of the Earth's axis. Express your answer in terms of $M_{S}, d_{SE}$, the angular speed $\omega$ of the Earth's rotation, $h_{\text{max}}, R$ and $\alpha$.
Calculate the precession period $T_{1}$ in years.
[["Award 0.2 pt if the answer gives the correct numerical result for the precession period as $T_1 \\approx 80600$ years, obtained by correctly substituting the given data into a dimensionally correct formula. Partial points: award 0 pt if the substitution is incorrect or if the formula used has a dimensional error."]]
["\\boxed{80600}"]
["Numerical Value"]
["years"]
[0.2]
text+variable figure
Mechanics
APhO_2025
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WZr3iHSvDOmPqOsXsdrbKcbmySx9AByT7CtEOpQOGBQjO7PGPWvn34x69ouuePfC+mPqtrPpUEoa98uYMkeXAbcR0+UfrS6qK6j0s5PoeleH/AIu+EfE2sw6Vp13cm7mJESvbOA2BnrjjgHriu6rmfDuo+DdXn/4p59Knms1HNrGu6JTxwQOM8iulJCgkkADkk1TJQtFeP+JPitZwfFPQ9Nstdt00WFXOoyo6tGzEHClvbA6etekaL4r0HxFJLHo+q2168KhpFhfdtB6E0lqrob0dmV/DXjTRfFk19DpM8kr2LhJw8RTaSSOM9ehroK8I+B9/aaZdeNby/uoba2jukLyzOFVfmk6k16XafE7wTe3a2sHiSxMrHaoZygJ+rAD9aFql5pA9G/JnWUUAggEHIPQis3WfEGkeHbUXOsajb2UJOFaZwNx9AOp/CjYDSorm9F8f+FPEN2LTStdtLi4P3YtxRm+gYAn8K6SgArD8TeL9C8IWSXWt36WyyHEaYLPIf9lRya2ZZY4ImllkWONBlnc4AHqTXzv4r13w7r3x706TU9SsrjQLKEAyGQPDuCs2Ceh+bGfpS3kkPZNnrHhv4p+FPFV1NbadeyCWGJp5PPhaNVRerFiMAD3NdNper6drdkLzS72C8tiSolhcMuR1HHesCGXwX4i0DVJrGXT5LE27293c2qqpSMrlgWA445pnw30jw1o3hg2/ha/a/sGnZmuGkDlnwMjIAHAx2qur9CTr6Ky9b8SaL4bt1n1nUreyjY4XzXwW+g6n8Kp6H458MeJJmh0nWrW5mUbjEGKvjudrYJFIZ0FFZ+ka5pmv2r3OlXsN5AjmNniOQGHUfqKYPEWjnXjoY1G3/tQLu+y7vnxjOcfTmgDToorL0zxHo+s3d1a6bqNvdT2jbZ44myYzkjB9OQfyoA1KKz7rXdKstVtdLub6GK+uhmCBmw0n0H4Vlan8QfCej6l/Z19rtpFebgphBLspPY7QcH60bgdLRUN1eW1jaSXV3cRQW8Y3PLK4VVHqSelctB8UvA9zdi1i8S2Xmk7RuJVSf94gD9aOtg6XOuZlRC7sFVRkknAAqK2u7a8jMlrcRTxg43ROGGfTIqQFZEyCGRh16givE9Kdvhl8a5NDQlNB8QYkgj/hikOcY/4FlfoR6ULWXL3/ADB/Dzdj26iiigAorB1zxt4a8NSiLWNZtLWYjPlM+Xx67Rk/pTtC8ZeHPEzsmjaxa3cijJjR8OB67Tg4/Cha7A9Nzcopk00dvBJPM4SKNS7seigDJNY58Y+HBog1k61ZDTSxQXBlAVmHUD1PsKANuiuX0v4j+DtZvEs7DxBZyXDnCRsxQsfQbgMn6V1FABRRRQAUUUUAFfO/xm8RWVt8XPD636yyWOlLHPMkIBYkvuIAJAzhV719EV4Z4HjTxN8fvFOsSKJYLJXhj3DIzkRj9FakrupG3S7+4b0g79dPvNQftG+DycDTtc/78Rf/AB2rHx11oRfC5I0Dxtqc0SBG4YL98g4+gFeofY7X/n2h/wC+BXi/xlJ134heDfC6cq8wllUejOB/JWoaUmo92gT5by7JnYvqKfDj4NW1yyDzbKwjVEP8UzAYH/fRrjvhZ8ObTxFp7+MfF8P9qX2pO0kUdz8yqmcbiOhJ7dgMVpftEPJH8PLWOMERtfxh8egVsfrXonhZbe28G6OImRbeOxhw2eANg5qk+Zzm+9v1JtyqMPK/6Hgfxe8LWuieLdL0bw8n2O01zyxcWcJxGzq+1W29vvdvSvV/itep4f8AhLqUUJ27oEs4gPRsL/6DmvNodZh+If7RWny2rebp2mZ8ph0YRgnd9C5/LFb/AO0TdO2iaFpKNgXl6Wb/AICMD/0Oos3SUf5n+Fy7pVW+y/Gx2Hwh0r+yfhho0RXDzxm4f6uSw/QiuJ+I3/FQ/HHwhoA+aK123Eq/8CLn9EH516+jWegaChnlSCzsrcBnc4Coq4z+leIfDC/Pjf42a74oKnyIIGEAb+FSQifjtB/OtG+asmul392xmlak79dPvOx+PGq/2d8M7iBWw97PHAPcZ3H9FrM+HvwsstQ8O6fq3i+D+0Lt7ZEtrWUkR20IHygKOrEcnPrVH43Mda8YeDvCycie482RfZmCj9A1e2IixoqKAFUYAHYVMPhcu7/Iqe6j2X5nn3xG8Q2/w2+HflaLDHbTSH7LYxoOIycksB7DJ+uK5vwn4J8FeHPDC6t40n0671S7Tz7mTUJVfYW52qpPJ55OMk1S/aJQST+FUuCy2LXEglYduUz+ma6rTvgb4CtnjuPsM94uAyie5YqfQ4XGaUbtOXd2HKysvmcr8DLVZPF/irU9Ihlh8OyP5dsrZAJ3krjPoufpkV7pVeysbTTrOO0sbaK3tohtSKJAqqPYCrFU9kl0J6t9zyf9oPVPsfw9jsVPz312keB3Vcsf1ArB0Tx5448M+FbLTYfhrfNBZW6xiU+Yd2ByxATv1qX4vZ1/4o+DfDKncgkE0q+zOM/+Ooa9w4VewAH5VMfgb7v8tCpfEl2X5nhPgq1PxW8XxeJvEWr2byaWQYdFt0ZTAQcgvuAyM9cZyQOR0r3evA/DE0Op/tL6peaIQ1gkb/aJIvuMdgVjxwcvXukF/Z3U0sNvdwTSwnEqRyBmQ+jAdPxqlrCNuupL+J3LFeMftC3jzaXoOgQn97f3u7aO+0bR+r/pXs9eH+LP+Kj/AGjfD+lj5odMiWVx6EZkP/stTa84xff8tSr2jKS7f8A9n0+zTT9NtbKMYS3hSJfooA/pVmiq8F/Z3U0sNvdwTSwnEqRyBmQ+jAdPxqm7u5KVlYsUUUUhnz38WNQu9K+OGgX1hYSX91BbRvFax53Snc/AwCf0roP+Fr+Pf+iXan+Uv/xuqPjj/k4/wn/1yi/9Ckr3KlD+H83+Y5/H8l+RheF9TvfEfhiK71nRn02efektlODlVyRyGAPI56d68khaT4J/EZopS/8AwiGtNlW5It3/APsc/ip9q94rw74h39x8TfGlt4A0Nl+x2knnahebdwRhwcH2zj3Jx2obfOuXf9BWXK+bb9eg3w/aTfGD4hyeJtQjYeGdJfy7GBxxMwOeR+TH8BXQ/tAf8kxf/r8h/rWb8J9euPDGr3Xw318JFd2js1jLjAmQ84Hrn7w/Edq0v2gP+SYv/wBfkP8AWlUsoRUdtPzKhdzd99fyIPh98MtD1DwrY614ktBq2qX8CStJdMWCIR8iqM4GFxXJfEDw/D8JvGGieKfDIe1s7iYx3FqHJXjBK89mXPHYivXvhxqEOp/DrQbiBwwFnHE2D0ZBtI/MV5v+0TdpdW3h/QoCHvZ7oyiNeTjG0fmW/StKmlRcvf8Ar8DOnZw97sd38U5Fm+E+uyocq9oGB9iy1X+DH/JKNF/3ZP8A0Y1SfEuE23we1iAnJjslQ/gVFZPw41J9H+AtvqUab3tLS4mVT3Ks5H8qltR530Vv1Gk5KC66/ob978PfBTa1d69qml2ktzdMGke7bMYIGOFPy849K8k+L+meGvDt3oeveE2sLW+jutskdhIoHHzK21Tx0I981d+G/gm1+J2n3PinxjfXepzPctFHb+eyJGBg9uR14AwMVlfG3wn4S8JWWj2+h6fFaX085dwsruxjAxzuY8ZP6UJOLjfuik1K/wAz174pP5nwn11z1a0B/wDHlrg/g78PdJ1zwlba94itxqc0m6G1iuSWjhiRiAAvTk5Nd18Tv+SRa1/15r/Nah+DH/JKNF/3ZP8A0Y1NK0p/L9SLtwj8/wAkeffGvwXo/hTTdM8S+HbRNMvIbxYyLb5VPBYNjoCCvb1r3PS7pr7SLK7cYaeBJD9SoP8AWvL/ANoj/kndv/2EI/8A0F63/EniC68MfBsatZAfaotPgWJiMhWYKu78M5qVK0JX6P8AQtxvOKXVfqTL8OfAOlXNxe3ek6e0tzK0rvfEOuSckKH4A+gry3xPZ6J4V+MvhS+8Jy2sUd5MkdxDZyAoMuFIwDxlW6e1bXw++F2i+LfDdp4n8VT3esX9/ukPm3LhUG4jHykEnj1/Cud8daB4b8NfFnwhpvh+zitXFzDJcojsxyZV253E84B/OriuWpCL7kyfNTk12O2+POhaU/gW81prCA6mjwxrdFfnC7xxn05NaXgDwJ4VuPBegalNoNi961rFKZzENxfAO7Prmk+OwJ+FV/gdJoSf++xXQ/Dd1f4b+HmVgR9hjGR7Cpp/DL1X5DnvH0f5nnf7Rf8AyC/Dn/X63/oIrsPir4nuPCvw4uLuycx3k+y2hcdULdWHuADXH/tF/wDIL8Of9frf+gitn47abNf/AAu82FS32OeKdwP7uCpP4bqiX8N+v+RS/iR9P1ZH8N/hV4di8JWWo6zpkGpalfxC4lku18zbuGQADx0PXrmuY+Jnhy3+GGtaR4y8KxmxQ3Hk3NtGT5bcZxjsCAQR06V618P9Vt9Z8BaLd2zqy/ZI43AP3XVQrA/iK88/aI1CN/D2k6HEQ97d3gkSJeW2gFenuWArSreM/d7/ANfgRStKPvdjrviZdJe/B/WbuL/Vz2SyL9CVI/nXD/B34e6TrnhK217xFbjU5pN0NrFcktHDEjEABenJya7Hx9aNYfBDULN/v2+mxxN9V2j+lP8Agx/ySjRf92T/ANGNRZKU7eX6iu3CN/P8keffGvwXo/hTTdM8S+HbRNMvIbxYyLb5VPBYNjoCCvb1r3PS7pr3SLK7cYaeBJD9SoP9a8v/AGiP+Sd2/wD2EI//AEF69I8Of8ixpP8A15w/+gClB+7Jdn+hU/ij6fqaZOBk18/eEtLh+LnxJ1zW9f3XOl6a/lWtoWITBJCg47YUk+pNfQDDcpHqMV4b8CpF0TxR4r8M3ZEd6k4dEbgsFLA4/NT+NEfj+TsEvg+aOu8XfCHwrq/h66j0/SLbT7+OMtbz2qbCHAyAQOCD05rO+DeuN4z+H91pOuKLxrN/ssom+bzYiMqG9e4/CvSNZ1K30fRb3UbuRY4LeFpHZj6Dp/SvJv2dLGZPDus6nIhWO8vAI899oOSPxbH4UR1cl0svzCW0X5/oc/deFNAT9oy20RdJtRpbW242vl/uyfKJzj6817ro3h/SPD1vJBpGnwWUUjb3SFdoZsYzXkV5/wAnU2n/AF6D/wBEtXt9EfgXz/Nifxv5fkQXtlbajZTWd5Ck9tMpSSJxlWU9Qa+fvD3hTQbn9oHXtGn0m1k02GBjHatH8iHEfIH4n86+iK8O8MsE/ae8QqxwWt22g9/ljNEP4nyY5fA/VHr2jeHtI8PQSQ6Pp1vZRStvdYV2hjjGTXzx8KvB1r4v8X68urb5tKsrgytahiqSylmClsdQAG/OvpqvEPgD/wAhbxl/19p/6FJRHWd32f6BLSGndfqdB4/+F3hOXwTqk9lo1rY3drbPPDNbpsIKAnBx1Bxjml+EfiKV/g6moX8jSf2csy7mOSUj5A/AcfhXZ+Mv+RI13/sHz/8AoBrzP4SWMmpfAnU7GLmS4+1xIPcrgVN2lO3ZP5lWV4X7nP8Aw1s/DvjC/wBV8XeOL7T7i8nuCkFre3ChUUAHOxjyOQB24NHxW03wv4dTTfFHgq80601K1uVV4tPnTDAgkNsU8cjB9Qeah+DXgjwZ4u0K9h1vTfP1ezuCJAbmWNvLIGPlVgOoYdK9M/4Uh8Pf+gC3/gZP/wDF1cla3LpaxCd738zs9F1AatoVhqIG37VbxzY9Nyg/1q9VewsbfTNPt7G0j8u2t41iiTcTtUDAGTyeKsUSs27BG6SufNll4bHi34+eI9Juppl0wzPPeRRuV85UI2qSO24ivW9V+E3gu+0aezj0GztnMZEc8KbZEbHB3dT+Oa4jwF/ycP4x/wByT/0NK9tk/wBW30NR/wAuY+hV/wB7L1PH/wBnnUbmfwrqemzyM8dhd7Ysn7qsMkD2yCfxrG1C2PxT+OF1ouoyyHQtEVs26sQHK4B6dyx6+gq/+zt/x4+Jf+v1f5Gq/gx18OftD+JdPvT5bakHe3ZuN+5hIAPwz+VXvUjftf52RL0hK3f8Lnfap8JfBWpaVJZLoVpasUwk9umyRD2OR1/HNcl8Dtbv4pdb8G6lM0z6PKRAzHJCBipX6AgEfWvYJZY4InlldUjRSzMxwAB1Jrw/4LbtY+IfjLxHCp+xzSskbY4bfIWH6AfnSg/fa6Wf/AHL4L9br/gmP460ibX/ANoeLR4rmW3jvLeOK4eJsMYtmXH4gEV6z/wqnwMNP+xf8I5Z7Nu3zNp8z6787s/jXBXv/J1Nn/16D/0S1e30or92vn+bBv338vyPD/gh52i+MvF3hVZnksrOYtEGPQq5XP4jGfpXpmoeAvCWpXs19f6BYT3Mp3yzSRglj6k15r8Lv+S1+O/+ukn/AKNrY+Lfi28L23gfw4TJreq4SUoeYYj1yexIz9Bk0XbhB7todkpzWyTOHi8LaH8RviabHw9pVtZeGdIP+lXNvHt+0NnoD7kYHsCa7f46eJLnQPB9ppOnSmCbU5fILq2CsSgbgD2zkD6ZrtfBPhGz8FeGbfSbQBnUb55scyyHqx/kPYCvMv2jLBn03QNSeIyWtvcvHMB6MFI+mdpFE7JKHS+v9f1oENW5eWhueH/B3wu0rQILK6k8P3twYx59xcXEbu745IJPy89MYrlfh7dQeEvjVqHhbSL5bnQb9DJAElEiq2zeMEHqPmX8q7LTvhB8NNV022v7TRvNt7iNZI3W9nIIIz/fra0P4WeDfDmrQ6ppWkmC8hz5cn2mV8ZBB4ZiOhPar2nd+ZG8LI4P9ouaW307w3PCcSx3juh/2gARXR+GvhHoI05b7xLaDV9avAJrue5Yth25IUZwAM4rnf2iv+Qf4b/6/X/kte0xf6lP90VMPhb8/wBEVJ6peX6s8X+M9/dT3/hzwBpUhtodQZFl2H+DcERfoME49hXb2Hwn8EWOmJZHw/aXAC7WmnTdI57nd1B+mK4D4vf8ST4reDvElwCLFGSOR+y7ZMn9Gz+Fe4o6yIrowZGAKsDkEetEdYXe7b/4AS0nbpZf8E8I0GJ/hh8bk8M2c0h0LWEDxwu2djEHb+IZSM9wa95rwrxLIviP9pPQrWxIk/stENwy8hSpZyD+YH1Ne60Rd6ab8/u6BLSbS8vv6nC/FfQtK1HwLq+oXlhBPd2dlKbeZ1y0Rxn5T2rk/g/4I8Ma18OLC+1PQ7K6unklDSyxgsQHIHNd78SQT8NfEQAyfsMn8qwPgU6t8KrAKwJWaYHHY7zRD7XovzYT2j6v8jnfjTqN5d6l4d8BaZKbePUnXztnHybgqr9BgnHsK7aw+E/gix0xLI+H7S4AXa006bpHPc7uoP0xXAfF7/iSfFbwd4kuARYoyRyP2XbJk/o2fwr3FHWRFdGDIwBVgcgj1ojrC73bf/ACXx26WX/BPCNBif4YfG5PDNnNIdC1hA8cLtnYxB2/iGUjPcGrn7Rc0tvp3hueE4ljvHdD/tAAiq/iWRfEf7SehWtiRJ/ZaIbhl5ClSzkH8wPqas/tFf8AIP8ADf8A1+v/ACWkruEL9/wvoPRTl6fjbU6Lw18I9BGnLfeJbQavrV4BNdz3LFsO3JCjOABnFUPjjr8/hzwVZaLpLGB9QkFsvlnBWJQMqPrlR9M16tF/qU/3RXin7RNvJHaeG9UClobW7dXx2J2kf+gGidm0tldCp3tfrZ/kdR4Z+DfhLS/D9vb6hpMF/etGDcTz5JLkc454A7Yry/xT4XXwf8YPC2mWU0x0eS8iubS3kcsIC0gDqM9sqDX0dY3kOoWFveW0iyQTxrIjKcggjIrw/wCKl/BP8bfBlnG4aW2lhMgH8JaUEA/gM/jV3fto+pP/AC6l6G9+0P8A8k5h/wCv+P8A9BevRPC3/Io6L/14wf8AoArz39oVGb4bxsASFvoyx9OGFd94PnjufBeiSwuHRrGHBB/2AKmG0/VfkVP4o+j/ADPKfjV/yUTwJ/18f+1Y67f4t+J7jwr8P7y7s3Md5Oy20Ljqhbqw9wAa88+MeowXHxY8HWEbq0trLG0oB+7vlXAP4Ln8a6n4/wCnTXvw2aaFSwtLuOZwOy4K5/8AHhUP+CvV/mi1/F+S/JmX8PvCfw9svClpca3caJfardxia5e9uI3ZC3O0BjxjP1zmsCGXTPAfxx0yLwvewSaNrASOe3t5xIiFiVxwT0OCPTNdP4L+F/w58TeENM1VNH82SaBfOIvJuJAMOCA/HOa6aw+D3gXTNQt7+00Ux3NvIssT/a5jtYHIOC+Dz61s9Kl30/IxWtO3f8zz/wCNDQw/EbwxN4iinl8Lqn7xUzt37juzjvjb74rvLHwd8M/Felh9N0nRrq2K432ihHX6lcMD9ea7LUdNsNYspLLUbSC7tn+9FMgZT+Brxjx18J7Pwppt34r8H6ldaRdWKGZoVlJRlB5CnqPoSQelZJqMbS2NGnJ3W57Rpun2uk6bbafZRCK2toxFEg7KBgVaJwMnpXK/DjxFd+KvAematfKBdSoyykDAZlYrux74zXUuu5GX1GKud033Ji00rHzx4ck0X4jfEnWtc8XX1r/Z1i/k2NndXCxoRkgcEjIAGT6k81o/FTw74Gj8Kyav4auNIstXsHSSL+z50VpBuAI2qeSOuevFc98LfBXhjWfE/iHw/wCKbDztStJiYFaeSMlQxDYCsM/wn8a9X/4Uh8Pf+gC3/gZP/wDF1Nvcjbsim/flfubPgLWX8V/D7S9QvlWSS5tylwGHDsCVbI98frXl8LSfBP4jNFKX/wCEQ1psq3JFu/8A9jn8VPtXtGiaHp/hzSYdL0qDyLOHPlx72fGSSeWJPUnvXj3xDv7j4m+NLbwBobL9jtJPO1C827gjDg4PtnHuTjtTk/3l49fyJivctLp/SG+H7Sb4wfEOTxNqEbDwzpL+XYwOOJmBzyPyY/gKtfHHWp7nU9C8GQXgs7fUZFe8mLBQI920ZPp94n6CpfhPr1x4Y1e6+G+vhIru0dmsZcYEyHnA9c/eH4jtWJ8btOs0+JPhfUNZhMmjTotvcfMVGFkJbkEEcPn8KGleEVtf7/X5ju/fb3X9afI7SLwj8JotHGmkaA67Nhna6jMxOPvb85zXM/BHVJNN8VeIvBq3gu9PtXaazkD7hgPtOCOMEFTx3rrk+Cfw6kjWRND3IwBVhezkEev362vDfw68LeEdQe+0TTDa3MkZiZzcSPlSQcYZiOoFNaSbYnrGyPK/jc+oJ8S/Co0mXytQeLy4H/uszlQf1r0DQ/hB4R0m0hFxpqX98CHlvLlmZ3k6luvHPpXG/FX/AJLR4F/34/8A0dXt9KnpTuu7/Mc9Z28kfPXxd8N6LYfELwlHaaZbQpf3JN0qJgTEypnd69T+de0aT4L8NaFe/bdK0Wzs7naU82GPa2D1FeV/GsiP4heBZHO1Bccseg/epXuNOGlNerCfx/JHz/rNzYeP/jZc6b4h1CKDw/oisqwzTiJJXGARkkcliffC1veOvCfw3vvCF9/ZcmhWeoW8LS20lpPGrFlGQpwfmzjHPrXIab4W0C++PPiHRPFdp5qXckk1mGmePLMQ4wVIzlSfyr1D/hSHw9/6ALf+Bk//AMXUJN0o+a/Epu1R+X5FP4U+MJ9Q+Ez6lqMjTTaWsscjscl1jXcMn1wQPwrjfhL4StPH13q3jLxVCNRlluTHDDNygOASSO4GQAOgxXqTeCdK0LwNrWieH7M20V3bzYj813y7R7erEnsK4v8AZ31GGTwZfaWWC3VpeMzxnrtYDBx9QR+FaJqVST8l/wAEzs4wS8/+GIfi58OdE0/wdea7oFlHpl5aLiUWo8tJomO1lZRx0Ofwrqfgt/ySjRvpL/6MapPjFqEFh8LtZ85wrTxiCME8szMOB+GT+FR/Bb/klGjfSX/0Y1TDaS9P1HP7PzO+r5/+OltcXvxI8KWlpM0NxPGIkkQ4KFpMZH519AV4L8Z76LTPir4NvpyBFBskcnsol5P5Ukk6kE+/6MbuoSt2PSLH4VeCbLTUsj4espwF2tNPHvkc9yWPIP0xXnHhKJ/h18c7nwnayyHR9Tj8yKJ2ztJUsp+owy57iveEdZEV0YMrDIIOQRXhV5IviD9qCzFmRImmQgTOvIBVGJ/VwKqL/eLzvf0sJpezf4eo7b/wrz9oQEfu9L8RL9FDsf6OPyavS/iL4iHhfwJqupBtswiMUH/XR/lX8s5/CuY+Ofh19V8FLq9qCL3R5RcIy9dn8X5cH/gNcV408QyfEtfAnh20fnUVW6vQv8JGVbP02yH8qhLmgqfW9vk9f8y78sud7Wv81/nodz8DfDh0TwBFezJi61RzcuT12dEH5c/8Cr0W9srbUbKazvIUntplKSROMqynqDTra3itLWK2hQJFEgRFHZQMAVLWk2pPyIiml5nzv4e8KaDc/tA69o0+k2smmwwMY7Vo/kQ4j5A/E/nXuujeHtI8PQSQ6Pp1vZRStvdYV2hjjGTXkPhlgn7T3iFWOC1u20Hv8sZr3GpX8OPp+o5fHL1/Q+ZfhV4OtfF/i/Xl1bfNpVlcGVrUMVSWUswUtjqAA3516X4/+F3hOXwTqk9lo1rY3drbPPDNbpsIKAnBx1Bxjmuf+AP/ACFvGX/X2n/oUleqeMv+RI13/sHz/wDoBqJ6UVbt+hUdarv3OV+CWq3OqfDGya7kaR7aSSAOxydqnj8gcfhXnnhyTRfiN8Sda1zxdfWv9nWL+TY2d1cLGhGSBwSMgAZPqTzXafAFd3wvC+t3MP5V538LfBXhjWfE/iHw/wCKbDztStJiYFaeSMlQxDYCsM/wn8a1lrV+V/yuZx/h/P8AzOh+Knh3wNH4Vk1fw1caRZavYOkkX9nzorSDcARtU8kdc9eK9R+HuvTeJfAekarcnNxNDiU+rqSpP4kZrE/4Uh8Pf+gC3/gZP/8AF12OiaHp/hzSYdL0qDyLOHPlx72fGSSeWJPUnvSWiaG9WmaFeH+IvBni7wL40vPF3giIX1reMXurDG48nLDb1YZ5G3kV7hR1qba3W5XSzPKfDPx00XU7xdN1+0n0PUMhCJ+Yt3oWwCv4j8a7vxcQ3gnW2BBBsJiCO/yGuM+OGhaLeeAL7U72GFL+1Cm2uMAPuLAbM9wRnineEpb2+/Z+U3W9520qdFLdWUBwv6AVM3enLy/yHDScfMq/s9/8k1b/AK/pf5LV347f8kqv/wDrtD/6GKzv2eJ45Ph3PCrgyRX0m9c8jKqRU37QGowWvw3a0d1E13cxrGmeTtO4n8MfrV1+ny/Qmh/n+p1nw5/5Jv4e/wCvGL+VeHfCrwfbeMPFuvR6sZJtIsbkzNabyElmZmClsdcAGvcfhz/yTfw9/wBeMX8q84+AP/IW8Zf9faf+hSVc/wCNL5/miI/wl8v1Og8f/C7wnL4J1Sey0a1sbu1tnnhmt02EFATg46g4xzVr4I6pc6p8MbE3UjSPbySW6sxydqn5R+AOPwrqvGX/ACJGu/8AYPn/APQDXEfs/wD/ACTJP+vyX+lRB6yXkvzLntF+b/I9Srw7TP8AieftQ6hLL8yaZbkRg9sIq/zc17jXhvho/wBnftOa/BLwbu3cpnvlUf8AkDRD+IvR/kEvgfy/M9g8Rf8AIsat/wBec3/oBr5/+DXgiPxtpZm1+SSfRdMmZbWyDlUeVsMzNjk4GK+gPEX/ACLGrf8AXnN/6Aa80/Z2/wCSfXX/AGEH/wDQEoh8Un5L8wn8MV5v8jtpPDOi+GvC+tR6Np0Nkk1rI0ixAgMQhANcR+zscfD68J6DUH/9ASvTfEH/ACLeqf8AXpL/AOgGvMf2dxu+Ht6PW/kH/jiUot3n6L8wltH1f5HN+DtIg+LPxL13XdfDXOm6e/l21qzHZjJCA+wCkkdya7bxz8MPD/8AwjV5qGhafFpWrWMTXFtcWY8o5UZwQODkDFcx8BZl0rxD4r8O3J8u8ScOEbgsEZlb+Y/OvWvF9/Bpng7WLy5cJFHaSZJPUlSAPxJApT0pK3b+vxKjrVd+557+ztz8Pron/oISf+gpXH+O9Hl8QftEQ6RHcSQJdwRxzPGcN5XlkuAfdQR+Ndf+zt/yT66/7CD/APoCVm3v/J1Nn/16D/0S1azV6kb/ANe6ZRdqcvn+Z3v/AAqnwMNP+xf8I5Z7Nu3zNp8z67/vZ/GvP/gosmleLfGHhFpWmsLWVvLVzkcOUP5jGfpXuVeI/C7/AJLX47/66Sf+jaiOtS3dMuWkL9mjF13wpoNv+0Louiw6Tappk1urSWoj+Rjtk5I/AflXuGjeFdB8OyyyaPpVrZPKAsjQptLAdAa8m8TMI/2nvD7Odoa2QAnudsgr3GnH4E/N/mEvjfogr578bSaXb/HtJfHMTyaE1uotPMVjEPlHJA6jduz74zX0JWbrWgaT4jsjZ6vYQXkGeFlXJU+oPUH3FT1T7D6NdzmB8P8A4deJdPSez0fSprdsFZrDCfqhH5GpvikixfCrXo0UKi2m1VHQAEV5j488Av8AC22Hi3wdrF1ZJHMiS2kkm5WycAD+8PZs/Wu98Z6m+tfAm+1SSPy5LvTEmZB2LbSaU9acmhw0qRTI/hVfJpnwTsb+QZS2t55mHqFdz/SuI+EvhK08fXereMvFUI1GWW5McMM3KA4BJI7gZAA6DFdb8PLOTUf2f0sohmS4srqNQO5JcCqH7O+owyeDL7SywW6tLxmeM9drAYOPqCPwrV/xZ+S/UyX8OPmyH4ufDnRNP8HXmu6BZR6ZeWi4lFqPLSaJjtZWUcdDn8K6j4LnHwn0YnpiX/0Y1S/GLUILD4Xaz5zhWnjEEYJ5ZmYcD8Mn8Kh+DK7vhLo6+qyj/wAiNWcW+WdvL9S5bx+Z5v4ck0X4jfEnWtc8XX1r/Z1i/k2NndXCxoRkgcEjIAGT6k81o/FTw74Gj8Kyav4auNIstXsHSSL+z50VpBuAI2qeSOuevFc98LfBXhjWfE/iHw/4psPO1K0mJgVp5IyVDENgKwz/AAn8a9X/AOFIfD3/AKALf+Bk/wD8XRb3I27Ibfvyv3Nv4e69N4l8B6Rqtyc3E0OJT6upKk/iRmumrP0TQ9P8OaTDpelQeRZw58uPez4ySTyxJ6k960KuTTbaIimlZngmoWx+KfxwutF1GWQ6Foitm3ViA5XAPTuWPX0Fei6p8JfBWpaVJZLoVpasUwk9umyRD2OR1/HNcD4MdfDn7Q/iXT70+W2pB3t2bjfuYSAD8M/lXuMsscETyyuqRopZmY4AA6k1CS9lG/Va+pbb9pL8PQ8d+COsXude8E6rIbg6VIyRFzn93uKsv0yBj61zvxF8KaBpnxX8HadZaTawWd26CeFI8LJmTByO/FanwW3ax8Q/GXiOFT9jmlZI2xw2+QsP0A/OpPip/wAlo8C/78f/AKNqo3cqTlu7X/EmWkaiWyvb8D1jRfCuheHZJX0fSrWyaYASGBNu4DpmtWRFljaN1DIwKsD3Bp1FJ67j2PnfXfCmg2/7Qui6LDpNqmmTW6tJaiP5GO2Tkj8B+Ve4aN4V0Hw7JLJo+lWtk8qhZGhTaWA6A15N4mYR/tPeH2c7Q1sgBPc7ZBXuNC/hp+v5hL4/kj5l+FXg618X+L9eXVt82lWVwZWtQxVJZSzBS2OoADfnXpfj/wCF3hOXwTqk9lo1rY3drbPPDNbpsIKAnBx1Bxjmuf8AgD/yFvGX/X2n/oUleqeMv+RI13/sHz/+gGonpRVu36FR1qu/c5X4Jarc6p8MbJruRpHtpJIA7HJ2qePyBx+FeeeHJNF+I3xJ1rXPF19a/wBnWL+TY2d1cLGhGSBwSMgAZPqTzXafAFd3wvC+t3MP5V538LfBXhjWfE/iHw/4psPO1K0mJgVp5IyVDENgKwz/AAn8a1lrV+V/yuZx/h/P/M6H4qeHfA0fhWTV/DVxpFlq9g6SRf2fOitINwBG1TyR1z14r1H4e69N4l8B6Rqtyc3E0OJT6upKk/iRmsT/AIUh8Pf+gC3/AIGT/wDxddjomh6f4c0mHS9Kg8izhz5ce9nxkknliT1J70lomhvVplm9srbUbKazvIEntplKSROMqynsa+f7rwpoCftGW2iLpNqNLa23G18v92T5ROcfXmvoevELz/k6m0/69B/6JalH418/yY5fA/66o9D1jw/pHh7wF4gg0jT4LKKSynd0hXaGbyyM1y37Pxx8MsnoL2X+S13fjD/kStc/68J//QDXCfs/jd8MSPW8mH6LSi3efovzCW0fV/kcj4O0iD4s/EvXdd18Nc6bp7+XbWrMdmMkID7AKSR3JrtvHPww8P8A/CNXmoaFp8WlatYxNcW1xZjyjlRnBA4OQMVzHwFmXSvEPivw7cny7xJw4RuCwRmVv5j869a8X38GmeDtYvLlwkUdpJkk9SVIA/EkClPSkrdv6/EqOtV37nnv7O3Pw+uif+ghJ/6ClZcf/J1cn/Xr/wC0K0/2dv8Akn11/wBhB/8A0BKynkW1/aqUzEIJrbahPG4mDA/ka1l/Fj6f+2mUf4cvX/249yrw/wCCX/I/+Ov+vk/+jZK9tmmjt4JJ5nVIo1LuzHAUDkk14V8BLtL/AMXeMbyP/VzyLKv0aRyP51EPj+T/AELl8HzRF8bn1BPiX4VGky+VqDxeXA/91mcqD+tegaH8IPCOk2kIuNNS/vgQ8t5cszO8nUt1459K434q/wDJaPAv+/H/AOjq9vop6U7ru/zCes7eSPCfidqEfir4q6V4LvdQWy0S2CzXjNKI1ZiC3JPHTAHuxrp9V8H/AAqv9Cl0+FvD9q5jKxXENzGJUbHB3ZyefXOa4XxpomkSftDwReJrfzNK1SJNpaRoxu2bF+ZSD95R3716P/wpD4e/9AFv/Ayf/wCLqYq9P1v9/wDwBt2n6WMH9n/xBd6h4c1HRbuYzf2XMEhcnP7ts4GfQFTj61U/aHgNtY+Hdbi+We0vSqsOvIDD9Ur0rwx4I8PeDvtP9hWBtftO3zczSSbtucfeY46npXnH7Rs4PhjRrJeZZ77cq9zhSP5sKqbbcWt7oILdPbU9itJxc2cE46Sxq/5jNY/jXXm8M+DNV1hADLbQExg9N54X9SK1dOhNvplpA3WOFEP4KBXMfFPTZtW+GeuWtupeXyPMVR1OxgxH5LSraKVgo68t/I4P4S/DzStd8PnxX4mtl1XUdSleQG6+dVUMRnB4JJB6+1RfFrwFp3hfSIfGHhWAaVf6fMhcW3yoyk4zjoCCR06gnNdb8EdVt9R+GOnQxOplsi8EyA8qdxIz9QRUHx11W3sPhneWsjqJr6SOKJM8thgxP4AU63uv3elrCpe98XW9zoLXW/8AhI/ha2sbQrXelySOo6BthDD8wa8e+B/gbT/FOl3Gpa+jXtnZzGG0tJGPlKxAZ2I79Vr0/wAL6dNpXwRt7S4UrKukyOynqNys2P1rn/2dv+SfXX/YQf8A9ASqslVn5L9Sbv2cP66FT4w/Dnw3Y+BrnWdJ0yDT72xZHDWy7A6lgpBA475z14r0P4e6ncax8P8AQ766cvPLar5jnqxHGT9cVk/GX/klGuf7kf8A6MWrPwn/AOSW+H/+vb/2Y1MHpJea/JlS3i/X9DsqKKKACiiigBrhjGwQgMQcE9jXD/Dj4ev4FTVXuNQW+udQmEryrFswBnjqe5JruqKFo7g9VYK4ef4d/avinD41uNU3iCLy4rL7P935Sud+71JP3e9dxRR1uHSxi+K/DFj4w8O3OjahuEU2CsifejYchh9K840z4Oa3BarpWq+Ob6fw9H/y5Qgx7067SSxwvtzXX+OrDxrcNYXfg3Uba3lg3ie3ufuzg4x1BGRg+nXrXFX+n/GnxLaPpV42kaXazDZNcQONxU9ehY/likuttxvpcpfBezttQ+IPirXLOBI7CDFpaBB8qpu4A/4Ci/nXovxC8AWfj/RYrOa5e0ubdzJb3Cru2EjBBHGQfqOlW/A/g6y8D+G4tJtGMrZMk87DBlkPU47DsB6CukqpJWUe39fmTFu7l3PK9L+E+q3Eluni/wAXXmtWFswMdgNyxOR035JLD2/Wuh8CeAE8F3OtXP24Xcup3HnEiDyhGuSQoG45+8fSuzoouFjiL34eC/8AihaeM7jVCy2kYjisvI4GFIzv3erE9K7eiiktFYe7uc/4x8H6Z420F9K1IMq7t8U0f34nHRh/h3rz21+E/jayt1062+JF3FpifKipE29U9B8/H4GvYqKVh3Mbwr4ej8LeH7fSY7ue78oszT3By7szFiT+JrZooqm76slKx5X4v+EF/wCJvGkniW18XTaXPsVIRBanfEAuOHEinnnsOtUH+CWt3imHVPiTrV5bNw0RV8MP+BSsP0r2OipSsrFN3dzmPCvgPRfBmkTWOjRPHJOuJbqQ7pXOOCT7egwK5v4Y/C2fwHqOp395qi3s92ojXYhUBc5yc9STXpdFVfW5NtLBXD6N8O/7M+JGqeMZ9U+1S3qMkdv9n2eSDt/i3HPC46Cu4opLR3G9VYZMhlgkjVyhZSoYdVyOteb/AAx+Fs/gPUdTv7zVFvZ7tRGuxCoC5zk56kmvS6KFo7oHqrBRRRQB5n49+E8/jPxRba7a+JJNKnt4FiTyrYuwILHcGEikferF/wCFK+Jv+io6v/36k/8Aj9ezUUkraIbd9WcboPg7WtD8G3ui/wDCVz3d/O7NHqVxAztCGAGApkOcYOPm6npTvh98P7PwFpc8Edyb29uZC9xePHsaT0GMnAH16kmuwoqr63JtpY4fx78N4PGdzp+oW2otpWrWLhoryOLzDtBzgjcvQ8g5459a5/46pPF8JUjuplnuFuYBJKsewO3OSFycZ9MmvWK4T4ueGdU8WeB20zSIVmujcxybWkCDaM55NZzXu2XdfmXH4rvscjovw01yLQNO1Lwb4ruNGW+tIprizdS8RkKDLL6Z+n41s+E/hE2neJB4l8T61Lrerod0RdSEjPY8kkkdugHpXd+GbKfTfC2k2N0oS4t7SKKRQQcMqgEZHXmtWtpO020ZRV4JMxvFmg/8JR4W1DRPtP2b7ZH5fneXv2cg525GenrVbwn4Ti8NeC7bw3PcC+iiR43kMWwSKxJI25OOuOtdFRUW38y+3keOxfBjWtBvrhvCPja60uxuG3NbtGW2/iGAP1wDVm/+BtnqejSR32vXd1rcsySyarcx+Y+Fz8iqW4Xn1r1mihaAYfifw7/wkfhC90H7V9n+0wiLz/L37cEc7cjPT1pvgzw1/wAIh4UstD+1/a/soYed5fl7ssW+7k46+tb1FHfzFbRLscl8RPBH/CfeHY9J/tH7DsuFn83yfNzgEYxuX19a1p/DtnfeFB4evx9otWtVtpCBtLAKBkeh4zWvRSsrNdyr6p9jxyx+DvijQt9noPxBu7LS2YsIvJJZM9cYbGfcYrS/4UnpqXOjXsWqXDahY3gu7m8uE82S8OVOGO4bR8vHXGa9Roqk2nclq5m6/odn4k0K70jUFLW10mxtpwR3BHuDg15lovwk8VaBLHaad4/uodISUOLdYSDjOSPvYGfb8q9fopLR3Q3qrM4n4i/D7/hP7XToP7U+wfYpjLu+z+bvyAMfeXHT3rsJrSG5sntLmNZoJIzHIjjIZSMEEVNRR0sHW55E/wAG9V0S9nl8F+MbzSLWdtzWjqXUH2IPP4jPvWl4W+EcOl6+viHxFrFxr2sIcxyTghIz2IBJJI7c4HpXpdFC0B6mN4s0H/hKPC2oaJ9p+zfbI/L87y9+zkHO3Iz09ai8GeGv+EQ8KWWh/a/tf2UMPO8vy92WLfdycdfWt6ihaX8wepyXxE8Ef8J94dj0n+0fsOy4WfzfJ83OARjG5fX1rpNOtP7P0y0st/mfZ4Ui34xu2gDOO3SrNFC0vbqD1t5BXn/jX4WWXijVI9b0/ULjRtciAxeW38WOm4Ag57ZBH416BRSsO549J8HvEeuvHB4r8d3l/p6MGNtEhXfj1JOPxwa9V0rSrLRNLt9N06BYLS3QJHGvYf1PvVyiqvpYm2tziJvh55vxUh8b/wBqY8uHyvsf2fr8hXO/d75+7Xb0UUulh9bhXmvjb4UN4i8RxeJdE1qXRtZQANKikh8DAPBBBxx3yO1elUUra3C/Q5fwX4e1zQLS6XXfEc2tXEzhld0KiIAdByev4VQ8AfDz/hBrvWZ/7U+2/wBpSiXb9n8vy8Fjj7xz9726V29FVfW4raWKOs6d/a+iX+m+b5X2u3eDzNu7buUjOMjPX1rE+H/g3/hBfDA0b7f9uxM8vneT5X3scY3N6etdTRSWjbXUb1t5Hl/ib4PR32vv4g8Ma1caBqshLSGEEo5PU8EEZ79QfSqI+FfjTU2EWvfES9ls8/PDbqw3j0PIH5g169RQtNgeo1F2IqjooxTqKKASscPoHw8/sP4iaz4s/tTz/wC0lYfZfs+3y8sD9/cc9PQV27DcpHqMUtFK3uqPRB1b7nE/Dv4ff8IDBqcX9qfb/ts4lz9n8rZgHj7zZ6+1P8dfDfS/HCwXEk0tjqlt/qL63++vOcEdxnnqCPWuzopvUE7XPHZvhJ4w1WH7BrXxFvLjTDw8SRtukX0OW/nmvSvDPhnTPCWiRaVpUPl28fJLHLSMerMe5NbFFO4rHDzfDzzvipD43/tTHlxeV9j+z9fkK537vfP3a7iiil0sPrc4jwt8Pf8AhGvGuu+Iv7U+0/2qzN9n+z7PKy+77247vToK5e6+C2rv4sv/ABFY+OriyvLuR23pZZdFY/d3eaOAMDt0r1+ikla1umg73v56nlX/AArDxt/0VbU//AQ//Ha9A1DQbPWfDraLq6/bYJIVjlZ+C5A+97HIzWrRTeqsLZ3PG4fg/wCKdAZ4PCvjy6s9PZiy28yE7PyOPxAFdR4L8A6r4f1mXWNb8VXutXkkJhCS5EcYJB4BY+nbFd5RTTsDVzifiL8Pv+E/t9Ni/tT7B9imMufs/m78gcfeXHT3rtUXairnOBilopLRWB66mN4n8L6X4u0SXStWhMkDncrKcPGw6Mp7GvNovhL4y06D+z9J+I15Bpg+VI2jbdGvoMN/LFexUUrDucb4E+G+leBYp5YJZbzUbn/X3s/325zgDsM8989zXZUUVTdyUrEN5aQX9lPZ3MYkgnjaORD/ABKRgivILT4M+IdAuLiLwz47utO02Z9xhMRLL+TAE+/Fey0VNtbjvpYwNc8I6d4m8MLoetb7pAijz84kDgY8wHnB/Pr3rzyL4S+MtOg/s/SfiNeQaYPlSNo23Rr6DDfyxXsVFPq33DpY43wJ8N9K8CxTywSy3mo3P+vvZ/vtznAHYZ5757mo/iL8Pv8AhP7fTYv7U+wfYpjLn7P5u/IHH3lx0967aihu9vIFoIi7UVc5wMVl+IvD2n+KdDuNI1OIyW045wcMpHRlPYg1q0Umr7gtNjxux+FHjfQUNhoXxAkt9L3HZG8JLID6DJA/AiuS8VeEoPCXxM8EwLd3F9eXN2k13e3DZkmfzVGT6AAcCvpGvL/iB4M1vX/iJ4U1fT7ZJLLTpFa4dpVUqBIGOATk8DtVRdpxfmKSvCS8jvfEOgWHifQrrSNSjL21wuG2nDKeoYHsQea8tsfhB4u0NDZaH8Qrm10wsSsRhOUB9Buxn6Yr2Wiptrcd9LHkz/AyxF1pF9HrVw+o2l39qu7u5j817s5U4PzDaBt469a9Tu7S3vrSa0uokmt5kKSRuMhlPBBqaim9VboHW5483wY1jQ72aXwX4xu9Ktpm3NayAso/EHn8Rn3rZ8MfDnX7DxFa614i8Z3urS227yrbBEQJUrk5Y+vYCvSKKE7A9TgvGnw81DxFrcWtaP4ovdFvo4RCfJBKOoJIzhgf4j61zsvwh8S64FtvFHj+9vdPDAtbRRld+PUlsfmDXr9FJKwN3KelaXZ6JpVtpthCIbW2QRxoOwH8zVyiim3fVglbQ878bfCey8UaqmuabqM+ja4mP9Ktxw5HQkAg57ZB/OsP/hWHj+9H2fUviTd/ZDw4gRgzD0zuH9a9gopJW0G3cxW0S6t/CCaHpmptbTx2q20V7JF5jLgY3bcjLY9+tZPw++H9n4C0ueCO5N7e3Mhe4vHj2NJ6DGTgD69STXYUVV9W+5NtEuxw/j34bweM7nT9QttRbStWsXDRXkcXmHaDnBG5eh5Bzxz61r6/4RsvFnhldH18i5baCbiJPLZZAPvqMnb9MnriuhoqbaW6FX1ueN2/wn8b6PF9i0T4h3EOnrxHHJG2UHoOSB+GK7PwN4KvPChvbjUvEN5rV9e7PMluM4XbnAXJJ/i9a7GiquyWjh/FXw8/4SbxpoXiL+1Ps39lMp+z/Z9/m4fd97cNvp0NdxRRSWisN6u5x/xC+H1j4/0mG2uLh7S6tnL29yi7ihPUEcZBwO46VneDfBPizQdWhuNY8a3GqWcMbIloYyA2RgEkt2/GvQaKFpsD13OI8efDPS/HPk3Tzy2Gq24xDewD5gOoDDjIB5HII9a5Zfhn8RHQW0vxLuRbfd3Ij78fXcD+tewUUkrDbuY3hbQB4Z8PW2ki9nvTDuLXE/33LMWJP4muD8QfBx5PEcviDwlr8+g30xLSpGpKMT1IwRjPUjkV6rRTerv1EtFY8oHwcutXtrhvFviq71m7aB47XepEVszDG8Ju+Yj8K7jwV4Z/4RDwnZaH9r+1/Zt377y/L3ZYt93Jx19a36KdxWCuF8X/AAzsvGfirS9W1K5zaWcLxSWflZ87OcHfuG3BPoeld1RU21uO/Q8il+FHi2xjNjoPxCv7bSvupBMrM0S+gYN/LFdV4B+G+meA7ed4ZpL3Ubn/AI+LyYYZu+AOcDPPU59a7OimnYGrlbUEtpNNukvdv2VoXE27pswd2fwzXgv7P/hyKfXtW8Qrve0tS1pYtJ1+Y5J/75x/30a6DxDo/wAXfFQudFnfSdP0idyj3ETfO0WehwSenUADNekeEvDFn4Q8N2ujWOWjhGXkIwZHPLMfqaIaNy8gnso+Zt0UUUAea+NvhQ3iLxHF4l0TWpdG1lAA0qKSHwMA8EEHHHfI7V0Xgvw9rmgWl0uu+I5tauJnDK7oVEQA6Dk9fwrqKKForIHq7s4jwB8PP+EGu9Zn/tT7b/aUol2/Z/L8vBY4+8c/e9uldTrOnf2vol/pvm+V9rt3g8zbu27lIzjIz19avUUmk1yvbYadnzLc5b4f+Df+EF8MDRvt/wBuxM8vneT5X3scY3N6etYnjb4T2XijVU1zTdRn0bXEx/pVuOHI6EgEHPbIP516JRTeruxLRWR4/wD8Kw8f3o+z6l8Sbv7IeHECMGYemdw/rXqmkacukaPZ6ckryrawpCJJPvMFGMn3q5RTvpYVtbiEZBHrXjZ+EfjLSbiX/hHfiBcwWrsWWCUOAme2AxH6CvZaKm2tyr6WPHI/gxrOuXsM3jbxhdarbwtuW1i3BT+JPH4DPvXrlvZ21rZR2UEKR20cYjSJR8oUDAGPTFT0U+lhdbnj0/wW1HSNYuL/AMF+LLjRo7g5e2KFlHfGQeQO2Rx61LcfBJ9Y028bxD4nu9U1iaMRwXcyFktRuBOxN3fGOo69K9copW0sO+tzL8OaP/wj/hvTtI8/z/scCw+bs278DGcZOPzrnPAHw8/4Qa71mf8AtT7b/aUol2/Z/L8vBY4+8c/e9uldvRVNtty6k2VuXoUdZ07+19Ev9N83yvtdu8Hmbd23cpGcZGevrWJ8P/Bv/CC+GBo32/7diZ5fO8nyvvY4xub09a6miktG2uo3rbyCvEvi3az+FPH3h7x/bRs1vHItvebR2Gev1UsPwFe21R1fSLHXtKuNM1K3We0uF2yRt39wex96Wqakt0PRpp7MLhYdc0GVLedfJvrZljmUbhtdeG9+ua5/4deB/wDhAfD0ulf2j9v8y4afzfI8rGQBjG5vT1rd0PRLPw7pEGl6eJRaQAiNZJC5UZzjJ5xWjVaJtrqTq0r9CtqFr9u026s9+zz4Xi34zt3AjOO/WuZ+HXgb/hAPD82lf2j9v8y4afzfI8rGQBjG5vT1rr6KS0u11G9beR5x4z+E0HiDXV8Q6Lq0+ia2uN1xCCVkI4yQCCDjjIPPpWLf/DPVP7JvNQ8aeMbvWbaygknjtCCkO5VJDPzzj6VqeIbH4q2PiO9u/Dd/pt5pc7horS6xui4AIyQOM8/ern9W8PfF/wAb2v8AZOszaVpOmyEef9nbJdfQ4LE/TIFTZuNo/wDDFXSldml+zwjL8O7hiMBr+QqfX5VFdHN8PPO+KkPjf+1MeXF5X2P7P1+Qrnfu98/droPC3huz8J+HLTRrHJit1wXbq7HlmP1NbFaSacrrp/lYzivds+v+dwriPC3w9/4RrxrrviL+1PtP9qszfZ/s+zysvu+9uO706Cu3oqVo7lPVWOB+Ifwxt/G89nqFtqMmmavZjEVzGu7IzkAgEHg8gg8Zq34K8K+JdBurifX/ABbNrIkjEccLRlVjOc7s55PbpXZ0ULTYHruFebeJfhnrGoeJbrXfD/jK+0ee62mWBVLRkhQvZh6DqDXpNFK2tx36Hka/BzVNbuoH8ZeM73WLWF962iIUQn3OT+gz716B4k8Nx694PvPD0My2UVxAIEdY9wjAxjC5GenrW5RTeq5eglo7mB4L8Nf8Ih4TstD+1/a/swYed5fl7ssW+7k46+tcT4g+DjyeI5fEHhLX59BvpiWlSNSUYnqRgjGepHIr1Wih6vme4LRWPKB8HLrV7a4bxb4qu9Zu2geO13qRFbMwxvCbvmI/Cu48FeGf+EQ8J2Wh/a/tf2bd++8vy92WLfdycdfWt+incVjzvxt8J7LxRqqa5puoz6NriY/0q3HDkdCQCDntkH86w/8AhWHj+9H2fUviTd/ZDw4gRgzD0zuH9a9goqUraFN3KekacukaPZ6ckryrawpCJJPvMFGMn3q5RRVN3d2SlZWOM8dfDfS/HCwXEk0tjqlt/qL63++vOcEdxnnqCPWuQm+EnjDVYfsGtfEW8uNMPDxJG26RfQ5b+ea9ioqUrFNmP4Z8M6Z4S0SLStKh8u3j5JY5aRj1Zj3JrA8VfDz/AISbxpoXiL+1Ps39lMp+z/Z9/m4fd97cNvp0NdvRVX95S6omys49GFFFFIZwPxD+GNv43ns9QttRk0zV7MYiuY13ZGcgEAg8HkEHjNWvBXhXxLoN1cT6/wCLZtZEkYjjhaMqsZznd15PbpXaUULTYHrucR4A+Hn/AAg13rM/9qfbf7SlEu37P5fl4LHH3jn73t0rqdZ07+19Ev8ATfN8r7XbvB5m3dt3KRnGRnr61eopNJrle2w07PmW5y3w/wDBv/CC+GBo32/7diZ5fO8nyvvY4xub09axPG3wnsvFGqprmm6jPo2uJj/SrccOR0JAIOe2Qfzr0Sim9XdiWisjx/8A4Vh4/vR9n1L4k3f2Q8OIEYMw9M7h/WvVNI05dI0ez05JXlW1hSESSfeYKMZPvVyinfSwra3CuIm+Hnm/FSHxv/amPLh8r7H9n6/IVzv3e+fu129FLrce6sUtY0/+1tEvtO83yvtVu8Pmbd23cpGcZGetYXw+8Gf8IJ4Z/sb7f9u/fvL5vk+V97HGNzenrXVUULRtrqD1t5HnHjP4TQeINdXxDourT6Jra43XEIJWQjjJAIIOOMg8+lYt/wDDPVP7JvNQ8aeMbvWbaygknjtCCkO5VJDPzzj6VqeIbH4q2PiO9u/Dd/pt5pc7horS6xui4AIyQOM8/ern9W8PfF/xva/2TrM2laTpshHn/Z2yXX0OCxP0yBU2bjaP/DFXSldml+zwjL8O7hiMBr+QqfX5VFbvxA+F1n42ubbUoL+XTNXtgFjuolzkA5AIyDwehB4rpvC3huz8J+HLTRrHJit1wXbq7HlmP1NbFaTs3ddDOF0jySL4UeJ9T22vijx7fX2mAjfawgp5wHZmJ6fga6LwR8N7bwPrutX1neB7bUWBitRDtFuoJIXduO7rjoOldzRSTtsNq+hw/ir4ef8ACTeNNC8Rf2p9m/splP2f7Pv83D7vvbht9OhruKKKS0VhvV3OW8ceAtI8d6YlrqIeKeElre6ixviJ6/UHuK4aL4YfEK0iFna/Em4WzT5U3I+8L/30f517FRSSsO5zXgrwpJ4R0ia0n1e61W4nmM8tzc/eZiAO5Jxx3JrzLxCD8RPjrp2k2/7zTPD4Ely45XeCGYfiQq/ga9wdd8bJll3AjKnBH0rE8NeENF8JxXKaRamJrqTzJpJJGkeRvdmJPr+Zqk/fUn0/PoTb3XFdf6Zu0hAIIIyD1BpaKQzynU/g5NaazPqvgvxJc6BLcHMtuiloj9MEYHsc+2KNK+DclxrcGseMvEVz4guIDmKGRSsS46ZyTkewwPrXq1FC02B67lXULP7fpd1ZB/LE8LxbsZ27lIzj8a5v4deB/wDhAfD0ulf2j9v8y4afzfI8rGQBjG5vT1rrqKFo2+4PW3kYPjLw3/wl3hS+0P7X9k+1Ko87y/M24YN93Iz09al8J6B/wi/hbT9E+0/afscfl+d5ezfyTnbk46+tbNFC0v5huFFFFABRRRQAUUyaaK3heaeRIokG53dgqqPUk9K8fg+LVhN8Xbq2k163i8NQWWxHLDy5Jsglg2OepHpxQtXYOlz166uY7O0mupiRFDG0jkDOFAyf5Vk+F/Fmk+MNMfUNGmeW2SUxFnjKHcACeD9RVW58Q6R4i8Ja1No+oQXsUVrKjtC2Qp8snBrzn4F6zpmhfDG7vNVvreztxqDjzJ3CgnYnAz1PsKFvJPok/wAQeyt1b/I9rormNL+IvhDWbxbSw8QWUtw5wkZcoWPoNwGT9K6egAorG13xZoHhlUOs6rbWZflEkf5mHqFHJ/Ko9C8Z+G/EztHo2sWt3KoyY0bDgeu04OPwoWuwPTc3aKKKAKFxrmkWk7QXOq2MMy/ejkuEVh9QTUX/AAkug/8AQb03/wAC0/xrwnU/DGm+Lv2jtU0rVUka1aEORG+05ESY5ruv+FA+Bv8An3vv/Ao/4UldxUu43o2ux6Xb3MF3As9tNHNC33ZI3DKfoRUtZug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3UnlSPImJIz7ZyQcZI5IODQul9Lg+ttbHulFRwTR3NvHPCwaKRQ6MO4IyDUlGwLUKKxvFXiO18J+Gr3WrwFo7ZMhAcF2PCqPqSK8n0Ox+JvxIshr0nij/AIR/T5yTa29shyVz14IOPckk0lq9B7LU9xqG8uUs7Ke6k+5DG0jfQDP9K8Xj8VeMfhh4osdM8Y36avod+2yK/wBuHjPAJJ68ZGQc8dDXc/ETTvEmpaFOdD1yDTrRLWVrlWtxI8y7c4DH7oxkfjSm7Q5kEfiszzDwhomv/GCTUvEGq+J9RsLSO4MVtbWjkKvGeBnAABHbJ9a9s8L6HJ4d0C30ybUrrUZIt2bm5Ys7ZJI6k4AGB+FeB/CXwz4x1jwpNcaB4u/sm0W6ZWt/I35bC5bP4j8q+kIEeO3jSR98ioAzf3jjk1o0oqy8iE+Z3fmSVzvinxjY+FJNKju4pZZNSu1tYUjxkE/xHPYZH510VfNfxZ0vxNH8QNAW/wDECTtd3J+weXBsWzHmKBx/EeRz3xUr4oruy/st9j6UrxnwPqN9P8fPFtpNeXEltEknlwvKxRPnTopOBXV+E/C3jTSNbF1rvjH+1bLy2X7N5Gz5j0OfavJbfUtdsvjp4otPDdvFJq1/I8EUk3+rgGVZpG9cBf8A9fSiOlRejFLWD9UfStFeM6n4J+KdhYzana+Pnu7yJTIbXy9qNjkhc5X8CBXVfCfxxceOPCr3N+iLqFpL5FxsGA5xkNjtkdvUU1rfyB6W8zvKK8m8ceNfEOo+NIfAvgt44b8rvvL1wD5IxnA4OMAjJxnkAVla5oPxN8D6XJ4htvGj6ylqPMubS4iOCnfAJOQPbBqU9LvYdtbLc9uorn/BPiqDxl4Vs9agTyzKCssWc+XIOGH+HsRXQVTTTsyU7q4V4Jb+NPid4j8aa9o/hy6sCmnXEihZ4kXCByo5I56V73Xz58Odf0jQPix42l1fUrWxjknkVGuJAgY+aeBmpWs0n2f6FPSDfmjf8v46/wDPfRvyj/wr1nSxejSrQaiVN95KfaCmMeZgbsY7ZzWGPiN4LJwPFGlf+BS/410UpeS1c2zoJGQ+WzDK5xwT6im3ZCtqS0V5Engf4o6zuudV8fDTZGOVgsYsqvoDtK/1qv4I8VeKtC+JUvgTxXfLqPmRl7a7I+b7u4c9SCAevII600ruwPRXPZaK8s+NHivVPCcPh650+9lto5Lwi5EYB8yMYJBz+NZa2nxM+Ia/21Z62vhvSJfmsrZciR4+zNtGeevJ/CpTvsN6bnqviDWrbw5oF7rF4GMFpEZGVeregHuTxTtC1aLXtCsdWgjeOK7hWZUfG5QRnBxXkXxr0rxLB4GSeTX1bS7eKCK4tRF89xLkAuz9SM4OKf4G8I+O5vD2hX1v44MWmtFFItl9nHEfB2Z+nGaqKvf1sJ6W9CT4m6jfWvxf8FW1veXEMEzx+ZFHKyq/73HIBwa9mrwH436i2k/EzwnqCQNO9tGJFiXq7CTIH4muhbwd8U9cjGoXvjZNKuJBuWxtYjsi9FJGP6/U1MH+7+bCXx/JHrtFeR/DTxr4jPjDUfBHi6RLjULRS8VyoALgYyDgDIIIIOM+teuVVtE11F1a7BRRXmXxP+IWpaDf2HhnwzAs+v6jjYWAYRKTgHB4yTnrwAM1LfQpI9NorxoeAPis0Ium+IIW8I3GH5vLB9M4x/47XqWlwarB4ctoL+7jn1ZbcCWfYNrS464GOM/Sm9FcXU06K8iTwP8AFHWd1zqvj4abIxysFjFlV9AdpX+tV/BHirxVoXxKl8CeK75dR8yMvbXZHzfd3DnqQQD15BHWmld2B6K57LRXlXxs8Wat4StdAu9Lu5IA923nomP3qAA7TkfWqsWi/EzxxbJrEnihfDtrcDzLaxtoyWVDyu8jByR7n8OlStb26A9Nz1+ivFfCfivxd4W+JUXgnxdfLqUV2ubW7x83IJU5wCQcEEHkGvaqromg62YV43+0Bf3ljYeHTZ3c9uXvGDGGQpuGBwcda9krxH9o2QRaX4dkYZCXjsQO+FFS3Zp+a/Ma6+j/ACPa4uYU/wB0U+vH4PDvxK8Z2cWsTeLf+EfhuEEltYWsZJjQ8rvYEHOMev8ASovCfjLxR4X8fp4I8a3KXv2kA2V8By2c7ecDIOCOeQaq15We5C0jfoey0VynxD8aQ+BfC0uqNGJrl2EVtCTw8h6Z9gASfpXBad4S+KPiXTo9ZvvHEmlT3CiWKyijIVAeQG2kAfkalO9/It6W8z2iivK/ht461ufxJqHgrxdsbWbIFo7hAB5yjGc44JwQQcDIr1Sqton3J8grhPF8Pj2TxloL+G5Y10RWH28MUH8Xzbg3zEbem3vXd15N8RfE+taR8UPCGmWGoSwWV7IguIVxiQGQDnj0pL44rzG/hk/I9Zorz34za7qfh3wC1/pN5JaXQuo08xMZwc5HNc1pkPxF+JOk2+r2/iFfDumugFvFEhaWbAwXYjB5IOOfw9Utb26A9LX6ns9FfPUXj/x54D8TXXhLV2XXb2dVXT5G6l3ICHPBK9cg85HWuhv/AAR8VpLOTU/+E7/4mAUyfYoUKRZ67QRx7crTvpzdA626nslFeefCDxxe+NPDdx/aoX+0rCbyZnVdvmAjIYgdD1B+laHjjTfG+qXFlbeFdXtdNtGVvtc0iZkU8Y28Hrz0x0605KzsCdzs6K8M8T+H/iR4H0WXxFbeO59UW1w89vNFgbc4JAYsCPyr1TwT4j/4SzwfputGMRyXMf7xF6K4JVse2QaFqm+wno15m/RXieueLvFnjzx5deFPBd6unWNgSLq/A5JBwTnqBngAcnHXFT3tn8R/hzYya1J4iHiTTYRm7tp0KyKndlJyePr+FTf3eZ7FW15Vuey1wmgw+PV+JGsSavLGfDLKfsagp6jbgD5gcZzmqPwT8Q6r4l8G3N7q95Jd3AvXRXfGQu1SBx9TWf4Q8T61f/G7xNot1qEsum2sbmC3bG1CGQDHGe5qkrTS8n+RLd4N+f6nrNFeVfGzxZq3hK10C70u7kgD3beeiY/eoADtOR9aqxaL8TPHFsmsSeKF8O2twPMtrG2jJZUPK7yMHJHufw6VK1vboN6bnr9FeK+E/Ffi7wt8SovBPi6+XUortc2t3j5uQSpzgEg4IIPINdb8UfH0vgvSraDTYVuNZ1F/KtI2GQvQFiO/JAA9TTeya1uC3afQ72ivG18B/FSey/tGTx+8WpFd/wBjCHyg3XaSPl9vu4re+FXj698VwX+la5EsWuaW+yfaNokGSN2OxBGDjjpTS6dRN9eh6NRXlnxT8f6vpOq6f4T8LKra5qGP3hAbylJwMA8ZOCcnoBVOHwL8UtOgF/B4++1XyjebOeMtC5/u5Ofp90fhUp3V+hTVnbqQeCtQvZv2gPFlpLeXEltHHIUhaVii/MnRc4FezV8+fCLU7jWfjR4hv7u1+y3U1q/nw5zskDIGH5g19B1SVoQ9P8yfty9f0QUUVzHje18W3mm28HhG+tbO5eXbPNcKDtjweVyDzn2PXtUspHT0V4vq/gj4l6PpNxq9r8Qrm8ureMzNatGVRgBkgZJB+hUV2Pwv8aTeNPBKaneoi3kEjQ3GwYDMoB3AdsgjinpZ+Qn08zt6K8J0TUfHPxa1DU7vTfEo8P6RaTeTHFAmZD3GcEE8d8/QV1fhzwl8Q9D8SWrXvjJdV0bJ+0JNH+8IxxjIOOcchqEr76A9L2PS6KKKAOE8Xw+PZPGWgv4bljXRFYfbwxQfxfNuDfMRt6be9dreXKWdlPdSfchjaRvoBn+leWfEXxPrWkfFDwhplhqEsFleyILiFcYkBkA549K6X4i6b4l1DQ7j+xNbh021jtpWula3EjygLnAJ+7xkfjUt2pXXd/16FJXqWfkeX+ENE1/4wSal4g1XxPqNhaR3Bitra0chV4zwM4AAI7ZPrXtnhfQ5PDugW+mTaldajJFuzc3LFnbJJHUnAAwPwrwP4S+GfGOseFJrjQPF39k2i3TK1v5G/LYXLZ/EflX0hAjx28aSPvkVAGb+8ccmtGlFWXkZp8zu/MkrnfFPjGx8KSaVHdxSyyaldrawpHjIJ/iOewyPzroq+a/izpfiaP4gaAt/4gSdru5P2Dy4Ni2Y8xQOP4jyOe+KlfFFd2X9lvsfSleM+B9Rvp/j54ttJry4ktokk8uF5WKJ86dFJwK6vwn4W8aaRrYutd8Y/wBq2Xlsv2byNnzHoc+1eS2+pa7ZfHTxRaeG7eKTVr+R4IpJv9XAMqzSN64C/wD6+lEdKi9GKWsH6o+laK8Z1PwT8U7Cxm1O18fPd3kSmQ2vl7UbHJC5yv4ECuq+E/ji48ceFXub9EXULSXyLjYMBzjIbHbI7eoprW/kD0t5neUV5N448a+IdR8aQ+BfBbxw35XfeXrgHyRjOBwcYBGTjPIArK1zQfib4H0uTxDbeNH1lLUeZc2lxEcFO+AScge2DUp6Xew7a2W57dRXP+CfFUHjLwrZ61AnlmUFZYs58uQcMP8AD2IroKppp2ZKd1cKKR2VEZ3ICqMknsK8Rh8QeM/ivr9/D4X1UaF4esX8v7WqZkmbsfXJ64BAAxmp3dkPpdnt9FeF6lrHjn4R6rYXGua2fEPh+6k8qR5ExJGfbOSDjJHJBwa9G8dWuuat4Qa78J6pNa38aCeHysYuFxnbyO46e9DaUeYEteU66iuB+G/xCt/FPhGS61GVLfUNNXbqCv8ALtwP9ZjsDg/Qg1geCfEPiP4heO73Wbe+uLPwlZP5cMCgD7Sw6ZOM+5/AVVve5RX92567RXknj3x74gufGEPgfwSI11Rlzc3bgEQgjOBnIGByTg9cDmq58AfFW2C3Fv8AEITXAILRShtn4ZBB/IUlrr0G9ND2OisPxH4gg8I+FLnV9Qcyi1iGcYBlfoAPTJryzRNM+JfxEsB4gm8WNoFncEtaWttGfudicEHHuSSaOrS6B0TfU9vorx/wj4x8S+HfHw8DeM7lL1513WV+owXzkgHgZBwRzyCO9W/iX4w8QReLdH8F+GZ4rK91FQ73koB2AkgAZBx90npnpijtbW4d79D1WivIJPh18S7VPPsviTNPcjny7iNhGT6clh/47XYa/wCINS8GfDSXV9TaO91W1tkEhVdqPMxA6DHGT+lJtJXYJNtJHX0V4joPhv4j+NdEtvEE/j+TTheL5sVvbRHaqnoDtKgfrXd+BdG8Z6PLew+KNeh1W2wv2RlTD99xY4B9OMmqt0Yr9UdnRRRSGFFeJeMfiJ4m0D4vvoumA3sM9skdrYFVC+c68MTjOAeTzVu88I/F94H1BPGtub0DeLOKMLHn+6Dtx7cj8aSd1zdB21sexUV5v8KfiHd+L4L3S9ahWDXNObbOFXaJFzjOOxBGCPpWr4403xvqlxZW3hXV7XTbRlb7XNImZFPGNvB689MdOtN6W8xLU7OivDPE/h/4keB9Fl8RW3jufVFtcPPbzRYG3OCQGLAj8q9U8E+I/wDhLPB2na0YxHJcx/vEXorglWx7ZBo3TfYHo15m/RXzx4a+IfjfW59V8NaRKbvWZbx/Ku7gDy7O3Xgnp64xkH8a9B8MeEfHekDUpdS8Yi+nntilt5is6QS5+9tPBH5ULVX/AK/roD0djpF8Y2L+PG8JJFK14lp9qeUY2KM/d9c8g/jXRV8waPoHi27+NGsabB4qMOtRQkzaj5OfMXCfLt7DkflXrM114i+HHgDWtV17WRr13EVa3LR7ApOFAOO2Tmi6UFJ9v1HZubiv60PRqK8R0Hw38R/GuiW3iCfx/JpwvF82K3tojtVT0B2lQP1ru/AujeM9HlvYfFGvQ6rbYX7Iyph++4scA+nGTTt0ZN+qOzoopsqGSJ0DFCykBh1HvSYx1FeT/B/xTrWpar4k0DxDfSXd9p1x8jSAA7QSpHA6ZA/Oq3xn8Ya7peo6Vofhm8kt7+SKW6nMWM+Wqkgcg/3WP4Um7JPuNK7a7HsNFcr8OPET+KfAel6nNJ5ly0fl3DdzIp2kn64z+Ncf4X8Ta34l+Nmu2sWoS/2Dpisn2dcbGcYT0z13Hr2qmrT5PX8CU/d5j1qivG9a8WeKvHPji78KeC71NNstPyL3USuSWBwQD254AHJwecVn6+nxF+FsEWuyeJj4h0pZFS6huUIKgn3JIHbIPXHFSmrJvRMprWy3R7pRVDRNXttf0Oy1azJNvdxLKmeoyOh9x0rwfw18Q/G+tz6r4a0iU3esy3j+Vd3AHl2duvBPT1xjIP403dS5eolZrm6H0PRXBeCPDHi3w/f3d54m8VtqsDw4WIs22Ns5Lc8dBXGw+IPGfxX1+/h8L6qNC8PWL+X9rVMyTN2Prk9cAgAYzR1sg6XZ7fRXhepax45+Eeq2FxrmtnxD4fupPKkeRMSRn2zkg4yRyQcGvcIJo7m3jnhYNFIodGHcEZBp7q6DZ2ZJRRRSAKKKKAIL25Sysbi6kOEhjaRj7AZP8q+avhv8MbP4lWmra9q17e25e9YJ9nKjcT8zE7gf7wr2/wCJs93D8OtaWxt57i6mg8iOOCMux3kKcAc9Cap/CDRJdC+GumW9xC8NzLvnljkUqylmOAQeQcYpRSbk32Q5OySXcyPDfwM0Dwz4hs9Zg1HUZ5rV96RzMm0nBHOFB75rn5/+Kk/aehT70OjW2T6Aqmf/AEKQflXuBOBmvHvhJouqt438W+JNX028snupisAuoGjLKzljjcBkYC1UX767K7+exMl7j87Iy/i+p1/4reEPDMhJtWZZJF7Hc+D/AOOp+te5gJDFjhI0X6AAV478XfD2uWvizQ/G+hWEl++nbVngjUs2FYsDgc4IJBx0qPWPGnijxt4cvYbPQbzw9pEdu8moaheEh/LC5ZIgQMk9M+/aoTtTfdNltXmu1kZ/wraLxL8ZvFfiWIbrePcsLf7zYU/98ofzqf4hf8VF8ePCmhD5orMLPIv4lz+iCtD9nXSvsvgm91Erhr27IU+qoAB+pas3xva674Q+MkHja20W51XTpYRGwt1LFDs2EHAOD3BPBq7KEoLt/kR8am11/wAz2rUb6DS9Nub+5cJBbxNK7HsAMmvH/gBA9+PE3iSZT5l/e7QT+Ln9XH5VF4q1Dxl8RvCmoeRoF9o2iwwGTynUtdX0g+6ioBkLnBPHOK7X4Q6FP4f+G+nW13byW91KXnmilQq6szHAIPIOAKIqzk32/P8A4YcndJLv+RwWvW0XjD9pOx06YCS00qBXkU8jKjfg/wDAmUV7tXj3wt0TVZPiP4u8S6tpl3Z/aJDHbG5gaPerOT8u4DIwq17DSjpCK+fzYS+OX3fcfOvjiTXtc+P8dvoUFtc3ulQo1vFdHEYwu8k8ju2fwFdPeeD/AIpeNITY+Jde0/S9Lc4mgsVy8g9OByPq2PY1D8QfDviLw38R7b4geG9PfUk2BLu1jBLcLtPA5wVxyAcEVcHxd8S6sottC+HuqNeNxvugyxR+5O0fqRSgvdS6jl8V/Q9I8OeH7DwvoVto+mxlLa3XALHLMTyWJ9Sa1abGXMSGQAPtG4Dse9Oqm23qSttDiPi80ifCvXjHnJhUHHoXXP6VU+CIiHwo0nysZLSl8f3vMb/61dprOlW+uaNeaXdgmC7haJ8dQCMZHvXgug6h4z+C93daTe6DcavoUkpeKa3BwD/eVgDjIxlTUxdnJPrYcldK3Rn0RRXk2m/F/Wde1S0s9K8C6mI5ZkWa4n3bYkJGWOFxwPUin+P/ABl4z0vx/o+ieHdOL2k4RpJDblxLliGG7ooAH61VtUu+gX0b7Hq1ZviHUl0fw3qeoscC2tpJfxCkj9a0q4T4wDUpvhxf2elWN1eXV2yQ+XawtIwUtljhQTjA/Ws6nwtIqHxK5zn7PWmtB4KvdUkH7y/vGO491UY/mWr16uY+HejPoHw/0XTpomimjtg0qMMFXb5mBHrk1zHxc8X+K/DR0m38L2LSyXbt5kwtzNgjGEA6DOT+Va1GlKy9DOCbV/menUVXsHuJNOtnvECXLRIZkXor4G4D8c1YpNWdhp3VwooopDCvDfi3/wAli8C/9dYv/Rwr3KvHviboGr6n8VPB19Y6bdXFpayRmeaKIskYEoJ3EdOOaI/xIeoS/hy9D2GvDfizGsvxk8DI4ypePIP/AF2r3KvHviVouq3/AMW/Bl7Z6ZeXFpbuhmnhgZ0i/e5+ZgMDjnmiP8SHqEv4cvQ9hrxG14/apu/+vP8A9orXt1eP22jaov7Slzqp028GnG12i7MDeST5SjG/GM5460R/iL0f5A/gfy/NHJ+KIvEN3+0dPFoF1aW2prAv2aS8GUC+SM/wtz97tXZnSPjcRg+IfDn/AH7P/wAZp3xR8Ea1Pr2neNfCah9YsMCSDvKozgj1OCQR3BqpF8bdUjiEN58P9ZW/HDxxq20t7ZTI/I0o25VHqhy+K/TQ1fhJ8P8AW/Azaw2sXFjKb543QWjswBG7OcquOor02ua8Fa3rfiDSJr3XNEbR5TMRDbOTv8vAwWzg5znsOnSulqnfqSurGvkRsR1wcV8w/Cu08d3txr8vhPUtLtJPtC/axerlmOWxj5G4+9X1BXhuqaB4o+GHjq+8S+GdLfVtE1ElrqziBLoSckYAJ4OSCAeDg1K0ld9UU9Y2Xcta34P+MHiLR7jStS13w7LaXACyIFZScEHqIsjkCvQfh94evfCvgjT9F1GWGS5tg4ZoWLJy5IwSAeh9K4b/AIXVq14PI0v4fazNeNwFkDBQfchOn5V6npM95c6PZz6hbi3vZIUaeFekbkcr1PQ1WyZL3R478Af+Qt4y/wCvtP8A0KSi8/5Ops/+vQf+iWq98EdF1XSdU8VvqWmXlms9yrRG5gaMSDc/K7gM9R09aLvRdVb9pS11VdMvDpy2wU3YgbyQfKYY34x1460o7w9P/bQltU9f1RU/aL/5Bfhz/r9b/wBBFdv8Uv8Akk2uf9eg/wDQlrlvj1o2qaxpugppmm3l80V2zSC2gaUoMDk7QcCup+KQI+E+ugjBFoP/AEJaiX8KXq/yRa/iR/rqU/gmsa/CjSPLxyZS2PXzGqn8e0ib4W3RkxuW5hMef727H8s1wvw48U+IvAng21ln0C61jQL3dNBPZDc9u2SGVhjpkZ7detS+Ib7xR8adRsdIsdCvNJ0GGUSXFxdKRk9Mk4AJAzhRnk1pVXPKy7r5EU3yq78z0zwppNt4j+D+kaXqsZkt7rTY45BnBxgYIPqMAiuFXwT8R/hxvbwfqqaxpKksNPuR8wHXhT/7KQT6V6drral4b8G48M6ct7dWUcccFq38aKQCOo525/8Ar1wifGfWETyrn4c68t4ODGiMQT9Smf0ok05ylEIq0Emb/wAOviZD42e60+7sX07WrMZntmzgjOCRnkYPUHp71xXw2G749+NGuP8Aj4HnbM9dvmr/AExWx8MvC+vzeNdZ8c+IbAabNfqUhsz94AkZJHbhQOeTycVF438JeIfD/jyPx94QtPtsrLtvrEfekGMEgd8gDpyCM80fDKMn2d/JsLXjKK7q3yPYK8M+EmE+MPjiO3/49fMk6dM+ccf1q9d/F/xNqdo9jongHV49VkXYGnRikR9fujOPfFdH8J/AVz4M0a5udVdZNY1FxLckHdsHOFz3OSST6miKtLm8n+ISd48vmvwOSv8A/k6ix/69B/6Jam/tEZZ/Cscn/Hu1zJv9P4P6ZrQvdF1V/wBpOy1VdMvDpy2wVrsQMYQfKYYL4x14611HxV8ESeOPCRtbQquoWz+faljgM2MFSe2R+uKm9oxfZ/qVvNruv0O3jCrGgTG0AAY9K8P+KyRj40eBnGPMMkYb6Cbj+ZqbRPir4p0PT4dH17wNrFzqVuoiEsEbYmxwCflPPuCQaw9Y0TxtrnxH8L+KdX0aeGOa7jC2kEbS/YoUdSDIwGATuJ5x0/AUl+9i1tch/wAOSe9j1j4h+P7TwDo0VzJbtdXly5jtrZTjew6knsBx+YrmrST4y63Et2D4e0aKQblhlV3kUHpnhufxFHxt8H6v4h07S9U0SA3N3pcrObdeWdTg5A7kFRx71Xtfi34m1C3S0svh5qp1Vl2nzQyQq3qSVGB9cfWpjrfuXLS3Y574ax6nD8ffEEes3EFxqK2jieWBdqM2Y+g49qv/ABU/5LR4F/34/wD0dTvh54T8S6H8Y9TvtchlmN1YtLJepEwhMrlGKK3Tg5H4Vc+JWi6rf/FvwZe2emXlxaW7oZp4YGdIv3ufmYDA455qo70vL/gky2qef/APYaKKKQzk/HvgLTvHujx2d3LJb3EDF7a5jGTGx68dweOPavOZb34qfDGDfeLD4l0KAfNLkmSNB6n7w+p3AV6B468TeJPDL2NxovhyTWrNt/2tIc+YmMbSMZP97+E9O1cdffFrX9Y0+fT9I+H2s/bp42jBnjby0yMZPy8/jipu0m4/cVo7cx6J4O8Xaf418PRavp4dEYlJIn+9G46qfzHPvXlnwBjX+3PGUuPn+0oufbdJXa/CTwbeeC/Bv2TUSovrmY3E0anIjJAAXPc4HNc38EdF1XSdU8VvqWmXlms9yrRG5gaMSDc/K7gM9R09a0slUdu3+RnduGvdfqei+M+fBGvf9g+f/wBANcR+z+cfDFM/8/kv9K7vxZDLc+D9aggieWaSxmVI0UszMUIAAHU1xvwS0q/0z4cCz1OxubKc3MpMVxE0b4OOcMAaiN7z9F+ZUto+r/Iy3+Jnijxd4gvdJ8AaTaSW9m22bUb5jszkjIAIxnBx1J9K5z4p2XxFh8B3EviXV9FmsPNjDwWcTB927jBKjoaj8Mz+Jfg5rmr2Fz4XvtV0y8lDw3NmhbOM4OQCOQeQcEVb8cv43+Jnha5kh8OXWk6XZ7Zo7WZWa5vZM4AC4BAAJPT8+yfwprXYpaTafyPRdC/5ItZ/9gMf+ia5P9nNYx4EvmXHmHUG3+v3ExXYaXbT2fwfgtrmGSGeLRdkkcilWRhFyCD0NeKfCXWvEfhDQLnWLPRptZ0O5nMdxDa5MtvIoGGxg5BDfp276tr2tT+upkk/Zw/roe3/ABQSJ/hj4hE2Nos2Iz/eHI/XFcX8O5bkfs7XbIW8xLW88r/x7GPxzWF4r8X+J/inaJ4Z8O+GNQsrWd1N1c3alRtBzgnGFGeepJxXsfhvw3a+HvCVnoCYlhgg8pyR/rCfvH8STWbi3Cfnp/wTTmSlHy1PB/hPp/xGuPCUknhLVtGtbA3Th47pCZPMwuSf3bcYx3rovE3gD4s+L9LGm6zrXh6a2EglCruQhhnByIvc1VsbPxZ8F9dv0sNFn1zwxdyeYv2cEvF6ZwDtIHByMHA5rdHxi1/VWFtoPw/1WS4Y433IYInucL/UVTtO1vISTjc9L8O2E+leGtM0+6dHuLW1jhkZCSpZVAOCQOOK06ahYopYYYjke9Ook7ttiikkkjyb9oYyj4cRBM7Dfx+Z9NrY/XFd/wCD1iXwXoYgx5X2CHbj/cFN8YeGrfxd4WvdFuG2CdPkkxnY45VvzFeUeH/F/jD4a6cnh3xB4Sv9St7XKWt5ZAsrJ2GQCD7dCPSpi7cyfVp/hYclfla6XRpftGLEfAlgzY80aguz1+4+f6V3m6Rvhlumz5p0fL59fJ5ry250zxT8Y/EunTatos+ieGLF/M8u4yHm9eCASTjGcYAz1r2XW4Gfw1qNvBGWY2cqRxoMknYQABUyTVKV+v8AlYpO9SNun+Z5r+zt/wAk9uf+v+T/ANBSvXK8u+A+lajo/gW4t9TsLqynN67CO5haNiu1ecMAccV6jW1Tf5L8jKG3zf5hXh/xp/5KN4E/6+B/6NSvcK8k+NfhbWtSOieIdCtXu7rSZSzQRruYjKsCB1OCvIHPNQnyzjJ7JmlrxlFdUet14b4DjVv2i/F7kZZEl2n0y6V2Pg34k6h4p1aHT5/CGqacPLZprmdWESMB0BKjqfXFc/4J0XVbT47eK9RudMvIbGdJBFcyQMscmXT7rEYPQ9KcVaovRkyd4P1R6/J/q2+hrxX9nbiw8Sj/AKfV/ka9qfmNgPQ15H8B9G1TR7PxAup6beWRlu1aMXMDR7xg8jcBkUo/FL0/UcvhXr+jOG0W38X3vxn8XHwvfWFpqKyzeY18uQYvMAwvyt/s13F74d+NGoWNxZ3Ov+HHgnjaKRdhGVYYI/1Xoah8b+EvEfhrx6vj3wfafbmkXF9YqMs3GDgDkggDpyCM1Kvxu1KRBFF8Ptbe9PHlYbG767M/pUxS5FF9FYcr87l31Ol+FHg3VPA/hafS9VntZZnummU2zsyhSqj+JRzkGu7rG8LahquqeHra91rThp1/LuL2vP7sbjtznvjFbNaSvfUmNraBXzn4F8JaH4t+K3jS31ywF3FBcSPGpkdNpMpGflIr6Mr5v0m+8XeB/iJ4o1Kz8D6vqcV9cyKjLbSqu3zCQwIQ5BqFb2iv2f6FO/I7d0eqD4MfD4EEeHUyP+nqb/4utrxh4rsPA3hiTVbtGeOPbHDCh5kc9FBP06+grzv/AIW745/6JXq//fE//wAarc+JnhvVPHvwytvsto0Opp5d59jc4bdtO6PnHI3HrjkUS5uXQI25rMztL1j4ueLrSLUtPttC0WwnXfCLre8jIeh79foK5Ozg1+3/AGjdEj8SXtpd6h5BJktU2pt8uTAxgc9a3tB+KniSw0e00ef4e6zNqltEsHyRsqOVGATlfl6e4qhpnhjxh/wuvQ/EmvWTsbuN5Zzbxs0VmNjqsTPyM42/iatWVRW21/JkNt03fexa/aNUPpnhxG6NeOD+Qr2m1jSG0hijUKiIqqo6AAcV5L8edG1TWLHw+umabeXzRXbNILaBpSgwOTtBwK9ciBESA8HaKmPwv1/RFS+Jen6nnPx3/wCSVX//AF2h/wDQxXRfDr/knHh7/rxi/wDQah+Jfhu58WeAtR0qzwbpgskKk4DMrBsZ98Yrz3wT8RPEOhaRp/hjUfA2sS3lrtthLHEwXZnAJ+U4wO4yOKIfaj1bX5BP7Mu1xnxZjWX4yeBkcZUvHkH/AK7V7lXj3xK0XVb/AOLfgy9s9MvLi0t3QzTwwM6Rfvc/MwGBxzzXsNEP4a9WEv4j9EeI2vH7VN3/ANef/tFa9urx+20bVF/aUudVOm3g042u0XZgbySfKUY34xnPHWvYKI/w4+n6sH8b+X5IK8MbEv7VYFzyEt/3Of8Arh2/M17nXknxS8Fa4/iLTvG/hSPztVsMCW3HWRRnBA78EgjqR0pJ2mpPb/MdrxaR63XP+M/Ftj4K8OTaxfK0iqQkcSHBkc9FHp359BXnifG/VfJEDfD/AFg6jjBhUMF3f98Z/StT4h+Hdb+IHwqtCtj9m1lCl2bInB3YIKc98Hv6UTvy3QRtezKel6x8XPF1pFqWn22haLYTrvhF1veRkPQ9+v0FcnZwa/b/ALRuiR+JL20u9Q8gkyWqbU2+XJgYwOetb2g/FTxJYaPaaPP8PdZm1S2iWD5I2VHKjAJyvy9PcVQ0zwx4w/4XXofiTXrJ2N3G8s5t42aKzGx1WJn5GcbfxNWrKorba/kyG26bvvYt/tGKH0zw4p6G8cH8hXtNuoS2iVRhVQAAdhivJPjzo2qaxY+H10zTby+aK7ZpBbQNKUGBydoOBXrkQIiQHg7RUx+F+v6IqXxL0/U8U8f/APJwvgw/9M4//Q3r26vH/G+japd/HTwlqFtpt5NYwIgmuY4GaOP53+8wGB1HWvYKIfw16v8AMJfH8kFeI/tHbTpfh3d937W+fptFe3V5H8dPDmqeJrbw5ZaZZ3E7NeMsjxRM6whgBucgcD3NJ7q3dfmNdfR/ker2wUWsITGwIu3HpivEPjR8vxM8DvB/x8+cvTrjzVx/WtO2+IXivwVZRaL4i8HahfzWqiKK+sctHcKOAehwcY759hVLwx4f8SeP/iPB418TaZJpen2IH2K0lBDEjJXg4OATuJIGTjFWtaiktk7kbU3F72sQ/tGmdl8MRRsqo08vL/dDfJjP5mtpdI+NoQbfEPhzbjjEZ6f9+a6b4neB/wDhOvCjWULrHf27+dau3TcBgqfYjj8q4bSfin4q8LWEWkeKfBeqXF3bKI1ubdSRKBwCeCCfcHmojomn3LlrZoteG/hz43h+J9t4v8R6jpM7KrJMbVmDMPLKjC+WB6V7HXB+C/G/iDxZrMoufCd1pGkJCWS4ut2+STIwBkDjGex6da7yqeiSJ6thXiHxX/5LJ4E/66x/+jhXt9ePfEzRdVv/AIr+C7yz0y8ubW3kQzTwwM6RfvQfmYDA455pR/iQ9Ry/hy9C/wDtAf8AJMX/AOvyH+tdn4GjWLwFoCIMKLCHj/gArlvjhpl/q3w7e102xub24+1xN5VtE0j4GcnCgnFdf4RgltvBuiwTxPFNHYwq8cilWVggyCD0NEPhl6r8gn8UfR/meT+MEV/2lvC4YAjyEP4jzMV7gehrx/xRouq3H7QnhzU4dMvJLCKBRJdJAxiQ/vOC4GB1HfvXsB6Ghfwvmxy/ifJHif7P3/H34vH/AE+J/N62df8Aibrd54xn8JeB9Igvr+2yLm6umIiiI68AjpnGSevGDVP4H6Nqmk3Xik6lpt5ZCe7VojcwNH5gy/K7gMjkdKw57bxH8LvijrGuweH7rWNH1Usxe1Usy7m3YOAcEHI54IpdYp7W/GyF/M1vf9TQ8Z2PxTHgjV59a1fQBYC2YzwW0TFyvcAlev411HwTz/wqTS8dczY/7+NXM+INY8ZfE7w/e6Zpvhq70XTPJaSee9B8y42jKxIuB1IAzz/j2Hwf0690r4Z6ZZ6haT2lyjS74Z4yjrmRiMg89KpLSS9P1FL7Pq/yOH/Z3CtL4qkkx9qNzHvJ64+f+ua9f8SJHJ4X1ZJQDG1nMGz6bDXjt/o/iX4VeP8AUPEGg6PNq+g6kS09vbgloyTnGACRgk4OCMHFXtZ8ceKfHOg32l6P4UvtJtZIH+16hf5VY4wCWCjAySMjr3/Gon71PTt9xcdKl/Mtfs7f8k+uv+wg/wD6AlZvgT/k4rxh/wBcpP8A0NK0v2dv+SfXX/YQf/0FKj8GaLqtr8efFWo3GmXkNjPG4iuZIGWKT5k+6xGD0PT0rV/xV/hf5IyX8N+v6sp/tGKH0zw4p6G8cH8hXtNuoS2iVRhVQAAdhivJPjzo2qaxY+H10zTby+aK7ZpBbQNKUGBydoOBXrkQIiQHg7RUR+F+v6IuXxL0/U8U8f8A/Jwvgw/9M4//AEN6zPjGupz/ABh8LQabNBDdGKP7JJcDMaymRsE8HuB2NdD430bVLv46eEtQttNvJrGBEE1zHAzRx/O/3mAwOo61sfFrwFe+LLCy1PRHCa3pj+ZACdvmDIO0HsQQCM/1qY6Ri30kxy1lJd0jP/sn43f9DD4c/wC/Z/8AjNHw6+Hninw7451PxF4gvNNna/hcSfZHbJkZlbOCigDg1RtPjNr+nW62mveBNW/tGMbXaCNgsh9QCvGfYmu18DeKdf8AFJvbjVfDc2i2abPsonJ8yXOdxOQPbt371a0d0S9rM88IEn7Vn+kchLf9zn/rh2/WvdK8i+Kfg3XR4k03xx4UhM+pWOFmt1GWkUZwQP4uCQR1x0pLf4veJNSiFnYfD3Vf7VYbcShlhRvUkqMD64+tTH4FHqhyXvX6Oxl+AUjT9ojxgseNvlynj1LoT+ua9yrw74X+FvEeg/FvWrjXLad2ntC73ohYQySOyOQrkYOCSPwr3GqStCC8v8xPWcn5/ogrzbxt8TL3SfE1v4T8MaUup69MASJGxHFkZGcEZ45PIAFek14f410jxF4P+LSeO9K0ebV7GaMLPFACzJ8mxgQASOACDjFT9pJ7FdHbc2buy+ME+l3M15q3hy1i8py8UcTMwXByOVI/Wqf7OXPgbUc/9BBv/RaVNP4y8XeP7OTRdD8KXujw3SmO51LUAVWJCMNtGBubHv8A41Z+B2h6r4f8IapaajY3FrcC/cxrPEU3jYoDDPUEjrVR05r9v1Jlry27/oUNW+E+v+Htaudc+Hmt/YpJ23y6fMf3bc5wCQQR1wGHHrVnwr8VtVj8TQ+FfHGj/wBm6pMQkM8YxHIx6ZGT17EEjPpUafFvxRpbG21/4e6oLhTjzbNWKP7jKkfkxrLSw8S/FL4haJrd74en0PRtJcSK11kSS4YNgAgE5IHbAGeaIbpdPyQ57N9fzPcqKKKQHiHxX/5LJ4E/66x/+jhXrviL/kWNW/685v8A0A15h8TNF1W/+K/gu8s9MvLm1t5EM08MDOkX70H5mAwOOea9R16N5vDupxRIzyPaSqqKMliUOAB3NRL+A15yKX8ZeiPM/wBnb/kntz/1/wAn/oKV65Xl3wH0rUdH8C3FvqdhdWU5vXYR3MLRsV2rzhgDjivUa2qb/JfkZQ2+b/MK8P8AjT/yUbwJ/wBfA/8ARqV7hXknxr8La1qR0TxDoVq93daTKWaCNdzEZVgQOpwV5A55qE+WcZPZM0teMorqj1uvDfAcat+0X4vcjLIku0+mXSux8G/EnUPFOrQ6fP4Q1TTh5bNNczqwiRgOgJUdT64rn/BOi6rafHbxXqNzpl5DYzpIIrmSBljky6fdYjB6HpTirVF6MmTvB+qPX5P9W30NeK/s7cWHiUf9Pq/yNe1PzGwHoa8j+A+japo9n4gXU9NvLIy3atGLmBo94weRuAyKUfil6fqOXwr1/RnDaLb+L734z+Lj4XvrC01FZZvMa+XIMXmAYX5W/wBmu4vfDvxo1CxuLO51/wAOPBPG0Ui7CMqwwR/qvQ1D438JeI/DXj1fHvg+0+3NIuL6xUZZuMHAHJBAHTkEZqVfjdqUiCKL4fa296ePKw2N312Z/SpilyKL6Kw5X53LvqdL8KPBuqeB/C0+l6rPayzPdNMptnZlClVH8SjnINd3WN4W1DVdU8PW17rWnDTr+XcXtef3Y3HbnPfGK2a0le+pMbW0MXxe0qeC9caHPmiwnK49dhrwb4T6f8RrjwlJJ4S1bRrWwN04eO6QmTzMLkn923GMd6+kJYknheGVQ0cilWU9weCK8HsbPxZ8F9dv0sNFn1zwxdyeYv2cEvF6ZwDtIHByMHA5qI6Sd+q/Up6xVujLXibwB8WfF+ljTdZ1rw9NbCQShV3IQwzg5EXua9e8O2E+leGtM0+6dHuLW1jhkZCSpZVAOCQOOK80Hxi1/VWFtoPw/wBVkuGON9yGCJ7nC/1FdX8Rtf1rRfCrJoOlX19q12PKj+y2zyiDI5dioOMds9/pTbcYuy3EknJHg3xX+yR+P9aHhdroQtAP7ZFt/qwdw3dO2duc8Zr6J8BLoi+CdKHh7B03yR5Z/iJ/i3f7Wc596wvhv8O7fwz4Slt9UiS41HVFLag0nzZ3D/V57gZOfUk1zPg/Tte+Gnj+68PLp+oX3hXUH8y3uYYHlW2Y9NxAIHoc+xpxXL+7/q/b/IUnze//AFbv/mUvhriX49+NJLjmdfOCZ6481R/LFe514v438LeI/CvxBHj7wnZHUElXF7ZICWPGG4HJBAB4yQRmpv8AhdmrXai3074f6xJfNwEcNtU++Ezj8qmPwRj1SsOS9+T6PUsftDtKvw5hCZ2Nfxh8em1sfriqGgaT8YT4d006br/h5LE2sZt1aM5Ee0bQf3XXGK9F8WeGk8aeC7jSLzEEtxErK2M+VKOQfwPH0ry3w9408Y/DbT08O+I/Cd9qFva5S2vLQFgU7DIBBHpyCB1FEfdck+//AAAeqi0WG+G3xE1fxvoviDxDquiTnTpoyTAzo3lq+4gARgE9etdp8Qvhra+OPs15DeyadrFmP9Hu4+eM5AIGD15BByKo+GPiL4h8VeIrW2h8GXun6Sd32i9u9wx8pICjAHXHc9ateNPGfibwrrkX2Lwncazozwhnltd3mRyZOQcBuMY6gfWm9EkC3bOLl8W/Ev4ZhP8AhKbGLXdGVgpvoT86jPdgOP8AgS8+tepI+i/EPwVnDT6XqcGCD8rD/BgR+YrzDxH4/wDEvjjQbrw9ongPVYpL1PKknu0KpGp68kAZ9yRXYaZpOufD/wCE9vZaRaR6nq9oodoBnbIWfLgcg8AnH06UPWL5gXxLlOOXwT8R/hxvbwfqqaxpKksNPuR8wHXhT/7KQT6V2Xw6+JkPjZ7rT7uxfTtasxme2bOCM4JGeRg9QenvWAnxn1hE8q5+HOvLeDgxojEE/Upn9Kd8MvC+vzeNdZ8c+IbAabNfqUhsz94AkZJHbhQOeTycU43bs9rf8MKVrXW/9XPW6KKKQzwzUljb9qmw8zHFupXPr5LYr3OvnPx7bavcftCRtoJjOqQW8c8CSHAkKJuKfiARXVXfxq1aC3e0/wCED1hNZxtEToxjD+uQuSPw/GlF+4vn+YNe+/l+RmeEcRftM+JEtuImikMgHTPyE/8Aj1dDr/xN1u88Yz+EvA+kQX1/bZFzdXTERREdeAR0zjJPXjBpvwg8E6vpNxqfinxIhTWNUYnym+9GpO4lvQk447AVzM9t4j+F3xR1jXYPD91rGj6qWYvaqWZdzbsHAOCDkc8EU7W5IS6L8Qvfmkur/A0PGdj8Ux4I1efWtX0AWAtmM8FtExcr3AJXr+NdT8EP+ST6T/vTf+jGrmPEGseMvid4fvdM03w1d6LpnktJPPeg+ZcbRlYkXA6kAZ5/x7D4P6de6V8M9Ms9QtJ7S5Rpd8M8ZR1zIxGQeelOO0r+X6il9n1f5HDfAKGM694xn2jzBcKgbuBuc4/QV7nXj3wR0XVdJ1TxW+paZeWaz3KtEbmBoxINz8ruAz1HT1r2Gkvhj6L8hv4perPD/C//ACc54k/692/9Bjr2HW9GsvEGjXWlahGZLW5QpIoOD7EHsQcGvGfFNl4h8B/GCbxnp+i3GraZfR7Zlt1LFcqAwOAcHKggkYPSu0tvHfiHW/CWp6rpHhG9gvbWSMQWt8pBuVJG/aOOgz0zzSVnTin0Vn943dVG11en3HIL4J+I/wAON7eD9VTWNJUlhp9yPmA68Kf/AGUgn0rsvh18TIfGz3Wn3di+na1ZjM9s2cEZwSM8jB6g9PesBPjPrCJ5Vz8OdeW8HBjRGIJ+pTP6U74ZeF9fm8a6z458Q2A02a/UpDZn7wBIySO3Cgc8nk4qo3bs9rf8MTK1rrf+rnrdFFFIZ4lKv/CJ/tLRSfctdet8H0LEY/8AQ0H50/wjEvjX42+JtdmHmWOnRGxhz0Ocp/IOf+BVofG3QdVuU0DX9CsLm81HTbv/AFdtE0j7ThgcKCcAr+tbHwa8N3Ph7wKj6hbyQajfzPc3CSoVdcnABB5BwM/jRBXWvS6+/b8Gwnvp1t+G/wCKRxvww1f/AIQoeOfDt42Bo7SXkIY9VAIP54Q/jWr8AtMkj8I6nr04zc6pdM249Sq5/wDZi1c38ZPC/iCLxnNqXh7Sr68i1ew+z3RtLd5NpBAOdoOMhV6+9ez+DtGHh7wdpOlbdrW9siuP9sjLfqTRG7g297Jfnr+CCWkrLa9/y/Vs+e/hXaeO7241+XwnqWl2kn2hftYvVyzHLYx8jcferuNb8H/GDxFo9xpWpa74dltLgBZECspOCD1EWRyBVXVNA8UfDDx1feJfDOlvq2iaiS11ZxAl0JOSMAE8HJBAPBwa0v8AhdWrXg8jS/h9rM143AWQMFB9yE6flS0cV+Q3dSbO5+H3h698K+CNP0XUZYZLm2DhmhYsnLkjBIB6H0rzP4BQxnXvGM+0eYLhUDdwNznH6CvZtJnvLnR7OfULcW97JCjTwr0jcjlep6GvK/gjouq6Tqnit9S0y8s1nuVaI3MDRiQbn5XcBnqOnrV3ftG32f5ojT2at3X6no/i9pU8F640OfNFhOVx67DXg3wn0/4jXHhKSTwlq2jWtgbpw8d0hMnmYXJP7tuMY719ISxJPC8Mqho5FKsp7g8EV4PY2fiz4L67fpYaLPrnhi7k8xfs4JeL0zgHaQODkYOBzUR0k79V+pb1irdGWvE3gD4s+L9LGm6zrXh6a2EglCruQhhnByIvc1694ds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None.
8
APhO_2025_1_E_1
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$. (C.1) Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$. It can be shown that the torque acting on the excess regions is equivalent to the torque acting on two point masses, each with a mass equal to $2m / 5$, positioned at the endpoints $A$ and $B$ of the polar diameter (see Figure C.1). (C.2) Given this idea, find the torque $\tau$ exerted by the Sun ring on the Earth. Express your answer in terms of $M_{E}, M_{S}, d_{SE}, R$ (the average radius), $h_{\max}$ and the angle $\alpha$. You can use that $h_{\max} \ll R$. [Part D: Angular speed of the precession of the Earth's axis] The Earth's axis of rotation moves very slowly around the $z$ axis in a conical motion. That is, it precesses. (D.1) Give an expression for the period $T_{1}$ of precession of the Earth's axis. Express your answer in terms of $M_{S}, d_{SE}$, the angular speed $\omega$ of the Earth's rotation, $h_{\text{max}}, R$ and $\alpha$. (D.2) Calculate the precession period $T_{1}$ in years. [Part E: The effect of the Moon] The value obtained in Part D is much larger than the observed value. The reason for this is that so far we have only considered the torque exerted by the Sun, and neglected the effect of the Moon. In the following calculations, assume that the Moon's orbit is in the ecliptic plane, and that the orbit of the Moon around the Earth is a circle of radius $d_{ME}$. Let us denote the mass of the Moon by $M_{M}$ and the period of precession in this modified model by $T_{2}$.
By what factor $T_{2} / T_{1}$ does the period of precession of the Earth's axis change if we also take into account the torque exerted by the Moon? Give your answer in terms of $d_{ME}, d_{SE}, M_{S}$ and $M_{M}$.
[["Award 0.3 pt if the answer explicitly states that the torques exerted by the Sun and the Moon add up. Otherwise, award 0 pt.", "Award 0.4 pt if the answer correctly calculates the torque exerted by the Moon or states that it is proportional to $M_M/d_{ME}^3$, where $M_M$ is the Moon's mass and $d_{ME}$ is the Earth-Moon distance. Otherwise, award 0 pt.", "Award 0.3 pt if the answer expresses the ratio $T_2/T_1$ correctly as $\\dfrac{T_2}{T_1} = \\dfrac{M_S/d_{SE}^3}{M_M/d_{ME}^3 + M_S/d_{SE}^3}$. Partial points: award 0 pt if the expression implies $T_1 < T_2$. Otherwise, award 0 pt."]]
["\\boxed{$T_2 / T_1 = \\frac{M_S / d_{SE}^3}{M_M / d_{ME}^3 + M_S / d_{SE}^3}$}"]
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Mechanics
APhO_2025
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None.
9
APhO_2025_1_E_2
[Precession of the Earth's axis] [Introduction] It has been known since ancient times that the Earth's axis of rotation precesses. That is, the axis itself rotates around the line perpendicular to the ecliptic plane, i.e., the plane containing the Earth's orbit around the Sun. Ancient Greek astronomer Hipparchus concluded that the annual angular displacement of the axis was approximately 45'' (seconds of arc), which would imply that the period of axial precession is around 29000 years. Modern measurements indicate that the period is approximately 25800 years. In this problem, you are asked to investigate this phenomenon using Newtonian mechanics. You may need the following constants: gravitational constant: $G = 6.67 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2}$ average radius of Earth: $R = 6.371 \times 10^{6} \mathrm{m}$ mass of the Earth: $M_{E} = 5.972 \times 10^{24} \mathrm{kg}$ average distance of the Sun from the Earth: $d_{SE} = 1.496 \times 10^{11} \mathrm{m}$ mass of the Sun: $M_{S} = 1.989 \times 10^{30} \mathrm{kg}$ average distance of the Moon from the Earth: $d_{ME} = 3.844 \times 10^{8} \mathrm{m}$ mass of the Moon: $M_{M} = 7.348 \times 10^{22} \mathrm{kg}$ Earth's axial tilt: $\alpha = 23.5^{\circ}$ [Part A: The shape of the Earth] The Sun and the Moon exert nonzero torques on the Earth because of its non-spherical shape, giving rise to its axial precession. The main reason behind the Earth's non-spherical shape is the centrifugal force caused by the Earth's rotation about its axis. The tectonic plates located on the Earth's surface have deformed over millions of years to minimize stress within them. Therefore, as an approximation, let us model the Earth as a large liquid droplet of uniform density whose shape is determined by centrifugal and gravitational forces. In this model, the Earth's surface is an oblate spheroid (ellipsoid of revolution) characterized by the polar radius $R_{p}$ and the equatorial radius $R_{e}$ (see Figure A.1). [figure1] Figure A.1. The ellipsoidal shape of the Earth. The polar and equatorial radii are indicated. $\alpha = 23.5^{\circ}$ is the angle between the Earth's axis of rotation and the normal of the ecliptic plane. The difference between the equatorial and polar radii of the Earth, $h_{\max} = R_{e} - R_{p}$ is much smaller than the average radius $R = (R_{e} + R_{p}) / 2$. Up to a dimensionless factor, the value of $h_{\max}$ can be expressed in terms of the angular speed of the Earth's rotation $\omega$, its mass $M_{E}$ and average radius $R$ as $h_{\max} \propto G^{-1} \omega^{\beta} M_E^{\gamma} R^{\delta}$ where $G$ is the gravitational constant, and $\beta, \gamma$ and $\delta$ are constant exponents. (A.1) Find the values of exponents: $\beta$, $\gamma$, and $\delta$. (A.2) Calculate the numerical value of $h_{\text{max}}$ in $km$ assuming that the dimensionless factor in the relation given above equals 1. Regardless of whether you were able to find $h_{\text{max}}$ in part A.2., use the empirical value $h_{\text{max}} = 21 \mathrm{km}$ in the following questions. [Part B: The time-averaged gravitational field of the Sun] To see why the Sun exerts a nonzero torque (with respect to the center of the Earth) on our planet, consider Figure B.1 below. The difference in distance from the Sun causes the gravitational force $F_{1}$ to be greater than its counterpart $F_{2}$. [figure2] Figure B.1. Explanation of the nonzero torques exerted by the Sun (right side of the figure) on the Earth (left side). The magnitude of this torque acting on the Earth varies continuously during the year. In the position shown in Figure B.1, the torque is maximal, a quarter of a year later, due to symmetry, the torque becomes zero. After half a year, it reaches the maximum again, three-quarters of a year later it is zero once again, and so on. Since the period of axial precession is much larger than one year, this time-dependent torque can be approximated well by its one-year average. To calculate the average torque exerted by the Sun on the Earth, let us determine first the time average of the gravitational field generated by the Sun in the vicinity of the Earth. This average can be calculated as the field of a uniformly dense mass ring, a Sun ring, whose mass equals the mass of the Sun $M_{S}$ and whose radius equals the average distance between the Sun and the Earth $d_{SE}$ (see Figure B.2). [figure3] Figure B.2. Time averaging is equivalent to uniformly spreading the Sun along the circle of radius $d_{SE}$. Let our cylindrical coordinate system have the origin at the center of the Earth, and let the $z$ axis be perpendicular to the ecliptic plane (i.e. the plane of the ring). The axis of rotation of the Earth makes an angle of $\alpha = 23.5^{\circ}$ with the $z$ axis. (B.1) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point on the $z$ axis. Write your answer in terms of $M_{S}, d_{SE}$, and the coordinate $z$. Assume that $|z| \ll d_{SE}$. (B.2) Find the direction and magnitude of the gravitational field generated by the Sun ring at a point in the ecliptic plane whose distance from the origin is $r$. Assume $r \ll d_{SE}$. [Part C: The torque acting on the Earth] In this section, you are asked to determine the torque exerted on the Earth due to the gravitational field obtained in Part B. For simplicity, consider the Earth as a rigid body with homogeneous mass distribution. Let us take into account that the rotational ellipsoid can be imagined as if we removed excess parts from a sphere with the equatorial radius of Earth $R_{e}$ (see Figure C.1). [figure4] Figure C.1. The ellipsoidal shape of the Earth can be imagined as if the excess parts were removed from a complete sphere of radius $R_{e}$. (C.1) Find the mass $m$ of one of the two excess regions indicated in Figure C.1. Express your answer in terms of $h_{\text{max}}$, the mass of the Earth $M_{E}$, and its polar radius $R_{p}$. It can be shown that the torque acting on the excess regions is equivalent to the torque acting on two point masses, each with a mass equal to $2m / 5$, positioned at the endpoints $A$ and $B$ of the polar diameter (see Figure C.1). (C.2) Given this idea, find the torque $\tau$ exerted by the Sun ring on the Earth. Express your answer in terms of $M_{E}, M_{S}, d_{SE}, R$ (the average radius), $h_{\max}$ and the angle $\alpha$. You can use that $h_{\max} \ll R$. [Part D: Angular speed of the precession of the Earth's axis] The Earth's axis of rotation moves very slowly around the $z$ axis in a conical motion. That is, it precesses. (D.1) Give an expression for the period $T_{1}$ of precession of the Earth's axis. Express your answer in terms of $M_{S}, d_{SE}$, the angular speed $\omega$ of the Earth's rotation, $h_{\text{max}}, R$ and $\alpha$. (D.2) Calculate the precession period $T_{1}$ in years. [Part E: The effect of the Moon] The value obtained in Part D is much larger than the observed value. The reason for this is that so far we have only considered the torque exerted by the Sun, and neglected the effect of the Moon. In the following calculations, assume that the Moon's orbit is in the ecliptic plane, and that the orbit of the Moon around the Earth is a circle of radius $d_{ME}$. Let us denote the mass of the Moon by $M_{M}$ and the period of precession in this modified model by $T_{2}$. (E.1) By what factor $T_{2} / T_{1}$ does the period of precession of the Earth's axis change if we also take into account the torque exerted by the Moon? Give your answer in terms of $d_{ME}, d_{SE}, M_{S}$ and $M_{M}$.
By substituting the data, calculate the period of precession $T_{2}$ in years.
[["Award 0.2 pt if the answer gives the correct numerical result for the precession period $T_2 \\approx 25400$ years, obtained by substituting values into a dimensionally correct formula. Partial points: award 0 pt if the result does not come from explicit substitution (e.g. if it is taken from the introduction), if the substitution is incorrect, or if the formula has a dimensional error."]]
["\\boxed{25400}"]
["Numerical Value"]
["years"]
[0.2]
text+variable figure
Mechanics
APhO_2025
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None.
10
APhO_2025_2_A_1
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass.
It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$.
[["Award 0.1 pt if the answer gives the correct result for the angular momentum of the planar loop, $\\vec{L} = M R^2 \\vec{\\omega}$, where $M$ is the mass, $R$ the radius, and $\\vec{\\omega}$ the angular velocity (Award 0.1 pt if only the magnitude is given in the answer). Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct result for the magnetic dipole moment, $\\vec{\\mu} = \\frac{Q}{2} R^2 \\vec{\\omega}$, where $Q$ is the charge (Award 0.1 pt if only the magnitude is given in the answer). Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct result for the gyromagnetic ratio, $\\gamma = \\frac{Q}{2M}$. Otherwise, award 0 pt."]]
["\\boxed{$\\gamma = \\frac{Q}{2M}$}"]
["Expression"]
[null]
[0.3]
text-only
Electromagnetism
APhO_2025
None.
11
APhO_2025_2_A_2
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1.
Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$.
[["Award 0.1 pt if the answer writes the torque equation for a magnetic dipole correctly as $\\vec{\\tau} = \\vec{\\mu} \\times \\vec{B} = \\dfrac{d \\vec{L}}{dt}$, where $\\mu$ is the magnetic dipole moment, $\\vec{B}$ the magnetic field, and $\\vec{L}$ the angular momentum. Otherwise, award 0 pt.", "Award 0.1 pt if the answer notes that only the perpendicular component of angular momentum, $L \\sin \\theta$, changes during precession. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct magnitude of the Larmor frequency as $|\\omega_L| = \\frac{\\mu}{L} B$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct sign for the Larmor frequency, $\\omega_L = - \\frac{\\mu}{L} B = - \\gamma B$, where $\\gamma$ is the gyromagnetic ratio. Otherwise, award 0 pt."]]
["\\boxed{$\\omega_L = -\\gamma B$}"]
["Expression"]
[null]
[0.4]
text+illustration figure
Electromagnetism
APhO_2025
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None.
12
APhO_2025_2_A_3
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2.
The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants.
[["Award 0.1 pt if the answer writes the interaction energy correctly as $U = - \\vec{\\mu}_2 \\cdot \\vec{B}_{1 on 2} = - \\frac{\\mu_0}{4 \\pi d^3} \\mu_1 \\mu_2 \\cos(\\pi - \\theta)$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct magnetic field magnitude, $|\\vec{B}_{1 on 2}| = \\frac{\\mu_0}{4 \\pi d^3} \\mu_1$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct magnetic field direction (with the correct minus sign in $\\vec{B}_{1 on 2}$). Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes the correct magnitude for $J_0$ as $J_0 = \\frac{\\mu_0 \\gamma^2}{4 \\pi d^3}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct sign for $J_0$ in the expression $U = J_0 \\vec{L}_1 \\cdot \\vec{L}_2$. Otherwise, award 0 pt."]]
["\\boxed{$J_0 = \\frac{\\mu_0 \\gamma^2}{4 \\pi d^3}$}"]
["Expression"]
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[0.5]
text+illustration figure
Electromagnetism
APhO_2025
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4k/652/8AOSvoTtQAtHeijvQAUdqKTtQAtHeijvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6SjvQAtFJRQAtFJS0AHejtSd6O1AC9qO9J2o70ALRRSUALRSUUAL3opO9FAC9qKTtRQAveijvSUAL2opO1FAC96KO9FAB2opO1LQAd6KTvRQAvaik7UUAL3oo70lAC9qKTtRQAveik70UALRSUUALR3pKO9AC9qO1J2o7UAL3o70d6O9AB2oo7UlAC96O9HejvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6Sl70AFHako7UALR3pKXvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6SjvQAtFJRQAtFJRQAveik70UAMuFLW0qgEkoQB+FeQfAHw9rHh/TtbTV9MurFppYjGLiMpuADZxn617FRmgBe9Hak70dqAF7UUnaloA4b4hfD5vGD6dqOn339n61pknmWtwU3KeQ2GH1AIPbng5rI1PwF4w8aeRaeMNfsYtJiYPJaaTE6m4I6bmfp+o9u9en0UAVtO0600nTrewsIEgtYECRRoOFAq1SUUAL3opO9FAC9qKTtWfrOu6V4fsTeatfwWduP4pXxk+gHUn2HNAGj3orwHxd+0RkvaeErHcT8ovbtf1SP8Aq35V7npiXMelWaXkhlulgQTSEAFn2jceOOTmgC32opO1FAC96KTvS0ALRR2ooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/wCRf0P/AK+n/wDQK9vrxD9pT/kX9D/6+n/9AoAy/wBmj/j78Sf9c7f+clfQfavnz9mj/j78Sf8AXO3/AJyV9B9qAFo70Ud6ACjtRR2oAKO9FHegBKO1FHagApe9JS96AEo7UUdqACl70lL3oAKSlpKAClpKWgA70dqO9HagA7Ud6O1HegApKWkoAKWkpaADvSUvekoAXtRR2ooAO9FHeigBO1LSdqWgA70Ud6KADtRR2ooAO9FHeigBO1FHaigBe9JS96SgA7UUdqKAF70Ud6KAEooooAWjvRR3oAO1J2pe1J2oAXvR3o70d6ADtSUvakoAXvR3o70d6AEpe1JS9qACjvRR3oASjtRR2oAKXvSUvegBKXtSUvagAo70Ud6ACjtRR2oASl70lL3oASjtRR2oAKXvSUvegApKWkoAKWkpaADvSUvekoAZOxS3kZTyqkj8q+ePh/Yar8UF1PULnWHtLmCRBIQmRIWBOQAQF6dK+hrn/j1m/wBw/wAq8O/Zq/5BfiH/AK7Q/wDoLVcJyg7xM6lKNRWkb/8AwqzxBBzbeKnB7cyJ/JjSf8In8SNP5tfEIuAOim5Zv0dcV6x3o7Vft59bP5GX1Sn0uvmzyb+3fifo3N5pS3qDqRCHyP8Atkas2fxihjl8nWNGuLaQcMYm3Y/4C2CPzNen9qq3um2OpReVe2cFwnpLGG/nR7SD+KP3B7GpH4J/fqZekeM/D+tkLZ6nCZT/AMspDsf8mxn8K3s1wWr/AAl0C/DPYmbT5T08tt6Z/wB0/wBCK546d8QfBHzWc51XT0/5ZjMgA/3T8w/4DxT9nCXwP7xe1qw/iRv5r/I9epa4Dw/8VtJ1Jlt9UQ6bdZwTIcxk/wC92/H8671JEkRXjcMjDIZTkEVlKEoO0kb06kKivF3Hd6Sl70lSWeU/F74geKfBsKR6TpCpaTDA1V/3iqx/h29FPu2QfSvmfVta1PXr5r3Vb6e8uG/jmctgeg9B7Divqn4w+N7Hwr4UlsnjhutQ1FGihtpVDqF6F2U9h29Tj3r5U03SdR1meSDTbKe7ljjaV0hQsQi9TgUAaPgjTf7Y8c6HYFdyTXsQcf7AYFv0Br7fr5R+AmmG++J0M7LxY20s5z2JGwf+h19XUAHalpO1LQAd6KO9FAC0UUUAFFFFABRRRQAUnelpO9AB2o7Unal7UAHeijvRQAUUlFAC0d6KO9ABR2pKO1AC14f+0p/yL+h/9fT/APoFe314h+0p/wAi/of/AF9P/wCgUAZf7NH/AB9+JP8Arnb/AM5K+hO1fPf7NH/H34k/652/85K+g+1AC0d6KO9ABR2oo7UAFHeijvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6Sl70AFFFJQAtFJS0AHejtR3o7UAHajvR2o70AFFFJQAtFJS0AHeijvSUAL2oo7UUAHeijvRQAdqKTtS0AHeijvRQAdqKO1FAB3oo70UAHaik7UUAL3oo70lAC9qKTtRQAveijvRQAUUlFAC0d6KO9AB2o7UdqTtQAvejvR3o70AHaijtSUAL3o70d6O9ABR2pKXtQAUd6KO9ABR2pKO1AC0d6Sl70AFHakpe1ABR3oo70AFHaijtQAUd6Sl70AFHako7UALR3pKXvQAUUUlAC0UlLQAd6KO9JQAMoZSrDIIwRWRoPhbQ/C8c0ei6dFZJOQ0gjJ+YjOOpPqa1nYRxs56KMnFct4J+IGkePYLybSYruNbRlWT7SiqSWBIxhj6UAdX3o7Ud6O1AB2oo7UUAFJS0lAHO+IvBGieJEZrq2EdyRxcw/K/4/wB78a8+ksvF/wANJDNZyf2jowOWXBKqPdeqH3HHrXsdBAYYPINawquKs9UYVKEZPmWj7o5vwt430rxTEBbv5N4Bl7aQ/MPcf3h7j9KueKPEth4T8P3WsajJthhX5UH3pHPRF9yf8egrjvGPw6tgJdb0KZdNu4AZnUP5cZxyWB/gP6fTrXhnxC8Uaz4rsdPmvb6OW0tV2qifKHY/xnsWxx7Y9zTlTi1zQJhVlGXJVWvfozm/EGuat458VSX9wrzXt3II4YI8naCcLGg9Ofx696+pvhd8PoPAnh0LMqPq10A93KOcHtGp9B+pyfTHEfAv4a/YbePxbq8OLmZf9Aicf6tD/wAtD7kdPbnvx7jWJ0mPYeFdG0zxDea3Y2SQX15GEuGj4D4Oc46ZJ6nvWzR3rzrVfjL4d0fVrvTbix1h5rWVoXaK0DKSpwcHdyKAPRO1LXhnjL4p6F4j0iOLT5vEumahbSi4tp4bXC+YAcBxu+ZTn/8AX0PYfCf4iyePdInW8tTDqNjsWd0H7uXdnDL6H5Tkf48AHofeijvRQAtFFFABRRRQAUUUUAFJ3paTvQAnal7Unal7UAHeijvRQAlFFFAC0d6KO9ACUdqKO1ABXiH7Sn/Iv6H/ANfT/wDoFe314h+0p/yL+h/9fT/+gUAZf7NH/H34k/652/8AOSvoPtXz5+zR/wAffiT/AK52/wDOSvoPtQAtHeijvQAUdqKO1ABR3oo70AJR2oo7UAFL3pKXvQAlHaijtQAUvekpe9ABSUtJQAUtJS0AHejtR3o7UAHajvR2o70AFJS0lABS0lLQAd6Sl70lAC9qKO1FAB3oo70UAJ2paTtS0AHeijvRQAdqKO1FAB3oo70UAJ2oo7UUAL3pKXvSUAHaijtRQAveijvRQAlFFFAC0d6KO9AB2pO1L2pO1AC96O9HejvQAdqSl7UlAC96O9HejvQAlL2pKXtQAUd6KO9ACUdqKO1ABS96Sl70AJS9qSl7UAFHeijvQAUdqKO1ACUvekpe9ACUdqKO1ABS96Sl70AFJS0lABS0lLQAd6Sl70lAEdz/AMes3+4f5V4d+zV/yC/EP/XaH/0Fq9zlTzIXQHG5SM/hXn/wr+Hd38PrTUobu/huzdujqYlK7doI5z9aAPQ+9HajvR2oAO1FHaigApKWkoAKWkrzX4v/ABHXwXon2GwlH9tXqERY5MCdDIffsPf6UAcJ8dfiT58knhDSJ/3aH/iYTIfvMP8AlkD6D+L347GuZ+Dnw6k8YaqNS1NGOhWMmSjfdnl67B7dC34DvxyXgvwjqHjrxRFptsWwx8y6uW58pM/Mx9T6epNfZOiaNY+H9GttK06ERWtsgRFHU+pPqSeSfU0AXwoVQqgADgAdqKO1FAC96SsTxlqx0PwZrOphtr29pI0Z/wBvaQv/AI8RXm/7PQ1G78O6tquoXt1c+dcrBF58zPgIuSRk9y/6UAeg+MtA1LxLpEem2GsPpkMsoF48SZkkhwdyKf4SeOf/ANRv6B4f0zwxpEOmaTapb20fYdWPdmPcn1ry/wDaF8QXWk+HNJsbK7mtp7q6aQvDIUYoi4IyO2XX8q9E8D2dxYeB9Et7uWWW5FpG8zysWYuw3NknnqSKAOg70Ud6KAFooooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/5F/Q/+vp//QK9vrxD9pT/AJF/Q/8Ar6f/ANAoAy/2aP8Aj78Sf9c7f+clfQfavnz9mj/j78Sf9c7f+clfQfagBaO9FHegAo7UUdqACjvRR3oASjtRR2oAKXvSUvegBKO1FHagApe9JS96ACkpaSgApaSloAO9HajvR2oAO1HejtR3oAKSlpKAClpKWgA70lL3pKAF7UUdqKADvRR3ooATtS0naloAO9FHeigA7UUdqKADvRR3ooATtRR2ooAXvSUvekoAO1FHaigBe9FHeigBKKKKAFo70Ud6ADtSdqXtSdqAF70d6O9HegA7UlL2pKAF70d6O9HegBKXtSUvagAo70Ud6AEo7UUdqACl70lL3oASl7UlL2oAKO9FHegAo7UUdqAEpe9JS96AEo7UUdqACl70lL3oAKSlpKAClpKWgA70lL3pKACgMD0IP0qO5/49Zv8AcP8AKvD/ANmti2l+IMkn99D1/wB1qAPde9HajvR2oAO1FHaigApKWoLu7t7CynvLuVIbeBDJJI5wFUDJJoAxvGXiyx8F+G7jV74g7BthhBw00h+6o/qewBNfHeoX2seOPFbXEoe71PUJgqRoO54VVHYAcfQVt/Ezx9ceO/EbTqXj0y2JSzhPZe7kf3m/Tgdq9k+CHw2/sKwTxNq0GNSuk/0aJxzBEe/szD8hx3NAHafDjwJa+BPDaWa7JNQnxJeTgfff+6P9leg/E967Cl70lAB2oo7UUAeV/tAar9g+HBs1bD391HCR/srlz+qj863/AISaT/Y/ww0SErh5oftL+/mEuP0IH4V5T+0jqhn1zRdIjyfs9u9y6j/bOBn6CM/nXX2Xxe0278O6dpHhG0uNQ8QSW6QRWfksqQMFA3SMeNq+xPTqOtAHG/F2dPFvxl0Tw3C++OAw20oH8LSPuf8AJSv5V7/rOpw6FoV7qk0bPDZW7zskYGSqqTgZ47V8yaa1p4E+OyS+J72R1tSZbm7ZGffK8JJfABON78YHpX0P4W8SQeN9Iubv+ybiDTnkaKE3iDF1Hj74X+6eRz/jgA4/RPHXjzxpYPqfhvw3pdpp24rFJqVy5M2ODtCgd+PTPerHgf4pXWueKbrwp4h0ldN1uDdgRvuRyvJHPQ45HJBH69/NLp2g6VJNJ5FlYWsZdiAESNRyeB0rxf4c6fdeNfizqnxD+zvb6UjvHaFxgzHYIx+SjJ9zj1oA92ooooAKKKKACiiigApO9LSd6AE7UvajtR2oAO9FHeigBKKWigAo70Ud6AEo7UtHagBK8Q/aU/5F/Q/+vp//AECvcK8P/aU/5F/Q/wDr6f8A9AoAy/2aP+PvxJ/1zt/5yV9B9q+fP2aP+PvxJ/1zt/5yV9CdqACjvRR3oAKO1FHagAo70Ud6AEo7UtHagBKXvRR3oASjtS0dqAEpe9FHegApKWigBKWiigA70dqO9HagA7Ud6O1HegApKWigBKWiigA70lL3ooAO1FHaigA70Ud6KAE7UtHaigA70Ud6KADtRR2ooAO9FHeigBO1FL2ooAO9JS96KAE7UUvaigA70Ud6KAEopaKACjvRR3oAO1J2pe1HagA70d6O9HegA7UlL2ooAO9HejvR3oASl7UUdqACjvRR3oASjtS0dqAEpe9FHegBKXtRR2oAKO9FHegAo7UUdqAEpe9FHegBKO1LTXdY42d2CooyWJwAPWgBaXvXkvin46aRpUz2uiWx1OZDgzF9kIPserfhgehrh3+M3jvU5CbC2t0H922tGkx+ZNWoNmbqxR9JUlfNv/C1/iPZ/PcQfKOvnaftH6AVfsP2gtZiYDUdGsrhR18h2iP67qPZsXton0HS15ho/wAdPCuoFUvku9NkPUyx70/Ncn8wK9B0zWdM1qDz9Mv7a7i7tDIGx9cdPxqWmty1JPZl7vSUveikURXAJtZQBklD/KvGP2ddOvtP03XlvbK4ti80JUTRMm75W6ZFe2UUAHejtR3o7UAHaijtRQAlfNvxy+JP9rXj+FdInzY27/6ZKh4mkB+4P9lT19T9K7v40fEn/hFdKOi6XNjWL1DudTzbRHgt7Meg/E+mfBfh94IvPHfiWOwi3R2keJLy4A/1aZ/9CPQfn0BoA7H4KfDb/hJNSXxDqsOdJs3/AHMbji4lH81Xv6nj1r6gqrpmm2mj6ZbadYQrDa26COONegA/z1q3QAd6Sl70UAJ2ope1FAHgWjXsfiP9p6/lYLJBZxzQIrDIwkflsPzLfnXt9ho+maWXOnabZ2Zk+/8AZ4Fj3fXAGa5zQ/hn4e8PeLLrxHYLcre3HmbkeXdGu85bAxn9e9djQBmX/h3RNVuo7rUdHsLu4jGElnt0dlHoCRmtAlIYskqkaDJJ4CgU/tWdrukRa/oV5pM9xcQQ3cZikkt2CuFPXBII5HHTvQB5Hc3F18aPEslpHcNaeCNNmxK6tta/kHYe38hz1Ix6YNc8PeHr/SPDMDxQzXStHZ2sC5Cqgyc4+6Mdz15rgP8AhnLwl/0E9b/7/Rf/AButfwx8E/DnhTxHaa3ZX2qS3NqWKJPLGUO5SpyAgPRj3oA9KooooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/wCRf0P/AK+n/wDQK9vrxD9pT/kX9D/6+n/9AoA4v4OeIpvCkOp3UFib5rzYjIGK+Xs3YPAPXd+lepf8LZv8f8i1J/39b/4iuM/Zo/4+/En/AFzt/wCclfQmOOlAHl3/AAtm/wD+hak/7+t/8RR/wtm/z/yLUn/f1v8A4ivUse1GOelAHlv/AAtm/wD+hak/7+t/8RR/wtm/x/yLUn/f1v8A4ivUce1GOOlAHlr/ABbvUXc/hxlUdSZmAH/jld34Y1z/AISPQYNTMHkGUsDHu3YwxHXA9KqePB/xQ+q/9cR/6EKpfDH/AJEWy/35f/QzQB19HaijtQAUvekpe9ACUdqKO1ABS96Sl70AFJS0lABS0lLQAd6O1HejtQAdqO9HajvQAUlLSUAFLSUtAB3pKXvSUAL2oo7UUAHeijvRQAnalpO1LQAd6KO9FAB2oo7UUAHeijvRQAnaijtRQAvekpe9JQAdqKO1FAC96KO9FACUUUUALR3oo70AHak7Uvak7UAL3o70d6O9AB2pKXtSUAL3o70d6O9ACUvakpe1ABR3oo70AJR2oo7UAFL3pKXvQAlL2pKXtQAUd6KO9ABR2oo7UAJS96Sl70AJXiPxz8ZXELw+FbCRl81BLeFDywP3Y/6n14r26vmvU0Gq/tECO5+ZP7UjUg9CEC4H/jtXBa3M6r0sup3/AMP/AIP6ZpOnwah4gtUvNTkUP5Eo3RwZ/h29Gb1J/D1PqUUMcEaxwxpHGvAVFwB+Ap/al71Lbe5UYqKshMVm6h4e0bVlI1DSrK6z3mgVj+ZGa06SkVY821n4H+E9SDNZpcabKehgk3Jn3Vs/oRXneqfBrxf4buPtugXn2zZyr2shhmH4Z/kTX0bRVqbRm6cWfOmjfGXxX4auvsHiOza8WPh1uEMM6/jjn8R+NeveFviR4b8WBY7K9EN43/Lrc4STPt2b8Ca2ta8OaR4itfs2rafBdR9i6/Mv+6w5H4GvHPFXwGmh33fha8L4+YWly2GH+6/T88fWn7svIm047anuczlIJHHVVJGfpXnHwg+IGr+PbLVZtWhtI2tJI1j+zRsoIYMTnLH0rzXSPid4u8Ezvo/iG2nuoUUqYbvKzIOmVc9R9cj0Irb/AGa7iFbPX7cyoJ2kidYyw3FQGyQOuKmUWi4zUj3rvR2o70dqksO1cv498aWXgbw1LqVzh7hvktbfPMsnYfQdSfT8K3dT1K00fTLjUb+ZYLW3QySSN0AH+elfHHxB8b3njzxNJfy7o7SPMdnbk/6tM/8AoR6n8ugFAGb/AMTnxx4r/jvNV1Kf8yf5KB+AA9q+vPAfguz8DeGotMtsSXDfPdXGOZZO5+g6Aen41yHwX+G3/CK6T/bWqQ41i9T5UYc28R5C+zHqfwHrn1agApaSloAO9JS96SgA7UUdqKAF70lL3pKADtS0naloAO9FHeigBaKKKACiiigAooooAKQ9aWk70AJ2o7UvajtQAneil71zWveP/DHhssmo6tCs6/8ALCI+ZJn3Vc4/HFCVxNpbnSUV4lrP7QcKFk0TRnk9JbyTaP8Avhc/+hCuXPxA+J3ixiulpdLE3bT7TCj/AIGQSP8AvqrVNkOrHofSjMqKWZgAOpJ6Vj3vi/w3pxIu9d06Jh1VrlN35ZzXgi/C34j+ImD6rM67ud2oXxc/kCxFbVl+zzeNg33iCCP1WC3L/qSv8qfLFbsXPJ7I9Duvi74Htcg62sjDtFBI36hcVlT/AB28HxZ2LqM3/XO3A/8AQmFZ9r+z94fQD7VqupTH/pmUQH/x01rQfBDwXEPntrub/rpcsP8A0HFHuB+8MqT9oHw6P9XpeqN/vLGP/ZjXmnxb+JVj450zTra0sLi2NtM0haZlOQVx2r2+P4QeBY+mhBj6tczH/wBnryz47+D9A8NaJpEuj6bHaSS3Dq7KzEsAucck0ny20GlO+py3wi8f2fgSfVnu7Ke5F2sQXyiBt2luuf8Aer1eP9oHw8f9ZpWpr/uiM/8AswrgPgL4W0XxNca8us2CXYgSAx72Ybcl89CPQV7LJ8IvAsg50FR/u3Mw/k9JONtQkp30MeD48eEJcb49Sh/34FP8mNatt8YPA9yQP7Z8pj2lt5F/Xbiqk/wS8FS/ctLqH/rncsf/AELNZNz+z/4ckybbU9ThP+2yOB/46P50/cF+8O+svGnhjUMC11/TZGPRftKhvyJzW0kiSIHR1ZT0KnINeFXv7PNwMmx8QxP6LPbFf1DH+VYb/CT4haA5k0qdZCOd1hemM/8Aj22nyxezDnmt0e4+PP8AkR9V/wCuI/8AQhVL4Y/8iLZf78v/AKGa8Vn1z4kWELaVr41H7BONkhu7fcCOvEmM9vWt7wx8YLbwnbJol/pUstvESwuIJBu+Y7vunA7+tS4O9kUqitdnvdHauU0H4keFPERWOz1WKOdukFx+6fPoAeD+BNdXnipasUmnsFL3oo70DEo7UtHagBKO9LR3oASilooASloooATvR2pe9HagBO1Hel7Ud6ACkpaKAEopaKAE70UveigBO1FL2ooAO9JS96KAE7UUvaigA70Ud6KAE7UtHaigBO9FL3ooATtRS9qKADvSUveigBO1FL2ooATvRS96KAEopaKAEo70tHegBO1Hal7UdqADvR3o70d6ADtSUvaigA70d6O9HegBKO1LR2oASl70Ud6AEo7UtHagBKXvRR3oASjtS0dqAEpe9FHegBKO1LR2oASl70Ud6AEr5q8dt/wjPxzTUn+WH7Vb3mfVPl3fqGr6WrxX4/8Ah9prHTvEEKZMDG2nI/utyh+gO4f8CFXB6mdVe7c9pBBUEHINHeuM+FviQeJPAljI77rq0X7LOM87lAAP4rg/ia7TvUtWdi07q4lFLRSGJRS0UAJ3ope9FAGTr/hrSPE1ibTV7GK5j/hLDDIfVWHIP0rwjxN8GdZ8I3J1bwncXF1DEd4EbEXMOPTH3vw59q+i3YIjM3RRk1geFvG2heNIrmXRLl50tmVZS8TJgnJH3gM9DVKViZRUkeW+Cfjg6OmneLVOQdov0Tkf9dFH8x+XevbbW6t721jubWeOaCRdySRsGVh6giuI8cfCvRvF6yXUSrY6rjIuY14kP+2vf69f5V8+atq3iv4dT6n4WXUGgEybJo4pA6bWH3l/ukj6HB+lN8rV0RHmTs9Tf+NfxJ/4STUj4f0qfOk2b/vZEPFxKP5qvb1PPpV74G/Db+1rxPFWrwZsbd/9CiccTSA/fP8AsqenqfpXD/DPwNJ478UJZu/l2FuBLdyA4bZn7q+56e3Jr7Es7S30+zgs7SFIbeBBHHGgwFUDAAqDUmopaKAEopaKAE70UveigBO1FL2ooAO9JS96KAE7UUvaigBO9LR3ooAXtRRRQAUUUUAFFFFABSd6WkPFACdq4bxl8VNB8I77beb7Ul4+ywMPkP8Att0X6cn2rgviT8Wrm6u5PD3hSV8bvKlvIeXkbpsjx27ZHJ7epf4G+CBlWPUvFpfLfOtgjYP/AG0YfyH59qtRSV5GTm27QOZu/GHxB+JN29npUdwlsTgwWIKIo/25D/Uge1dF4f8A2f5pAs3iHVRHnk29mNzfi7DH5A/Wvb7GwtNMtI7Sxtora3jGFjiQKo/AVZoc+wKkt5anJ6L8NvCWhBTa6NBJKv8Ay1uR5rZ9fmzj8MV1SqqKFUAAcAAdKWipbbNEktgpe9FHekMSjtRR2oAK8Q/aU/5F/Q/+vp//AECvb68Q/aU/5F/Q/wDr6f8A9AoAy/2aP+PvxJ/1zt/5yV9B9q+fP2aP+PvxJ/1zt/5yV9B9qAFo70Ud6ACkpaO1AHOePP8AkR9V/wCuI/8AQhXIeEfAvhvxP4ItJdU0uGW4ZpAZ1yknDnHzLgnHvXX+PP8AkR9V/wCuI/8AQhVL4Y/8iLZf78v/AKGaL2E0nuefeIP2flIeXw9qpB6i3vRkfg6j+Y/GuUh134ifC+4SC9W4+xg4WK6/ewOPRWB4+gI+lfTdRXNtb3ls9vcwxzQyDDxyKGVh6EHrVqb6mbpLeOhwHg34v6F4naO0uz/ZmotgCKZv3ch/2X/ocH616L3rxbxx8D7a4SS/8K4gnHzNYu3yP/uE/dPsePpWJ8P/AIp6h4b1BfD3iszG1R/KEswPmWp6YbPJX9R9OKbimrxBTcXaR9B0dqSN1kjV0YMjDKsDkEeope1ZmoUvekpe9ABSUtJQAUtJS0AHejtR3o7UAHajvR2o70AFJS0lABS0lLQAd6Sl70lAC9qKO1FAB3oo70UAJ2paTtS0AHeijvRQAdqKO1FAB3oo70UAJ2oo7UUAL3pKXvSUAHaijtRQAveijvRQAlFFFAC0d6KO9AB2pO1L2pO1AC96O9HejvQAdqSl7UlAC96O9HejvQAlL2pKXtQAUd6KO9ACUdqKO1ABS96Sl70AJS9qSl7UAFHeijvQAUdqKO1ACUvekpe9ACVna9o9t4g0G90q6H7m6iMZOOVPZh7g4P4Vo0dqAPmr4b65c/D74hXOhasfKt7iT7LcZPypID8j/Tnr6NmvpWvGvjh4IN7Zr4osIsz26hLxVHLR9n+q9D7fStz4QeOh4m0IaZfS51WwQKxY8zRdA/uR0P4HvWkveXMjGD5XyM9KpKKKzNgpaSloAO9JS96SgCO5/wCPWb/cP8q8O/Zq/wCQX4h/67Q/+gvXuUyGSCRB1ZSBn6V5P8OvDNz8IvDWvX/ii7s1t2KShrdy3CgjHIHJJAA70AdX8R/Hdr4E8NveNtkv58x2cB/jf+8f9lep/Ad6+TNPsNY8ceK0t4i93qeoTFnkc9zyzMewA5+gq3408W6h468US6lchsOfLtbZefKTPyqPU+vqTX0d8IPhwvgzQ/t1/EP7bvUBlJ5MCdRGPfuff6CgDy/xF8NvEPwynh1rRLyWe2hwzXcK7XibvvXn5T+I7H39Q+HfxYs/FSx6bqnl2msYwoziO4919G/2fy9vSXRXQo6hlYYIIyCK8M+I/wAHmgaTW/CkTDafMlsY+q990X/xP5elaJqSszKSlF80T3SivFfhn8X/ALQ0WheKJts/CQX0hxvPZZPQ/wC13788n2rtUOLW5cZKSugpaSlpFB3pKXvSUAHaijtRQAvekpe9JQAdqWk7UtAB3oo70UALRRRQAUUUUAFFFFABXmnxp8WS+HvCqWNpIY7zUy0QYHBWMD5yPfkD8TXpdfPf7Qvmf8JHpGc+V9kbb/vbzn/2WqgryM6jtFm/8FfAMFppsfinUYg93cA/Y1cf6qPpv+rdvb617H2rO8PiEeG9LFtjyPskXl46bdgx+laXalJ3ZUYpKyDvRR3opFCUUUUALR3oo70AJR2oo7UAFeIftKf8i/of/X0//oFe3145+0LpWo6poOjrp9hdXZjuXZxbwtIVBXAJwDigDn/2aP8Aj78Sf9c7f+clfQfavk34fa54w+HsuoPZ+Er26N6sYYTWsw27d2MYH+1Xsfw++IfijxT4ik0/WfDD6ZarbtKJzFKuWBUBcsMdz+VAHqFHeivD9T+L/jmz1a8tYPBEk0MM7xxyfZ5zvUMQDwMcgUAe4Udq8FHxn8fE4/4QOT/wHn/wr3lSSoJ6kUAc748/5EfVf+uI/wDQhVL4Y/8AIi2X+/L/AOhmsH4r+JNZ082+iWOizXllfwH7RcRQySGLDcY2gjt3rhtK+JPjDwzp6aXp3g25u7aIkrLLazqx3HJ4x6mgD6Go7Vynw98S6t4q8Oy3+s6U2mXK3DRCAo65UKpDYbnqT+VaXizVr3Q/C1/qWnWZvbu3QNHbhS3mHIGMDnv2oA2a8v8AjD4Bg13RZtcsYguqWUZd9o/18Q6g+pA5H0x6Y5b/AIXR4+/6EOT/AMB5/wDCug8FfErxT4l8SR6ZrXhRtPsJIpGkuHhlULhScEsMc007O5MoqSsxnwK8WS6po1xoF3IXm08BoGY8mE8Y/wCAn9GA7V652r5t+B2R8SLj7Pnyfscuf93cuP1xXVeIPiz410rxFqOn2fguS5tba4eKKcQTHzFBIDZAxz7VU1Zk0neJ7RS968F/4XR4+/6EOT/wHn/wr3GwnkutOtbiaPy5ZYkd0xjaSASOfSoNCzSVwfxJ8aa/4Q/s3+w9BbVftPmebtjkfy9u3H3PXcevpXBf8Lo8ff8AQhyf+A8/+FAHvNLXF/DnxZrXi3S7y51vRm0uaGYRxxlHXeu0HPze9dF4gv7nS/Duo6hZ2xubm2tnligAJ8xlUkLgc8n0oA0u9HavBf8AhdHj7/oQ5P8AwHn/AMK2/CHxR8Ya94qsdM1Lwg9jZzswkuDDMuwBSRywx1AH40Aev9qO9HavHvFvxS8Y6F4pv9M07we97aW7hY7gQTN5g2g5yox1J6UAew0leDf8Lo8ff9CFJ/4Dz/4V7ToV9can4e06/u7c29zc2sU0sJBHluyglcHngnHNAGhS1xPxH8W634S06yuNE0VtUlnlKSIsbtsAGc/LXnf/AAujx9/0Icn/AIDz/wCFAHvXekrhfht4y17xdHqTa5oTaUbYxiING6eZu3Z+/wCmB09a7HUrmW00q8uYIvNmhheRI8E72CkgcepoAtdqK8F/4XR4+/6EKT/wHn/wrT8OfFfxpq3iTTtPvfBklra3E6xyzmCYeWpPJyRj86APZ+9FHevJvG/xL8W+HPFV1pmleE31CziVClwIZW3EqCeVGOCSKAPWO1LXgv8Awujx9/0Icn/gPP8A4V7F4W1S81rwxp+pahZmzu7iLfLblSPLOTxg8/nQBsd6K5H4h+J9X8KeH4b/AEXSW1S5e6WFoQjthCrEtheeqgfjXmf/AAujx9/0IUn/AIDz/wCFAHvXaivPPhx458ReLry/h1vw82lJbxq0bNFIu8kkEfN9K9AkYpEzKMkAkD1oAf3orwX/AIXR4+z/AMiHJ/4Dz/4Vb0n4veOL7WLG0uPBEkME9xHFJL9nmGxWYAtyMcA5oA9u7UUdq8v+IHxF8U+F/Ei6fo/hd9StTAknniGVvmJORlRjsPzoA9R70leDf8Lo8ff9CFJ/4Dz/AOFeteCtb1DxF4Ts9U1SwNheTeZ5lsVZdm12UcNzyAD+NAG/2ormvHfiDU/DPhiTUtI006jdrKiC3CM2QTycLzxXlf8Awujx9/0Icn/gPP8A4UAe9d6K80+HfxA8TeLNduLLWvDT6Xbx2xlSZopF3MGUbcsMdCT+Fel0AJRXhd38Y/HcF5PDH4FkdEkZVb7PP8wBwD0psHxl8eS3EUb+BJFVnClvs8/AJ69KAPd6O9JXm/xF8feJfCes2tpovht9Uglt/NeVYpG2tuI2/KMdAD+NAHpPak7V4N/wujx9/wBCHJ/4Dz/4V6l4C8Q6p4n8MrqOr6YdNujM6GAoy/KMYOG55oA6jvR3rB8Z61f+H/Cd9qmmWBv7yAJ5dsFZt+XVTwvPAJP4V5H/AMLo8ff9CFJ/4Dz/AOFAHvXakry3wD8RvFXifxKNO1fws+m2pheTzzDKvzDGBlhjnNepUAL3o714lrPxc8b6fruoWVt4Jknt7e5kiimEEx8xVYgNkDHIGeKpf8Lo8ff9CHJ/4Dz/AOFAHvNL2qOB2kt43ddrMoJHocVwPxI8ceIfCNxp8eieH21VbhHaVljkfyyCMD5fXJ6+lAHoVHevBf8AhdHj7/oQ5P8AwHn/AMK9L+HfijWPFmhXF7rWkNpdxHcmJYSjruUKp3YbnqSPwoA66jtWT4m1O70bwzqGo2Fobu6t4S8UABPmMO2Bz+VeOf8AC6PH3/Qhyf8AgPP/AIUAe80vevJPBXxN8XeIvFlnpeqeEn0+zmD+ZcmGVdm1GYcsMckAfjXrfegBKXtXjXib4reM9H8S6hp1j4Nku7W3mMcU4gmPmKO+QMflWV/wujx9/wBCHJ/4Dz/4UAe9Ud6p6VdTXuj2N3cQ+TPPBHJJFgjYzKCV554JxXI/EjxjrvhGDTn0PQ21VrhpBKFjd/LChcfd9cnr6UAd1R2rwX/hdHj7/oQ5P/Aef/CvQ/hx4v1zxbY382t6I2lSQSKsaNG67wQST81AHbUveqGtXk+n6FqF7awGe4t7aSWKEAnzGVSQuBzyRjivFP8AhdHj7/oQpP8AwHn/AMKAPeaO1eO+Ffip4y1rxPYabqHg6SztLiTZLcGCYeWME5yRj869i7UANliSaJopVV43BVlYZBB6givmjxj4e1H4VeN7fWNGLLYySGS1c5IH96Fvw/Me4Nd74y+J/i/w/wCLL7S9M8Ivf2cBTy7kQytvyiseVGOCSPwrjfEXxI8X+J9FuNK1H4fSPBMOCLefcjdmU44IqoysyJw5l5nuXhLxRY+L9Ah1SybG4bZYictE46qf88jBrcr5S8K67r/ww161uL2znit7yFJJ7WQFfNjPIIz0Zefocg17d4u+IN5p/hPTdc8Kab/bSXkwTaiO2xdpJJC8ggjBzRKNtUEJ30e539LXgv8Awujx9/0Icn/gPP8A4V3fw28a+IPF8mpDXNAbShbCMxFo5E8zduz9/wBMDp61JZ3/AHpKhvJnt7KeaNN8kcbMqf3iBkCvDP8AhdHj7/oQ5P8AwHn/AMKAPeWIVSzEADkk9q+UvjH8SD4w1n+y9NlP9i2TnaVPFxIOC/0HIH4nvxr+MPil481vwxeWE3hm40q2lXFxcpbygiPuMsMAHgE+nHeuY+FPw9k8c+Id90rLo9mQ90443ntGD6nv6D8KAO5+BXw28+SPxfq8P7tD/wAS+Fx95h/y1I9B/D789hX0L2qOCGK2hjggjWOKNQiIgwFUDAAHYVJ2oAO1FHaigDyT4n/CaPXFm1vQIlj1MZaa3Xhbj1I9H/n9awPhh8VJdOmj8N+J5WWJW8qC6m4aEjjZJnt2BPToeOnvNeVfFT4XJ4ihk1vRYlTVkXMsS8C5A/8AZ/fv09K0jK+kjKUWnzRPVQQQCDxS14T8Jvia9tLF4W8QysoB8q0uJeCh6eU+fyB7dPTHutRKLTLjJSV0L3pKXvSUig7UUdqKAF70lL3pKADtS0naloAO9FHeigBaKKKACiiigAooooAK8y+NfhSXX/CseoWkZe70wtJtAyWiI+cD6YB/A16bSEZ4PSmnZ3FJcysePfBXx5DfaXH4Y1CUJe2wItGY/wCtj67R7r6en0New9q8E+JHwnu9OvH8Q+FI38sN5strBkPC3XdHjnHfA5Hbjpb8DfG9NkeneLMq6/Kt+i8H/roo6H3H5d6uUb6xMoz5fdke4d6KgtL221C2jurO4iuIJBlJImDKw9iKnrM2EooooAWjvRR3oASjtRR2oAKXvSUvegBKO1FHagBaO9FHegAo7UUdqACjvRR3oASjtRUc88NtA888qRRINzvIwVVHqSelAEleZfF/x5B4f0ObRbOYNqt9GUIU8wxHgsfQkcD8+1ZPjj432lkklh4X23VzyrXrL+7j/wB0H7x9+n1rm/APww1LxZqI8ReKjMLOR/N2TE+Zdn1PcL79+3rWkY21kZSnf3YnU/AnwpLpuj3PiC7jKS34CW4I5EQOS3/Aj+ig969e7U2ONIYljjRURFCqqjAAHQAU7tUN3dy4x5VYKXvSUvekUFJS0lABS0lLQAd6O1HejtQAdqO9HajvQAUlLSUAFLSUtAB3pKXvSUAL2oo7UUAHeijvRQAnalpO1LQAd6KO9FACdqWjtRQAd6KO9FACdqKO1FAC96Sl70lABRR2ooAXvRR3ooASiiigBaO9FHegA7Unal7UnagBe9HejvR3oAO1JS9qSgBe9HejvR3oASl7UlL2oAKO9FHegBKO1FHagApe9JS96AEpe1JS9qAEpe9FHegAo7UUdqAEpe9JS96AEo7UUdqACl70lL3oA5nxt4MsPGuiNZXYEdwmWtrgDLRP/UHuO/1xXhPhnxJrfwk8VT6Tq0EjWLOPtEAOQR0EsZ+n59Dgjj6crlfHHgbTvG2km3uQIryIE210B80Z9D6qe4q4yto9jOcL6rc39N1Oz1jToL+wuEntZl3JIh4I/ofardfMXh/xH4h+EXiaXS9Ugd7FmzNb5+Vx0EkR6Z/njBwRx9G6Lren+INLh1HTLhJ7aUcMvUHuCOxHpSlGw4T5vUv96KXvSVJYjokkbJIqsjDDKwyCPQ1S0nRtN0Ky+x6VZQ2ltvaTy4lwNzHJP+fYdqv0UAHejtR3o7UAHaijtRQAUlLSUAeNfF/4aC+im8TaJB/paDdeQIP9ao/jUf3h39Rz162vg/8AEg63bJ4e1ebOpQr/AKPM55nQdj6sB+Y+hr1vtXzv8V/A83hLWovFOghoLSSYO3lcfZps5BHopPT0PHcVpF8y5WYyXK+ZH0R3orkfh341h8a+HUuTtS/gxHdxDs3Zh/st1H4jtXXVDVtDVNNXQdqKO1FIYvekpe9JQAdqWk7UtAB3oo70UALRRRQAUUUUAFFFFABSd6Wk70AJ2rgfGfwm0HxWZLuIf2fqTcm4gX5XP+2vQ/UYPvXfdqXtTTa2E0noz5kufDPxC+GN091pzzm0By01mTLCw9XQjj6kfQ11Hh/9oAgLD4h0rJ6G4sj/ADRj/I/hXuVctr3w68LeIyz32lQrO3WeD93Jn1JXr+OavmT+JGfs3H4WO0X4h+FNeCiy1m2Erf8ALGZvKfPphsZ/DNdOCCAR0rw7Wf2fBln0TWsekV4n/s6//E1zX/CGfFLwic6c18YV6fYbnzEP/AM5P/fNHLF7MOeS3R9L0d6+bI/i78QNBcRarbpIRxtvrMxt/wCO7a3bL9oaUYF/4eRvVoLkr+hU/wA6Xs5AqsT3ajtXk9r8fvDUoAuNP1OA+yI4/wDQgf0rWg+NXgmYfPqE8P8A10tn/oDS5ZdiuePc9Co71xcfxY8Dy426/EP96GRf5rVgfE3wW3I8Q2f4kj+lLlfYfNHudZR2rkz8TPBY6+IbP8CT/SoJPiv4HjHza/Cf92KRv5LRysOaPc7OjvXn0/xp8ERfc1Kab/rnayf1ArKufj74XiyLey1Oc9v3aKP1bP6U+WXYXtI9z1ajtXhd7+0MeRY+HgPRp7n+gX+tYM3xl8d625h0u2giY8BbO0Mr/wDj27+VP2ciXVifSVc7rPjrwxoG4ajrNrHIvWJH8yT/AL5XJrwr/hGfit4v/wCP06kIX6i7n8lB/wAAyP8A0Gt/Rv2fJ2KvretIg7xWabj/AN9tj/0E0+VLdhzyeyLfiD9oC3QNF4f0ppW6Ce8O1fwRTk/iRXHppvxE+Kc6y3BnNiTlXm/c2ye6r/F9QCa9t0H4YeE/DxWS20uOe4XpPdfvWz6jPAP0ArrwMDA6UcyXwoOSUviZ5v4N+Dmh+G2jvNQI1PUFwQ0q4ijP+ync+5z+Fek0lL3qG29zRRS0QUdqSjtSGLR3pKXvQAUUUlAC0UlLQAd6O1HejtQAdqO9HajvQAUUUlAC0UlLQAd6KO9JQAvaijtRQAd6KO9FAB2opO1LQAd6KO9FAB2oo7UUAHeijvRQAdqKTtRQAveijvSUAef+Lfi3pfgzUGtNT0PXNu7bHcpboIZTgE7GZxnGfSul8JeJ7bxh4dt9atLa4t7ednCLcABjtYqTwSMZBryL9pTUVWy0HTAQXeSW4b2AAUfnub8q9a8FaT/YfgjRdNK7XgtIxIP9sjLf+PE0Ab/eijvRQAUUlFAC0d6KO9AB2o7UdqTtQAvejvR3o70AHaijtSUAL3o70d6O9ABR2pKXtQAUd6KO9ABR2pKO1AC0d6Sl70AFHakpe1ABR3oo70AFHaijtQAUd6Sl70AFHako7UALR3pKXvQAUUUlAHPeL/Bul+M9JNnqEe2VcmC4QfPC3qPUeo7/AK14DHL4q+DPigo6+ZaSnlcnyLpB3How/Me46/T9Z2uaFp3iLTJNO1S2Se3k7Hqp7Mp7EetXGVtHsZzhfVblDwl4y0nxlpou9Nm/eLgTW7nEkR9CPT0PQ10NfM3ibwT4j+F2sLreiXU0lirfJdRjlAf4JV6Y7Z6H2PFepeAPixpvitY7DUPLsdXIx5ZOEmP+wT3/ANk8+maHDqgjPpLc9HoooqDQO9HajvR2oAO1FHaigAoopKAFqpqWnWurabcafexLLbXCGORD3B/rVqloA+X7aXUPg98TGjlLyWROH/6b2zHhv94fzUjpX03bXMN5axXNvIskMyCSN1OQykZBH4V578YvCA8ReFHv7ePOoaaDMmBy8f8AGv5DI+nvWN8CfFZ1DR5/Dt1Jmex/eW+TyYSeR/wFj+TD0rSXvK5jH3Jcp7B2opO1FZmwveijvSUAL2opO1LQAd6KO9FAC0UUUAFFFFABRRRQAUnelpO9ACdqXtSdqXtQAd6KO9FACUUUUANkjSVCkiK6nqrDINYd74I8L6gSbrw/prserC3VW/MAGt+jvRcTSZwd18HPA9zkjSWhY94rmQfoWI/Ssmf4C+EpeY7jVIfZJ0I/VDXqNHaq5n3FyR7HkEn7Pmhn/VazqK/7wRv6CoD+zzpueNfuh9YFP9a9mpe9HPLuL2cOx4wP2edO76/dH6QL/jU0f7PmiD/WazqDf7qov9DXsFHajnl3D2cOx5bD8A/CcZBkutVl9mmQD9EFatt8GfBFuQW0uScjvLcyfyBArvqO9HM+4+SPY56y8CeFLDBt/D2nBh0ZoFdh+LZNbsUEVvGI4Y0jQdFRQAPwFSUdqm40ktgo70Ud6BiUdqKO1ABS96Sl70AJR2oo7UAFL3pKXvQAUlLSUAFLSUtAB3o7Ud6O1AB2o70dqO9ABSUtJQAUtJS0AHekpe9JQAvaijtRQAd6KO9FACdqWk7UtAB3oo70UAHaijtRQAd6KO9FACdqKO1VdTvotL0q71CfiG1geZ/91VJP8qAPPfiZ8VP+ETuYtD0S2W+8QXG0LGQWWHdwuQOSx7L+J7Zq6f4J+JOpWYvtW8fzWF/INwtba2Vo4z6HBAPvgfia4L4KWUvjD4map4p1QebJbAz88gTSEhfwChsemB6V9JMyojO5CqoySewoA+Rr2bX/ABp8VtL0TxJPHdXlpeLp8rxoFDIkpLnAAHTd2HAFfXVfNHwhiHib426nr23McRubxSR0MjFVH5Ofyr6XoAX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None.
13
APhO_2025_2_B_1
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2. (A.3) The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants. [Part B: Spin Waves] In what follows we investigate the dynamics of spins. A spin is a particle with intrinsic angular momentum $\vec{S}$, which has an associated magnetic moment $\vec{\mu}$ related to $\vec{S}$ via the gyromagnetic ratio as in Part A.1, $\vec{\mu} = \gamma \vec{S}$. The magnetic dipoles of two spins interact with each other. However, this interaction is negligible compared to another interaction arising from a quantum mechanical origin, which is not present in classical systems. Interestingly, the energy associated with this quantum interaction has the same form which we found in Part A.3, scaling with $\vec{S}_{1} \cdot \vec{S}_{2}$, albeit with the opposite sign. Now we will look at a very long chain of spins. The positions of the spins are fixed along the $x$-axis, with a distance $a$ separating them, see Figure B.1. We will approximate the total energy of the system by considering the interactions between nearest neighbors only, so that the energy can be written as $E = -J \sum_i \vec{S}_i \cdot \vec{S}_{i+1}$ where $J > 0$ is the interaction strength, and $\vec{S}_{i}$ is the spin angular momentum vector of the $i$-th dipole, with magnitude $S$. The spin vectors are free to rotate in three dimensions. Notice that the sign of the energy is different from the last part. This interaction is purely quantum mechanical. [figure3] Figure B.1.
The energy terms containing $\vec{S}_{i}$ in the sum above can be viewed as the interaction energy between an effective magnetic field $\vec{B}_{i, \text{eff}}$ and the magnetic moment of $\vec{S}_{i}$. Find $\vec{B}_{i, \text{eff}}$ and express your answer in terms of $J$, the gyromagnetic ratio $\gamma$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$)
[["Award 0.2 pt if the answer explicitly shows the understanding that spins $i-1$ and $i+1$ are the contributors to the interaction energy of spin $i$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct effective magnetic field as $\\vec{B}{i, \\text{eff}} = \\frac{J}{\\gamma}( \\vec{S}{i-1} + \\vec{S}_{i+1})$, where $J$ is the coupling constant and $\\gamma$ the gyromagnetic ratio. Otherwise, award 0 pt."]]
["\\boxed{$\\vec{B}_{i,\\text{eff}} = \\frac{J}{\\gamma} (\\vec{S}_{i-1} + \\vec{S}_{i+1})$}"]
["Expression"]
[null]
[0.3]
text+variable figure
Modern Physics
APhO_2025
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None.
14
APhO_2025_2_B_2
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2. (A.3) The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants. [Part B: Spin Waves] In what follows we investigate the dynamics of spins. A spin is a particle with intrinsic angular momentum $\vec{S}$, which has an associated magnetic moment $\vec{\mu}$ related to $\vec{S}$ via the gyromagnetic ratio as in Part A.1, $\vec{\mu} = \gamma \vec{S}$. The magnetic dipoles of two spins interact with each other. However, this interaction is negligible compared to another interaction arising from a quantum mechanical origin, which is not present in classical systems. Interestingly, the energy associated with this quantum interaction has the same form which we found in Part A.3, scaling with $\vec{S}_{1} \cdot \vec{S}_{2}$, albeit with the opposite sign. Now we will look at a very long chain of spins. The positions of the spins are fixed along the $x$-axis, with a distance $a$ separating them, see Figure B.1. We will approximate the total energy of the system by considering the interactions between nearest neighbors only, so that the energy can be written as $E = -J \sum_i \vec{S}_i \cdot \vec{S}_{i+1}$ where $J > 0$ is the interaction strength, and $\vec{S}_{i}$ is the spin angular momentum vector of the $i$-th dipole, with magnitude $S$. The spin vectors are free to rotate in three dimensions. Notice that the sign of the energy is different from the last part. This interaction is purely quantum mechanical. [figure3] Figure B.1. (B.1) The energy terms containing $\vec{S}_{i}$ in the sum above can be viewed as the interaction energy between an effective magnetic field $\vec{B}_{i, \text{eff}}$ and the magnetic moment of $\vec{S}_{i}$. Find $\vec{B}_{i, \text{eff}}$ and express your answer in terms of $J$, the gyromagnetic ratio $\gamma$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$)
Using the concept of effective magnetic field, express the rate of change of the $i$-th spin vector, $d \vec{S}_{i} / d t$, in terms of $J$, $\vec{S}_{i}$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$).
[["Award 0.1 pt if the answer writes the rate of change of spin using the effective magnetic field, i.e. $\\frac{d \\vec{S}_i}{dt} = \\vec{\\mu}_i \\times \\vec{B}_{i,\\text{eff}}$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer gives the correct explicit equation $\\frac{d \\vec{S}_i}{dt} = J \\vec{S}_i \\times ( \\vec{S}_{i-1} + \\vec{S}_{i+1})$, where $J$ is the coupling constant. Otherwise, award 0 pt."]]
["\\boxed{$\\frac{d \\vec{S}_i}{dt} = J \\vec{S}_i \\times (\\vec{S}_{i-1} + \\vec{S}_{i+1})$}"]
["Expression"]
[null]
[0.3]
text+variable figure
Modern Physics
APhO_2025
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None.
15
APhO_2025_2_B_3
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2. (A.3) The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants. [Part B: Spin Waves] In what follows we investigate the dynamics of spins. A spin is a particle with intrinsic angular momentum $\vec{S}$, which has an associated magnetic moment $\vec{\mu}$ related to $\vec{S}$ via the gyromagnetic ratio as in Part A.1, $\vec{\mu} = \gamma \vec{S}$. The magnetic dipoles of two spins interact with each other. However, this interaction is negligible compared to another interaction arising from a quantum mechanical origin, which is not present in classical systems. Interestingly, the energy associated with this quantum interaction has the same form which we found in Part A.3, scaling with $\vec{S}_{1} \cdot \vec{S}_{2}$, albeit with the opposite sign. Now we will look at a very long chain of spins. The positions of the spins are fixed along the $x$-axis, with a distance $a$ separating them, see Figure B.1. We will approximate the total energy of the system by considering the interactions between nearest neighbors only, so that the energy can be written as $E = -J \sum_i \vec{S}_i \cdot \vec{S}_{i+1}$ where $J > 0$ is the interaction strength, and $\vec{S}_{i}$ is the spin angular momentum vector of the $i$-th dipole, with magnitude $S$. The spin vectors are free to rotate in three dimensions. Notice that the sign of the energy is different from the last part. This interaction is purely quantum mechanical. [figure3] Figure B.1. (B.1) The energy terms containing $\vec{S}_{i}$ in the sum above can be viewed as the interaction energy between an effective magnetic field $\vec{B}_{i, \text{eff}}$ and the magnetic moment of $\vec{S}_{i}$. Find $\vec{B}_{i, \text{eff}}$ and express your answer in terms of $J$, the gyromagnetic ratio $\gamma$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$) (B.2) Using the concept of effective magnetic field, express the rate of change of the $i$-th spin vector, $d \vec{S}_{i} / d t$, in terms of $J$, $\vec{S}_{i}$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$). For the rest of Part B, assume that the system is highly magnetized along the $z$ direction, so we can use the approximations $S_{i, z} \approx S$ and $d S_{i, z} / d t \approx 0$ for each spin, see Figure B.2. In this regime, the set of equations describing the spins time evolution is satisfied by a traveling wave solution for $S_{i, x}$ and $S_{i, y}$ characterized by a wave vector $k$ and angular frequency $\omega$. [figure4] Figure B.2.
Find the relationship between $\omega$ and $k$ (known as the dispersion relation, $\omega(k)$) for the spin waves in terms of $J$, $S$ and $a$. Hint: express the position of the $i$-th spin as $x = a \cdot i$.
[["Award 0.25 pt if the answer writes the traveling wave as a function of $kx \\pm \\omega t$ (either sign and either trigonometric functions $\\cos$ or $\\sin$ or complex exponentials are acceptable). Otherwise, award 0 pt.", "Award 0.25 pt if the answer explicitly shows that the amplitudes of $S_x$ and $S_y$ are equal, i.e., $\\delta S_x = \\delta S_y$, where $\\delta$ is the wave amplitude. Otherwise, award 0 pt.", "Award 0.25 pt if the answer correctly identifies the phase relation between $S_x$ and $S_y$ as a difference of $\\pi/2$, e.g., $S_{i,x} = \\delta S \\cos(kx - \\omega t)$ and $S_{i,y} = \\delta S \\sin(kx - \\omega t)$. Otherwise, award 0 pt.", "Award 0.5 pt if the answer writes the explicit equation of motion for either $S_x$ or $S_y$, such as $\\frac{d S_{i,x}}{dt} \\approx JS(2 S_{i,y} - S_{i-1,y} - S_{i+1,y})$ or $\\frac{d S_{i,y}}{dt} \\approx -JS(2 S_{i,x} - S_{i-1,x} - S_{i+1,x})$, where $J$ is the exchange coupling constant and $S$ is the spin magnitude. Otherwise, award 0 pt.", "Award 0.25 pt if the answer explicitly uses the approximation $S_{i,z} \\approx S$, where $S$ is the spin magnitude. Otherwise, award 0 pt.", "Award 0.5 pt if the final dispersion relation is correctly given as $\\omega(k) = 2JS [1 - \\cos(ka)]$ (with $\\pm$ accepted), where $a$ is the lattice spacing. Otherwise, award 0 pt."]]
["\\boxed{$\\omega(k) = 2JS[1 - \\cos(ka)]$}"]
["Expression"]
[null]
[2.0]
text+variable figure
Modern Physics
APhO_2025
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None.
16
APhO_2025_2_B_4
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2. (A.3) The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants. [Part B: Spin Waves] In what follows we investigate the dynamics of spins. A spin is a particle with intrinsic angular momentum $\vec{S}$, which has an associated magnetic moment $\vec{\mu}$ related to $\vec{S}$ via the gyromagnetic ratio as in Part A.1, $\vec{\mu} = \gamma \vec{S}$. The magnetic dipoles of two spins interact with each other. However, this interaction is negligible compared to another interaction arising from a quantum mechanical origin, which is not present in classical systems. Interestingly, the energy associated with this quantum interaction has the same form which we found in Part A.3, scaling with $\vec{S}_{1} \cdot \vec{S}_{2}$, albeit with the opposite sign. Now we will look at a very long chain of spins. The positions of the spins are fixed along the $x$-axis, with a distance $a$ separating them, see Figure B.1. We will approximate the total energy of the system by considering the interactions between nearest neighbors only, so that the energy can be written as $E = -J \sum_i \vec{S}_i \cdot \vec{S}_{i+1}$ where $J > 0$ is the interaction strength, and $\vec{S}_{i}$ is the spin angular momentum vector of the $i$-th dipole, with magnitude $S$. The spin vectors are free to rotate in three dimensions. Notice that the sign of the energy is different from the last part. This interaction is purely quantum mechanical. [figure3] Figure B.1. (B.1) The energy terms containing $\vec{S}_{i}$ in the sum above can be viewed as the interaction energy between an effective magnetic field $\vec{B}_{i, \text{eff}}$ and the magnetic moment of $\vec{S}_{i}$. Find $\vec{B}_{i, \text{eff}}$ and express your answer in terms of $J$, the gyromagnetic ratio $\gamma$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$) (B.2) Using the concept of effective magnetic field, express the rate of change of the $i$-th spin vector, $d \vec{S}_{i} / d t$, in terms of $J$, $\vec{S}_{i}$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$). For the rest of Part B, assume that the system is highly magnetized along the $z$ direction, so we can use the approximations $S_{i, z} \approx S$ and $d S_{i, z} / d t \approx 0$ for each spin, see Figure B.2. In this regime, the set of equations describing the spins time evolution is satisfied by a traveling wave solution for $S_{i, x}$ and $S_{i, y}$ characterized by a wave vector $k$ and angular frequency $\omega$. [figure4] Figure B.2. (B.3) Find the relationship between $\omega$ and $k$ (known as the dispersion relation, $\omega(k)$) for the spin waves in terms of $J$, $S$ and $a$. Hint: express the position of the $i$-th spin as $x = a \cdot i$. The spin wave described above carries energy and momentum. At low energies, the relation between its energy and momentum resembles that of a massive classical particle with an effective mass $m_{\text{eff}}$, a concept known as a quasi-particle.
For small $k$ ($k \ll 1 / a$), find the effective mass $m_{\text{eff}}$ of the spin wave. Express your answer in terms of $J, S, a$ and fundamental constants.
[["Award 0.2 pt if the answer gives the correct Taylor expansion for small $k$, namely $\\omega(k) \\approx 2JS \\left[1 - 1 + \\frac{1}{2}(ka)^2 \\right] = JSa^2 k^2$, where $J$ is the exchange coupling constant, $S$ is the spin magnitude, and $a$ is the lattice spacing. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses the correct relation between momentum and wave vector, $p = \\hbar k$, where $p$ is the momentum and $\\hbar$ is the reduced Planck constant. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses the correct relation between energy and angular frequency, $E = \\hbar \\omega$, where $E$ is the energy and $\\omega$ is the angular frequency. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly identifies the effective mass as $m_{\\text{eff}} = \\frac{\\hbar}{2JSa^2}$, where $m_{\\text{eff}}$ is the effective mass. Otherwise, award 0 pt."]]
["\\boxed{$m_{\\text{eff}} = \\frac{\\hbar}{2 J S a^2}$}"]
["Expression"]
[null]
[0.6]
text+variable figure
Modern Physics
APhO_2025
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4k/652/8AOSvoTtQAtHeijvQAUdqKTtQAtHeijvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6SjvQAtFJRQAtFJS0AHejtSd6O1AC9qO9J2o70ALRRSUALRSUUAL3opO9FAC9qKTtRQAveijvSUAL2opO1FAC96KO9FAB2opO1LQAd6KTvRQAvaik7UUAL3oo70lAC9qKTtRQAveik70UALRSUUALR3pKO9AC9qO1J2o7UAL3o70d6O9AB2oo7UlAC96O9HejvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6Sl70AFHako7UALR3pKXvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6SjvQAtFJRQAtFJRQAveik70UAMuFLW0qgEkoQB+FeQfAHw9rHh/TtbTV9MurFppYjGLiMpuADZxn617FRmgBe9Hak70dqAF7UUnaloA4b4hfD5vGD6dqOn339n61pknmWtwU3KeQ2GH1AIPbng5rI1PwF4w8aeRaeMNfsYtJiYPJaaTE6m4I6bmfp+o9u9en0UAVtO0600nTrewsIEgtYECRRoOFAq1SUUAL3opO9FAC9qKTtWfrOu6V4fsTeatfwWduP4pXxk+gHUn2HNAGj3orwHxd+0RkvaeErHcT8ovbtf1SP8Aq35V7npiXMelWaXkhlulgQTSEAFn2jceOOTmgC32opO1FAC96KTvS0ALRR2ooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/wCRf0P/AK+n/wDQK9vrxD9pT/kX9D/6+n/9AoAy/wBmj/j78Sf9c7f+clfQfavnz9mj/j78Sf8AXO3/AJyV9B9qAFo70Ud6ACjtRR2oAKO9FHegBKO1FHagApe9JS96AEo7UUdqACl70lL3oAKSlpKAClpKWgA70dqO9HagA7Ud6O1HegApKWkoAKWkpaADvSUvekoAXtRR2ooAO9FHeigBO1LSdqWgA70Ud6KADtRR2ooAO9FHeigBO1FHaigBe9JS96SgA7UUdqKAF70Ud6KAEooooAWjvRR3oAO1J2pe1J2oAXvR3o70d6ADtSUvakoAXvR3o70d6AEpe1JS9qACjvRR3oASjtRR2oAKXvSUvegBKXtSUvagAo70Ud6ACjtRR2oASl70lL3oASjtRR2oAKXvSUvegApKWkoAKWkpaADvSUvekoAZOxS3kZTyqkj8q+ePh/Yar8UF1PULnWHtLmCRBIQmRIWBOQAQF6dK+hrn/j1m/wBw/wAq8O/Zq/5BfiH/AK7Q/wDoLVcJyg7xM6lKNRWkb/8AwqzxBBzbeKnB7cyJ/JjSf8In8SNP5tfEIuAOim5Zv0dcV6x3o7Vft59bP5GX1Sn0uvmzyb+3fifo3N5pS3qDqRCHyP8Atkas2fxihjl8nWNGuLaQcMYm3Y/4C2CPzNen9qq3um2OpReVe2cFwnpLGG/nR7SD+KP3B7GpH4J/fqZekeM/D+tkLZ6nCZT/AMspDsf8mxn8K3s1wWr/AAl0C/DPYmbT5T08tt6Z/wB0/wBCK546d8QfBHzWc51XT0/5ZjMgA/3T8w/4DxT9nCXwP7xe1qw/iRv5r/I9epa4Dw/8VtJ1Jlt9UQ6bdZwTIcxk/wC92/H8671JEkRXjcMjDIZTkEVlKEoO0kb06kKivF3Hd6Sl70lSWeU/F74geKfBsKR6TpCpaTDA1V/3iqx/h29FPu2QfSvmfVta1PXr5r3Vb6e8uG/jmctgeg9B7Divqn4w+N7Hwr4UlsnjhutQ1FGihtpVDqF6F2U9h29Tj3r5U03SdR1meSDTbKe7ljjaV0hQsQi9TgUAaPgjTf7Y8c6HYFdyTXsQcf7AYFv0Br7fr5R+AmmG++J0M7LxY20s5z2JGwf+h19XUAHalpO1LQAd6KO9FAC0UUUAFFFFABRRRQAUnelpO9AB2o7Unal7UAHeijvRQAUUlFAC0d6KO9ABR2pKO1AC14f+0p/yL+h/9fT/APoFe314h+0p/wAi/of/AF9P/wCgUAZf7NH/AB9+JP8Arnb/AM5K+hO1fPf7NH/H34k/652/85K+g+1AC0d6KO9ABR2oo7UAFHeijvQAUdqSjtQAtHekpe9ABR2pKO1AC0d6Sl70AFFFJQAtFJS0AHejtR3o7UAHajvR2o70AFFFJQAtFJS0AHeijvSUAL2oo7UUAHeijvRQAdqKTtS0AHeijvRQAdqKO1FAB3oo70UAHaik7UUAL3oo70lAC9qKTtRQAveijvRQAUUlFAC0d6KO9AB2o7UdqTtQAvejvR3o70AHaijtSUAL3o70d6O9ABR2pKXtQAUd6KO9ABR2pKO1AC0d6Sl70AFHakpe1ABR3oo70AFHaijtQAUd6Sl70AFHako7UALR3pKXvQAUUUlAC0UlLQAd6KO9JQAMoZSrDIIwRWRoPhbQ/C8c0ei6dFZJOQ0gjJ+YjOOpPqa1nYRxs56KMnFct4J+IGkePYLybSYruNbRlWT7SiqSWBIxhj6UAdX3o7Ud6O1AB2oo7UUAFJS0lAHO+IvBGieJEZrq2EdyRxcw/K/4/wB78a8+ksvF/wANJDNZyf2jowOWXBKqPdeqH3HHrXsdBAYYPINawquKs9UYVKEZPmWj7o5vwt430rxTEBbv5N4Bl7aQ/MPcf3h7j9KueKPEth4T8P3WsajJthhX5UH3pHPRF9yf8egrjvGPw6tgJdb0KZdNu4AZnUP5cZxyWB/gP6fTrXhnxC8Uaz4rsdPmvb6OW0tV2qifKHY/xnsWxx7Y9zTlTi1zQJhVlGXJVWvfozm/EGuat458VSX9wrzXt3II4YI8naCcLGg9Ofx696+pvhd8PoPAnh0LMqPq10A93KOcHtGp9B+pyfTHEfAv4a/YbePxbq8OLmZf9Aicf6tD/wAtD7kdPbnvx7jWJ0mPYeFdG0zxDea3Y2SQX15GEuGj4D4Oc46ZJ6nvWzR3rzrVfjL4d0fVrvTbix1h5rWVoXaK0DKSpwcHdyKAPRO1LXhnjL4p6F4j0iOLT5vEumahbSi4tp4bXC+YAcBxu+ZTn/8AX0PYfCf4iyePdInW8tTDqNjsWd0H7uXdnDL6H5Tkf48AHofeijvRQAtFFFABRRRQAUUUUAFJ3paTvQAnal7Unal7UAHeijvRQAlFFFAC0d6KO9ACUdqKO1ABXiH7Sn/Iv6H/ANfT/wDoFe314h+0p/yL+h/9fT/+gUAZf7NH/H34k/652/8AOSvoPtXz5+zR/wAffiT/AK52/wDOSvoPtQAtHeijvQAUdqKO1ABR3oo70AJR2oo7UAFL3pKXvQAlHaijtQAUvekpe9ABSUtJQAUtJS0AHejtR3o7UAHajvR2o70AFJS0lABS0lLQAd6Sl70lAC9qKO1FAB3oo70UAJ2paTtS0AHeijvRQAdqKO1FAB3oo70UAJ2oo7UUAL3pKXvSUAHaijtRQAveijvRQAlFFFAC0d6KO9AB2pO1L2pO1AC96O9HejvQAdqSl7UlAC96O9HejvQAlL2pKXtQAUd6KO9ACUdqKO1ABS96Sl70AJS9qSl7UAFHeijvQAUdqKO1ACUvekpe9ACUdqKO1ABS96Sl70AFJS0lABS0lLQAd6Sl70lAEdz/AMes3+4f5V4d+zV/yC/EP/XaH/0Fq9zlTzIXQHG5SM/hXn/wr+Hd38PrTUobu/huzdujqYlK7doI5z9aAPQ+9HajvR2oAO1FHaigApKWkoAKWkrzX4v/ABHXwXon2GwlH9tXqERY5MCdDIffsPf6UAcJ8dfiT58knhDSJ/3aH/iYTIfvMP8AlkD6D+L347GuZ+Dnw6k8YaqNS1NGOhWMmSjfdnl67B7dC34DvxyXgvwjqHjrxRFptsWwx8y6uW58pM/Mx9T6epNfZOiaNY+H9GttK06ERWtsgRFHU+pPqSeSfU0AXwoVQqgADgAdqKO1FAC96SsTxlqx0PwZrOphtr29pI0Z/wBvaQv/AI8RXm/7PQ1G78O6tquoXt1c+dcrBF58zPgIuSRk9y/6UAeg+MtA1LxLpEem2GsPpkMsoF48SZkkhwdyKf4SeOf/ANRv6B4f0zwxpEOmaTapb20fYdWPdmPcn1ry/wDaF8QXWk+HNJsbK7mtp7q6aQvDIUYoi4IyO2XX8q9E8D2dxYeB9Et7uWWW5FpG8zysWYuw3NknnqSKAOg70Ud6KAFooooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/5F/Q/+vp//QK9vrxD9pT/AJF/Q/8Ar6f/ANAoAy/2aP8Aj78Sf9c7f+clfQfavnz9mj/j78Sf9c7f+clfQfagBaO9FHegAo7UUdqACjvRR3oASjtRR2oAKXvSUvegBKO1FHagApe9JS96ACkpaSgApaSloAO9HajvR2oAO1HejtR3oAKSlpKAClpKWgA70lL3pKAF7UUdqKADvRR3ooATtS0naloAO9FHeigA7UUdqKADvRR3ooATtRR2ooAXvSUvekoAO1FHaigBe9FHeigBKKKKAFo70Ud6ADtSdqXtSdqAF70d6O9HegA7UlL2pKAF70d6O9HegBKXtSUvagAo70Ud6AEo7UUdqACl70lL3oASl7UlL2oAKO9FHegAo7UUdqAEpe9JS96AEo7UUdqACl70lL3oAKSlpKAClpKWgA70lL3pKACgMD0IP0qO5/49Zv8AcP8AKvD/ANmti2l+IMkn99D1/wB1qAPde9HajvR2oAO1FHaigApKWoLu7t7CynvLuVIbeBDJJI5wFUDJJoAxvGXiyx8F+G7jV74g7BthhBw00h+6o/qewBNfHeoX2seOPFbXEoe71PUJgqRoO54VVHYAcfQVt/Ezx9ceO/EbTqXj0y2JSzhPZe7kf3m/Tgdq9k+CHw2/sKwTxNq0GNSuk/0aJxzBEe/szD8hx3NAHafDjwJa+BPDaWa7JNQnxJeTgfff+6P9leg/E967Cl70lAB2oo7UUAeV/tAar9g+HBs1bD391HCR/srlz+qj863/AISaT/Y/ww0SErh5oftL+/mEuP0IH4V5T+0jqhn1zRdIjyfs9u9y6j/bOBn6CM/nXX2Xxe0278O6dpHhG0uNQ8QSW6QRWfksqQMFA3SMeNq+xPTqOtAHG/F2dPFvxl0Tw3C++OAw20oH8LSPuf8AJSv5V7/rOpw6FoV7qk0bPDZW7zskYGSqqTgZ47V8yaa1p4E+OyS+J72R1tSZbm7ZGffK8JJfABON78YHpX0P4W8SQeN9Iubv+ybiDTnkaKE3iDF1Hj74X+6eRz/jgA4/RPHXjzxpYPqfhvw3pdpp24rFJqVy5M2ODtCgd+PTPerHgf4pXWueKbrwp4h0ldN1uDdgRvuRyvJHPQ45HJBH69/NLp2g6VJNJ5FlYWsZdiAESNRyeB0rxf4c6fdeNfizqnxD+zvb6UjvHaFxgzHYIx+SjJ9zj1oA92ooooAKKKKACiiigApO9LSd6AE7UvajtR2oAO9FHeigBKKWigAo70Ud6AEo7UtHagBK8Q/aU/5F/Q/+vp//AECvcK8P/aU/5F/Q/wDr6f8A9AoAy/2aP+PvxJ/1zt/5yV9B9q+fP2aP+PvxJ/1zt/5yV9CdqACjvRR3oAKO1FHagAo70Ud6AEo7UtHagBKXvRR3oASjtS0dqAEpe9FHegApKWigBKWiigA70dqO9HagA7Ud6O1HegApKWigBKWiigA70lL3ooAO1FHaigA70Ud6KAE7UtHaigA70Ud6KADtRR2ooAO9FHeigBO1FL2ooAO9JS96KAE7UUvaigA70Ud6KAEopaKACjvRR3oAO1J2pe1HagA70d6O9HegA7UlL2ooAO9HejvR3oASl7UUdqACjvRR3oASjtS0dqAEpe9FHegBKXtRR2oAKO9FHegAo7UUdqAEpe9FHegBKO1LTXdY42d2CooyWJwAPWgBaXvXkvin46aRpUz2uiWx1OZDgzF9kIPserfhgehrh3+M3jvU5CbC2t0H922tGkx+ZNWoNmbqxR9JUlfNv/C1/iPZ/PcQfKOvnaftH6AVfsP2gtZiYDUdGsrhR18h2iP67qPZsXton0HS15ho/wAdPCuoFUvku9NkPUyx70/Ncn8wK9B0zWdM1qDz9Mv7a7i7tDIGx9cdPxqWmty1JPZl7vSUveikURXAJtZQBklD/KvGP2ddOvtP03XlvbK4ti80JUTRMm75W6ZFe2UUAHejtR3o7UAHaijtRQAlfNvxy+JP9rXj+FdInzY27/6ZKh4mkB+4P9lT19T9K7v40fEn/hFdKOi6XNjWL1DudTzbRHgt7Meg/E+mfBfh94IvPHfiWOwi3R2keJLy4A/1aZ/9CPQfn0BoA7H4KfDb/hJNSXxDqsOdJs3/AHMbji4lH81Xv6nj1r6gqrpmm2mj6ZbadYQrDa26COONegA/z1q3QAd6Sl70UAJ2ope1FAHgWjXsfiP9p6/lYLJBZxzQIrDIwkflsPzLfnXt9ho+maWXOnabZ2Zk+/8AZ4Fj3fXAGa5zQ/hn4e8PeLLrxHYLcre3HmbkeXdGu85bAxn9e9djQBmX/h3RNVuo7rUdHsLu4jGElnt0dlHoCRmtAlIYskqkaDJJ4CgU/tWdrukRa/oV5pM9xcQQ3cZikkt2CuFPXBII5HHTvQB5Hc3F18aPEslpHcNaeCNNmxK6tta/kHYe38hz1Ix6YNc8PeHr/SPDMDxQzXStHZ2sC5Cqgyc4+6Mdz15rgP8AhnLwl/0E9b/7/Rf/AButfwx8E/DnhTxHaa3ZX2qS3NqWKJPLGUO5SpyAgPRj3oA9KooooAKKKKACiiigApO9LSd6AE7Uvak7UvagA70Ud6KAEooooAWjvRR3oASjtRR2oAK8Q/aU/wCRf0P/AK+n/wDQK9vrxD9pT/kX9D/6+n/9AoA4v4OeIpvCkOp3UFib5rzYjIGK+Xs3YPAPXd+lepf8LZv8f8i1J/39b/4iuM/Zo/4+/En/AFzt/wCclfQmOOlAHl3/AAtm/wD+hak/7+t/8RR/wtm/z/yLUn/f1v8A4ivUse1GOelAHlv/AAtm/wD+hak/7+t/8RR/wtm/x/yLUn/f1v8A4ivUce1GOOlAHlr/ABbvUXc/hxlUdSZmAH/jld34Y1z/AISPQYNTMHkGUsDHu3YwxHXA9KqePB/xQ+q/9cR/6EKpfDH/AJEWy/35f/QzQB19HaijtQAUvekpe9ACUdqKO1ABS96Sl70AFJS0lABS0lLQAd6O1HejtQAdqO9HajvQAUlLSUAFLSUtAB3pKXvSUAL2oo7UUAHeijvRQAnalpO1LQAd6KO9FAB2oo7UUAHeijvRQAnaijtRQAvekpe9JQAdqKO1FAC96KO9FACUUUUALR3oo70AHak7Uvak7UAL3o70d6O9AB2pKXtSUAL3o70d6O9ACUvakpe1ABR3oo70AJR2oo7UAFL3pKXvQAlL2pKXtQAUd6KO9ABR2oo7UAJS96Sl70AJXiPxz8ZXELw+FbCRl81BLeFDywP3Y/6n14r26vmvU0Gq/tECO5+ZP7UjUg9CEC4H/jtXBa3M6r0sup3/AMP/AIP6ZpOnwah4gtUvNTkUP5Eo3RwZ/h29Gb1J/D1PqUUMcEaxwxpHGvAVFwB+Ap/al71Lbe5UYqKshMVm6h4e0bVlI1DSrK6z3mgVj+ZGa06SkVY821n4H+E9SDNZpcabKehgk3Jn3Vs/oRXneqfBrxf4buPtugXn2zZyr2shhmH4Z/kTX0bRVqbRm6cWfOmjfGXxX4auvsHiOza8WPh1uEMM6/jjn8R+NeveFviR4b8WBY7K9EN43/Lrc4STPt2b8Ca2ta8OaR4itfs2rafBdR9i6/Mv+6w5H4GvHPFXwGmh33fha8L4+YWly2GH+6/T88fWn7svIm047anuczlIJHHVVJGfpXnHwg+IGr+PbLVZtWhtI2tJI1j+zRsoIYMTnLH0rzXSPid4u8Ezvo/iG2nuoUUqYbvKzIOmVc9R9cj0Irb/AGa7iFbPX7cyoJ2kidYyw3FQGyQOuKmUWi4zUj3rvR2o70dqksO1cv498aWXgbw1LqVzh7hvktbfPMsnYfQdSfT8K3dT1K00fTLjUb+ZYLW3QySSN0AH+elfHHxB8b3njzxNJfy7o7SPMdnbk/6tM/8AoR6n8ugFAGb/AMTnxx4r/jvNV1Kf8yf5KB+AA9q+vPAfguz8DeGotMtsSXDfPdXGOZZO5+g6Aen41yHwX+G3/CK6T/bWqQ41i9T5UYc28R5C+zHqfwHrn1agApaSloAO9JS96SgA7UUdqKAF70lL3pKADtS0naloAO9FHeigBaKKKACiiigAooooAKQ9aWk70AJ2o7UvajtQAneil71zWveP/DHhssmo6tCs6/8ALCI+ZJn3Vc4/HFCVxNpbnSUV4lrP7QcKFk0TRnk9JbyTaP8Avhc/+hCuXPxA+J3ixiulpdLE3bT7TCj/AIGQSP8AvqrVNkOrHofSjMqKWZgAOpJ6Vj3vi/w3pxIu9d06Jh1VrlN35ZzXgi/C34j+ImD6rM67ud2oXxc/kCxFbVl+zzeNg33iCCP1WC3L/qSv8qfLFbsXPJ7I9Duvi74Htcg62sjDtFBI36hcVlT/AB28HxZ2LqM3/XO3A/8AQmFZ9r+z94fQD7VqupTH/pmUQH/x01rQfBDwXEPntrub/rpcsP8A0HFHuB+8MqT9oHw6P9XpeqN/vLGP/ZjXmnxb+JVj450zTra0sLi2NtM0haZlOQVx2r2+P4QeBY+mhBj6tczH/wBnryz47+D9A8NaJpEuj6bHaSS3Dq7KzEsAucck0ny20GlO+py3wi8f2fgSfVnu7Ke5F2sQXyiBt2luuf8Aer1eP9oHw8f9ZpWpr/uiM/8AswrgPgL4W0XxNca8us2CXYgSAx72Ybcl89CPQV7LJ8IvAsg50FR/u3Mw/k9JONtQkp30MeD48eEJcb49Sh/34FP8mNatt8YPA9yQP7Z8pj2lt5F/Xbiqk/wS8FS/ctLqH/rncsf/AELNZNz+z/4ckybbU9ThP+2yOB/46P50/cF+8O+svGnhjUMC11/TZGPRftKhvyJzW0kiSIHR1ZT0KnINeFXv7PNwMmx8QxP6LPbFf1DH+VYb/CT4haA5k0qdZCOd1hemM/8Aj22nyxezDnmt0e4+PP8AkR9V/wCuI/8AQhVL4Y/8iLZf78v/AKGa8Vn1z4kWELaVr41H7BONkhu7fcCOvEmM9vWt7wx8YLbwnbJol/pUstvESwuIJBu+Y7vunA7+tS4O9kUqitdnvdHauU0H4keFPERWOz1WKOdukFx+6fPoAeD+BNdXnipasUmnsFL3oo70DEo7UtHagBKO9LR3oASilooASloooATvR2pe9HagBO1Hel7Ud6ACkpaKAEopaKAE70UveigBO1FL2ooAO9JS96KAE7UUvaigA70Ud6KAE7UtHaigBO9FL3ooATtRS9qKADvSUveigBO1FL2ooATvRS96KAEopaKAEo70tHegBO1Hal7UdqADvR3o70d6ADtSUvaigA70d6O9HegBKO1LR2oASl70Ud6AEo7UtHagBKXvRR3oASjtS0dqAEpe9FHegBKO1LR2oASl70Ud6AEr5q8dt/wjPxzTUn+WH7Vb3mfVPl3fqGr6WrxX4/8Ah9prHTvEEKZMDG2nI/utyh+gO4f8CFXB6mdVe7c9pBBUEHINHeuM+FviQeJPAljI77rq0X7LOM87lAAP4rg/ia7TvUtWdi07q4lFLRSGJRS0UAJ3ope9FAGTr/hrSPE1ibTV7GK5j/hLDDIfVWHIP0rwjxN8GdZ8I3J1bwncXF1DEd4EbEXMOPTH3vw59q+i3YIjM3RRk1geFvG2heNIrmXRLl50tmVZS8TJgnJH3gM9DVKViZRUkeW+Cfjg6OmneLVOQdov0Tkf9dFH8x+XevbbW6t721jubWeOaCRdySRsGVh6giuI8cfCvRvF6yXUSrY6rjIuY14kP+2vf69f5V8+atq3iv4dT6n4WXUGgEybJo4pA6bWH3l/ukj6HB+lN8rV0RHmTs9Tf+NfxJ/4STUj4f0qfOk2b/vZEPFxKP5qvb1PPpV74G/Db+1rxPFWrwZsbd/9CiccTSA/fP8AsqenqfpXD/DPwNJ478UJZu/l2FuBLdyA4bZn7q+56e3Jr7Es7S30+zgs7SFIbeBBHHGgwFUDAAqDUmopaKAEopaKAE70UveigBO1FL2ooAO9JS96KAE7UUvaigBO9LR3ooAXtRRRQAUUUUAFFFFABSd6WkPFACdq4bxl8VNB8I77beb7Ul4+ywMPkP8Att0X6cn2rgviT8Wrm6u5PD3hSV8bvKlvIeXkbpsjx27ZHJ7epf4G+CBlWPUvFpfLfOtgjYP/AG0YfyH59qtRSV5GTm27QOZu/GHxB+JN29npUdwlsTgwWIKIo/25D/Uge1dF4f8A2f5pAs3iHVRHnk29mNzfi7DH5A/Wvb7GwtNMtI7Sxtora3jGFjiQKo/AVZoc+wKkt5anJ6L8NvCWhBTa6NBJKv8Ay1uR5rZ9fmzj8MV1SqqKFUAAcAAdKWipbbNEktgpe9FHekMSjtRR2oAK8Q/aU/5F/Q/+vp//AECvb68Q/aU/5F/Q/wDr6f8A9AoAy/2aP+PvxJ/1zt/5yV9B9q+fP2aP+PvxJ/1zt/5yV9B9qAFo70Ud6ACkpaO1AHOePP8AkR9V/wCuI/8AQhXIeEfAvhvxP4ItJdU0uGW4ZpAZ1yknDnHzLgnHvXX+PP8AkR9V/wCuI/8AQhVL4Y/8iLZf78v/AKGaL2E0nuefeIP2flIeXw9qpB6i3vRkfg6j+Y/GuUh134ifC+4SC9W4+xg4WK6/ewOPRWB4+gI+lfTdRXNtb3ls9vcwxzQyDDxyKGVh6EHrVqb6mbpLeOhwHg34v6F4naO0uz/ZmotgCKZv3ch/2X/ocH616L3rxbxx8D7a4SS/8K4gnHzNYu3yP/uE/dPsePpWJ8P/AIp6h4b1BfD3iszG1R/KEswPmWp6YbPJX9R9OKbimrxBTcXaR9B0dqSN1kjV0YMjDKsDkEeope1ZmoUvekpe9ABSUtJQAUtJS0AHejtR3o7UAHajvR2o70AFJS0lABS0lLQAd6Sl70lAC9qKO1FAB3oo70UAJ2paTtS0AHeijvRQAdqKO1FAB3oo70UAJ2oo7UUAL3pKXvSUAHaijtRQAveijvRQAlFFFAC0d6KO9AB2pO1L2pO1AC96O9HejvQAdqSl7UlAC96O9HejvQAlL2pKXtQAUd6KO9ACUdqKO1ABS96Sl70AJS9qSl7UAFHeijvQAUdqKO1ACUvekpe9ACVna9o9t4g0G90q6H7m6iMZOOVPZh7g4P4Vo0dqAPmr4b65c/D74hXOhasfKt7iT7LcZPypID8j/Tnr6NmvpWvGvjh4IN7Zr4osIsz26hLxVHLR9n+q9D7fStz4QeOh4m0IaZfS51WwQKxY8zRdA/uR0P4HvWkveXMjGD5XyM9KpKKKzNgpaSloAO9JS96SgCO5/wCPWb/cP8q8O/Zq/wCQX4h/67Q/+gvXuUyGSCRB1ZSBn6V5P8OvDNz8IvDWvX/ii7s1t2KShrdy3CgjHIHJJAA70AdX8R/Hdr4E8NveNtkv58x2cB/jf+8f9lep/Ad6+TNPsNY8ceK0t4i93qeoTFnkc9zyzMewA5+gq3408W6h468US6lchsOfLtbZefKTPyqPU+vqTX0d8IPhwvgzQ/t1/EP7bvUBlJ5MCdRGPfuff6CgDy/xF8NvEPwynh1rRLyWe2hwzXcK7XibvvXn5T+I7H39Q+HfxYs/FSx6bqnl2msYwoziO4919G/2fy9vSXRXQo6hlYYIIyCK8M+I/wAHmgaTW/CkTDafMlsY+q990X/xP5elaJqSszKSlF80T3SivFfhn8X/ALQ0WheKJts/CQX0hxvPZZPQ/wC13788n2rtUOLW5cZKSugpaSlpFB3pKXvSUAHaijtRQAvekpe9JQAdqWk7UtAB3oo70UALRRRQAUUUUAFFFFABXmnxp8WS+HvCqWNpIY7zUy0QYHBWMD5yPfkD8TXpdfPf7Qvmf8JHpGc+V9kbb/vbzn/2WqgryM6jtFm/8FfAMFppsfinUYg93cA/Y1cf6qPpv+rdvb617H2rO8PiEeG9LFtjyPskXl46bdgx+laXalJ3ZUYpKyDvRR3opFCUUUUALR3oo70AJR2oo7UAFeIftKf8i/of/X0//oFe3145+0LpWo6poOjrp9hdXZjuXZxbwtIVBXAJwDigDn/2aP8Aj78Sf9c7f+clfQfavk34fa54w+HsuoPZ+Er26N6sYYTWsw27d2MYH+1Xsfw++IfijxT4ik0/WfDD6ZarbtKJzFKuWBUBcsMdz+VAHqFHeivD9T+L/jmz1a8tYPBEk0MM7xxyfZ5zvUMQDwMcgUAe4Udq8FHxn8fE4/4QOT/wHn/wr3lSSoJ6kUAc748/5EfVf+uI/wDQhVL4Y/8AIi2X+/L/AOhmsH4r+JNZ082+iWOizXllfwH7RcRQySGLDcY2gjt3rhtK+JPjDwzp6aXp3g25u7aIkrLLazqx3HJ4x6mgD6Go7Vynw98S6t4q8Oy3+s6U2mXK3DRCAo65UKpDYbnqT+VaXizVr3Q/C1/qWnWZvbu3QNHbhS3mHIGMDnv2oA2a8v8AjD4Bg13RZtcsYguqWUZd9o/18Q6g+pA5H0x6Y5b/AIXR4+/6EOT/AMB5/wDCug8FfErxT4l8SR6ZrXhRtPsJIpGkuHhlULhScEsMc007O5MoqSsxnwK8WS6po1xoF3IXm08BoGY8mE8Y/wCAn9GA7V652r5t+B2R8SLj7Pnyfscuf93cuP1xXVeIPiz410rxFqOn2fguS5tba4eKKcQTHzFBIDZAxz7VU1Zk0neJ7RS968F/4XR4+/6EOT/wHn/wr3GwnkutOtbiaPy5ZYkd0xjaSASOfSoNCzSVwfxJ8aa/4Q/s3+w9BbVftPmebtjkfy9u3H3PXcevpXBf8Lo8ff8AQhyf+A8/+FAHvNLXF/DnxZrXi3S7y51vRm0uaGYRxxlHXeu0HPze9dF4gv7nS/Duo6hZ2xubm2tnligAJ8xlUkLgc8n0oA0u9HavBf8AhdHj7/oQ5P8AwHn/AMK2/CHxR8Ya94qsdM1Lwg9jZzswkuDDMuwBSRywx1AH40Aev9qO9HavHvFvxS8Y6F4pv9M07we97aW7hY7gQTN5g2g5yox1J6UAew0leDf8Lo8ff9CFJ/4Dz/4V7ToV9can4e06/u7c29zc2sU0sJBHluyglcHngnHNAGhS1xPxH8W634S06yuNE0VtUlnlKSIsbtsAGc/LXnf/AAujx9/0Icn/AIDz/wCFAHvXekrhfht4y17xdHqTa5oTaUbYxiING6eZu3Z+/wCmB09a7HUrmW00q8uYIvNmhheRI8E72CkgcepoAtdqK8F/4XR4+/6EKT/wHn/wrT8OfFfxpq3iTTtPvfBklra3E6xyzmCYeWpPJyRj86APZ+9FHevJvG/xL8W+HPFV1pmleE31CziVClwIZW3EqCeVGOCSKAPWO1LXgv8Awujx9/0Icn/gPP8A4V7F4W1S81rwxp+pahZmzu7iLfLblSPLOTxg8/nQBsd6K5H4h+J9X8KeH4b/AEXSW1S5e6WFoQjthCrEtheeqgfjXmf/AAujx9/0IUn/AIDz/wCFAHvXaivPPhx458ReLry/h1vw82lJbxq0bNFIu8kkEfN9K9AkYpEzKMkAkD1oAf3orwX/AIXR4+z/AMiHJ/4Dz/4Vb0n4veOL7WLG0uPBEkME9xHFJL9nmGxWYAtyMcA5oA9u7UUdq8v+IHxF8U+F/Ei6fo/hd9StTAknniGVvmJORlRjsPzoA9R70leDf8Lo8ff9CFJ/4Dz/AOFeteCtb1DxF4Ts9U1SwNheTeZ5lsVZdm12UcNzyAD+NAG/2ormvHfiDU/DPhiTUtI006jdrKiC3CM2QTycLzxXlf8Awujx9/0Icn/gPP8A4UAe9d6K80+HfxA8TeLNduLLWvDT6Xbx2xlSZopF3MGUbcsMdCT+Fel0AJRXhd38Y/HcF5PDH4FkdEkZVb7PP8wBwD0psHxl8eS3EUb+BJFVnClvs8/AJ69KAPd6O9JXm/xF8feJfCes2tpovht9Uglt/NeVYpG2tuI2/KMdAD+NAHpPak7V4N/wujx9/wBCHJ/4Dz/4V6l4C8Q6p4n8MrqOr6YdNujM6GAoy/KMYOG55oA6jvR3rB8Z61f+H/Cd9qmmWBv7yAJ5dsFZt+XVTwvPAJP4V5H/AMLo8ff9CFJ/4Dz/AOFAHvXakry3wD8RvFXifxKNO1fws+m2pheTzzDKvzDGBlhjnNepUAL3o714lrPxc8b6fruoWVt4Jknt7e5kiimEEx8xVYgNkDHIGeKpf8Lo8ff9CHJ/4Dz/AOFAHvNL2qOB2kt43ddrMoJHocVwPxI8ceIfCNxp8eieH21VbhHaVljkfyyCMD5fXJ6+lAHoVHevBf8AhdHj7/oQ5P8AwHn/AMK9L+HfijWPFmhXF7rWkNpdxHcmJYSjruUKp3YbnqSPwoA66jtWT4m1O70bwzqGo2Fobu6t4S8UABPmMO2Bz+VeOf8AC6PH3/Qhyf8AgPP/AIUAe80vevJPBXxN8XeIvFlnpeqeEn0+zmD+ZcmGVdm1GYcsMckAfjXrfegBKXtXjXib4reM9H8S6hp1j4Nku7W3mMcU4gmPmKO+QMflWV/wujx9/wBCHJ/4Dz/4UAe9Ud6p6VdTXuj2N3cQ+TPPBHJJFgjYzKCV554JxXI/EjxjrvhGDTn0PQ21VrhpBKFjd/LChcfd9cnr6UAd1R2rwX/hdHj7/oQ5P/Aef/CvQ/hx4v1zxbY382t6I2lSQSKsaNG67wQST81AHbUveqGtXk+n6FqF7awGe4t7aSWKEAnzGVSQuBzyRjivFP8AhdHj7/oQpP8AwHn/AMKAPeaO1eO+Ffip4y1rxPYabqHg6SztLiTZLcGCYeWME5yRj869i7UANliSaJopVV43BVlYZBB6givmjxj4e1H4VeN7fWNGLLYySGS1c5IH96Fvw/Me4Nd74y+J/i/w/wCLL7S9M8Ivf2cBTy7kQytvyiseVGOCSPwrjfEXxI8X+J9FuNK1H4fSPBMOCLefcjdmU44IqoysyJw5l5nuXhLxRY+L9Ah1SybG4bZYictE46qf88jBrcr5S8K67r/ww161uL2znit7yFJJ7WQFfNjPIIz0Zefocg17d4u+IN5p/hPTdc8Kab/bSXkwTaiO2xdpJJC8ggjBzRKNtUEJ30e539LXgv8Awujx9/0Icn/gPP8A4V3fw28a+IPF8mpDXNAbShbCMxFo5E8zduz9/wBMDp61JZ3/AHpKhvJnt7KeaNN8kcbMqf3iBkCvDP8AhdHj7/oQ5P8AwHn/AMKAPeWIVSzEADkk9q+UvjH8SD4w1n+y9NlP9i2TnaVPFxIOC/0HIH4nvxr+MPil481vwxeWE3hm40q2lXFxcpbygiPuMsMAHgE+nHeuY+FPw9k8c+Id90rLo9mQ90443ntGD6nv6D8KAO5+BXw28+SPxfq8P7tD/wAS+Fx95h/y1I9B/D789hX0L2qOCGK2hjggjWOKNQiIgwFUDAAHYVJ2oAO1FHaigDyT4n/CaPXFm1vQIlj1MZaa3Xhbj1I9H/n9awPhh8VJdOmj8N+J5WWJW8qC6m4aEjjZJnt2BPToeOnvNeVfFT4XJ4ihk1vRYlTVkXMsS8C5A/8AZ/fv09K0jK+kjKUWnzRPVQQQCDxS14T8Jvia9tLF4W8QysoB8q0uJeCh6eU+fyB7dPTHutRKLTLjJSV0L3pKXvSUig7UUdqKAF70lL3pKADtS0naloAO9FHeigBaKKKACiiigAooooAK8y+NfhSXX/CseoWkZe70wtJtAyWiI+cD6YB/A16bSEZ4PSmnZ3FJcysePfBXx5DfaXH4Y1CUJe2wItGY/wCtj67R7r6en0New9q8E+JHwnu9OvH8Q+FI38sN5strBkPC3XdHjnHfA5Hbjpb8DfG9NkeneLMq6/Kt+i8H/roo6H3H5d6uUb6xMoz5fdke4d6KgtL221C2jurO4iuIJBlJImDKw9iKnrM2EooooAWjvRR3oASjtRR2oAKXvSUvegBKO1FHagBaO9FHegAo7UUdqACjvRR3oASjtRUc88NtA888qRRINzvIwVVHqSelAEleZfF/x5B4f0ObRbOYNqt9GUIU8wxHgsfQkcD8+1ZPjj432lkklh4X23VzyrXrL+7j/wB0H7x9+n1rm/APww1LxZqI8ReKjMLOR/N2TE+Zdn1PcL79+3rWkY21kZSnf3YnU/AnwpLpuj3PiC7jKS34CW4I5EQOS3/Aj+ig969e7U2ONIYljjRURFCqqjAAHQAU7tUN3dy4x5VYKXvSUvekUFJS0lABS0lLQAd6O1HejtQAdqO9HajvQAUlLSUAFLSUtAB3pKXvSUAL2oo7UUAHeijvRQAnalpO1LQAd6KO9FACdqWjtRQAd6KO9FACdqKO1FAC96Sl70lABRR2ooAXvRR3ooASiiigBaO9FHegA7Unal7UnagBe9HejvR3oAO1JS9qSgBe9HejvR3oASl7UlL2oAKO9FHegBKO1FHagApe9JS96AEpe1JS9qAEpe9FHegAo7UUdqAEpe9JS96AEo7UUdqACl70lL3oA5nxt4MsPGuiNZXYEdwmWtrgDLRP/UHuO/1xXhPhnxJrfwk8VT6Tq0EjWLOPtEAOQR0EsZ+n59Dgjj6crlfHHgbTvG2km3uQIryIE210B80Z9D6qe4q4yto9jOcL6rc39N1Oz1jToL+wuEntZl3JIh4I/ofardfMXh/xH4h+EXiaXS9Ugd7FmzNb5+Vx0EkR6Z/njBwRx9G6Lren+INLh1HTLhJ7aUcMvUHuCOxHpSlGw4T5vUv96KXvSVJYjokkbJIqsjDDKwyCPQ1S0nRtN0Ky+x6VZQ2ltvaTy4lwNzHJP+fYdqv0UAHejtR3o7UAHaijtRQAUlLSUAeNfF/4aC+im8TaJB/paDdeQIP9ao/jUf3h39Rz162vg/8AEg63bJ4e1ebOpQr/AKPM55nQdj6sB+Y+hr1vtXzv8V/A83hLWovFOghoLSSYO3lcfZps5BHopPT0PHcVpF8y5WYyXK+ZH0R3orkfh341h8a+HUuTtS/gxHdxDs3Zh/st1H4jtXXVDVtDVNNXQdqKO1FIYvekpe9JQAdqWk7UtAB3oo70UALRRRQAUUUUAFFFFABSd6Wk70AJ2rgfGfwm0HxWZLuIf2fqTcm4gX5XP+2vQ/UYPvXfdqXtTTa2E0noz5kufDPxC+GN091pzzm0By01mTLCw9XQjj6kfQ11Hh/9oAgLD4h0rJ6G4sj/ADRj/I/hXuVctr3w68LeIyz32lQrO3WeD93Jn1JXr+OavmT+JGfs3H4WO0X4h+FNeCiy1m2Erf8ALGZvKfPphsZ/DNdOCCAR0rw7Wf2fBln0TWsekV4n/s6//E1zX/CGfFLwic6c18YV6fYbnzEP/AM5P/fNHLF7MOeS3R9L0d6+bI/i78QNBcRarbpIRxtvrMxt/wCO7a3bL9oaUYF/4eRvVoLkr+hU/wA6Xs5AqsT3ajtXk9r8fvDUoAuNP1OA+yI4/wDQgf0rWg+NXgmYfPqE8P8A10tn/oDS5ZdiuePc9Co71xcfxY8Dy426/EP96GRf5rVgfE3wW3I8Q2f4kj+lLlfYfNHudZR2rkz8TPBY6+IbP8CT/SoJPiv4HjHza/Cf92KRv5LRysOaPc7OjvXn0/xp8ERfc1Kab/rnayf1ArKufj74XiyLey1Oc9v3aKP1bP6U+WXYXtI9z1ajtXhd7+0MeRY+HgPRp7n+gX+tYM3xl8d625h0u2giY8BbO0Mr/wDj27+VP2ciXVifSVc7rPjrwxoG4ajrNrHIvWJH8yT/AL5XJrwr/hGfit4v/wCP06kIX6i7n8lB/wAAyP8A0Gt/Rv2fJ2KvretIg7xWabj/AN9tj/0E0+VLdhzyeyLfiD9oC3QNF4f0ppW6Ce8O1fwRTk/iRXHppvxE+Kc6y3BnNiTlXm/c2ye6r/F9QCa9t0H4YeE/DxWS20uOe4XpPdfvWz6jPAP0ArrwMDA6UcyXwoOSUviZ5v4N+Dmh+G2jvNQI1PUFwQ0q4ijP+ync+5z+Fek0lL3qG29zRRS0QUdqSjtSGLR3pKXvQAUUUlAC0UlLQAd6O1HejtQAdqO9HajvQAUUUlAC0UlLQAd6KO9JQAvaijtRQAd6KO9FAB2opO1LQAd6KO9FAB2oo7UUAHeijvRQAdqKTtRQAveijvSUAef+Lfi3pfgzUGtNT0PXNu7bHcpboIZTgE7GZxnGfSul8JeJ7bxh4dt9atLa4t7ednCLcABjtYqTwSMZBryL9pTUVWy0HTAQXeSW4b2AAUfnub8q9a8FaT/YfgjRdNK7XgtIxIP9sjLf+PE0Ab/eijvRQAUUlFAC0d6KO9AB2o7UdqTtQAvejvR3o70AHaijtSUAL3o70d6O9ABR2pKXtQAUd6KO9ABR2pKO1AC0d6Sl70AFHakpe1ABR3oo70AFHaijtQAUd6Sl70AFHako7UALR3pKXvQAUUUlAHPeL/Bul+M9JNnqEe2VcmC4QfPC3qPUeo7/AK14DHL4q+DPigo6+ZaSnlcnyLpB3How/Me46/T9Z2uaFp3iLTJNO1S2Se3k7Hqp7Mp7EetXGVtHsZzhfVblDwl4y0nxlpou9Nm/eLgTW7nEkR9CPT0PQ10NfM3ibwT4j+F2sLreiXU0lirfJdRjlAf4JV6Y7Z6H2PFepeAPixpvitY7DUPLsdXIx5ZOEmP+wT3/ANk8+maHDqgjPpLc9HoooqDQO9HajvR2oAO1FHaigAoopKAFqpqWnWurabcafexLLbXCGORD3B/rVqloA+X7aXUPg98TGjlLyWROH/6b2zHhv94fzUjpX03bXMN5axXNvIskMyCSN1OQykZBH4V578YvCA8ReFHv7ePOoaaDMmBy8f8AGv5DI+nvWN8CfFZ1DR5/Dt1Jmex/eW+TyYSeR/wFj+TD0rSXvK5jH3Jcp7B2opO1FZmwveijvSUAL2opO1LQAd6KO9FAC0UUUAFFFFABRRRQAUnelpO9ACdqXtSdqXtQAd6KO9FACUUUUANkjSVCkiK6nqrDINYd74I8L6gSbrw/prserC3VW/MAGt+jvRcTSZwd18HPA9zkjSWhY94rmQfoWI/Ssmf4C+EpeY7jVIfZJ0I/VDXqNHaq5n3FyR7HkEn7Pmhn/VazqK/7wRv6CoD+zzpueNfuh9YFP9a9mpe9HPLuL2cOx4wP2edO76/dH6QL/jU0f7PmiD/WazqDf7qov9DXsFHajnl3D2cOx5bD8A/CcZBkutVl9mmQD9EFatt8GfBFuQW0uScjvLcyfyBArvqO9HM+4+SPY56y8CeFLDBt/D2nBh0ZoFdh+LZNbsUEVvGI4Y0jQdFRQAPwFSUdqm40ktgo70Ud6BiUdqKO1ABS96Sl70AJR2oo7UAFL3pKXvQAUlLSUAFLSUtAB3o7Ud6O1AB2o70dqO9ABSUtJQAUtJS0AHekpe9JQAvaijtRQAd6KO9FACdqWk7UtAB3oo70UAHaijtRQAd6KO9FACdqKO1VdTvotL0q71CfiG1geZ/91VJP8qAPPfiZ8VP+ETuYtD0S2W+8QXG0LGQWWHdwuQOSx7L+J7Zq6f4J+JOpWYvtW8fzWF/INwtba2Vo4z6HBAPvgfia4L4KWUvjD4map4p1QebJbAz88gTSEhfwChsemB6V9JMyojO5CqoySewoA+Rr2bX/ABp8VtL0TxJPHdXlpeLp8rxoFDIkpLnAAHTd2HAFfXVfNHwhiHib426nr23McRubxSR0MjFVH5Ofyr6XoAX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None.
17
APhO_2025_2_B_5
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part A. Precession and interactions of magnetic dipoles] Consider a ring of radius $R$, total mass $M$, and charge $Q > 0$ distributed uniformly. The ring rotates with an angular speed $\omega$ around a perpendicular axis that passes through its center of mass. (A.1) It is possible to write the ring's magnetic moment $\vec{\mu}$ in terms of its angular momentum $\vec{L}$ as $\vec{\mu} = \gamma \vec{L}$. Find the constant $\gamma$, called the gyromagnetic ratio, of this system in terms of $Q$ and $M$. The ring is placed in a weak uniform magnetic field $\vec{B} = B \hat{z}$, making an angle $\theta$ with $\vec{\omega}$, see Figure A.1. [figure1] Figure A.1. (A.2) Find the angular frequency $\omega_{L}$ of the angular momentum precession (the so-called Larmor frequency) due to the external magnetic field in terms of $B$ and $\gamma$. Take the positive direction to be counter-clockwise with respect to $+z$. Now we turn off the external magnetic field and place an identical ring at a horizontal distance $d \gg R$ from the original ring such that the magnetic moment of the new ring $\vec{\mu}_{2}$ makes an angle $\theta$ with $\vec{\mu}_{1}$, see Figure A.2. [figure2] Figure A.2. (A.3) The magnetic interaction energy between the two rings can be written as $U = J_{0} \vec{L}_{1} \cdot \vec{L}_{2}$, where $J_{0}$ is a constant and $\vec{L}_{i}$ is the angular momentum of the $i$-th ring. Find $J_{0}$ in terms of $\gamma$, $d$ and fundamental constants. [Part B: Spin Waves] In what follows we investigate the dynamics of spins. A spin is a particle with intrinsic angular momentum $\vec{S}$, which has an associated magnetic moment $\vec{\mu}$ related to $\vec{S}$ via the gyromagnetic ratio as in Part A.1, $\vec{\mu} = \gamma \vec{S}$. The magnetic dipoles of two spins interact with each other. However, this interaction is negligible compared to another interaction arising from a quantum mechanical origin, which is not present in classical systems. Interestingly, the energy associated with this quantum interaction has the same form which we found in Part A.3, scaling with $\vec{S}_{1} \cdot \vec{S}_{2}$, albeit with the opposite sign. Now we will look at a very long chain of spins. The positions of the spins are fixed along the $x$-axis, with a distance $a$ separating them, see Figure B.1. We will approximate the total energy of the system by considering the interactions between nearest neighbors only, so that the energy can be written as $E = -J \sum_i \vec{S}_i \cdot \vec{S}_{i+1}$ where $J > 0$ is the interaction strength, and $\vec{S}_{i}$ is the spin angular momentum vector of the $i$-th dipole, with magnitude $S$. The spin vectors are free to rotate in three dimensions. Notice that the sign of the energy is different from the last part. This interaction is purely quantum mechanical. [figure3] Figure B.1. (B.1) The energy terms containing $\vec{S}_{i}$ in the sum above can be viewed as the interaction energy between an effective magnetic field $\vec{B}_{i, \text{eff}}$ and the magnetic moment of $\vec{S}_{i}$. Find $\vec{B}_{i, \text{eff}}$ and express your answer in terms of $J$, the gyromagnetic ratio $\gamma$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$) (B.2) Using the concept of effective magnetic field, express the rate of change of the $i$-th spin vector, $d \vec{S}_{i} / d t$, in terms of $J$, $\vec{S}_{i}$, and other spins $\vec{S}_{j}$ (specify the indices $j$ in relation to $i$). For the rest of Part B, assume that the system is highly magnetized along the $z$ direction, so we can use the approximations $S_{i, z} \approx S$ and $d S_{i, z} / d t \approx 0$ for each spin, see Figure B.2. In this regime, the set of equations describing the spins time evolution is satisfied by a traveling wave solution for $S_{i, x}$ and $S_{i, y}$ characterized by a wave vector $k$ and angular frequency $\omega$. [figure4] Figure B.2. (B.3) Find the relationship between $\omega$ and $k$ (known as the dispersion relation, $\omega(k)$) for the spin waves in terms of $J$, $S$ and $a$. Hint: express the position of the $i$-th spin as $x = a \cdot i$. The spin wave described above carries energy and momentum. At low energies, the relation between its energy and momentum resembles that of a massive classical particle with an effective mass $m_{\text{eff}}$, a concept known as a quasi-particle. (B.4) For small $k$ ($k \ll 1 / a$), find the effective mass $m_{\text{eff}}$ of the spin wave. Express your answer in terms of $J, S, a$ and fundamental constants. Spin waves can be experimentally probed using inelastic neutron scattering. Although neutrons have zero net charge, they have a finite spin, allowing them to interact with other spins. [figure5] Figure B.3.
Suppose that initially, all the spins in the chain are pointing along the $z$ direction. A neutron with low energy travels on the $x-y$ plane making an incident angle $\theta_{\text{in}}$ with the chain and scatters with an angle $\theta_{\text{out}}$ as shown in Figure B.3. Assuming the neutron excites a single low wave vector spin wave, find the effective mass $m_{\text{eff}}$ of the spin wave, in terms of $\theta_{\text{in}}, \theta_{\text{out}}$ and the neutron mass $m_{n}$. Assume that the chain stays at rest.
[["Award 0.4 pt if the answer applies conservation of momentum along the $y$-axis, i.e., $p_{\\text{in}} \\cos \\theta_{\\text{in}} = p_{\\text{out}} \\cos \\theta_{\\text{out}}$, where $p_{\\text{in}}$ and $p_{\\text{out}}$ are the incident and outgoing neutron momenta, and $\\theta_{\\text{in}}$, $\\theta_{\\text{out}}$ are their respective scattering angles. Otherwise, award 0 pt.", "Award 0.3 pt if the answer applies conservation of momentum along the $x$-axis, i.e., $p_s = p_{\\text{in}} \\sin \\theta_{\\text{in}} - p_{\\text{out}} \\sin \\theta_{\\text{out}}$, where $p_s$ is the spin-wave momentum. Otherwise, award 0 pt.", "Award 0.2 pt if the answer uses conservation of energy, i.e., $E_s = E_{\\text{in}} - E_{\\text{out}}$, where $E_s$ is the spin-wave energy, $E_{\\text{in}}$ and $E_{\\text{out}}$ are the neutron energies before and after scattering. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct relation between $E_{\\text{out}}$ and $E_{\\text{in}}$, namely $E_{\\text{out}} = \\left( \\frac{\\cos \\theta_{\\text{in}}}{\\cos \\theta_{\\text{out}}} \\right)^2 E_{\\text{in}}$. Otherwise, award 0 pt.", "Award 0.3 pt if the answer derives the correct final expression for the effective mass, either as $m_{\\text{eff}} = \\frac{\\sin^2(\\theta_{\\text{in}} - \\theta_{\\text{out}})}{\\cos^2 \\theta_{\\text{out}} - \\cos^2 \\theta_{\\text{in}}} m_n$ or equivalently $m_{\\text{eff}} = \\frac{\\sin(\\theta_{\\text{in}} - \\theta_{\\text{out}})}{\\sin(\\theta_{\\text{in}} + \\theta_{\\text{out}})} m_n$, where $m_n$ is the neutron mass. Otherwise, award 0 pt (0.2 pt if partially correct)."]]
["\\boxed{$m_{\\text{eff}} = \\frac{\\sin(\\theta_{\\text{in}} - \\theta_{\\text{out}})}{\\sin(\\theta_{\\text{in}} + \\theta_{\\text{out}})} m_n$}"]
["Expression"]
[null]
[1.3]
text+variable figure
Modern Physics
APhO_2025
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None.
18
APhO_2025_2_C_1
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1.
Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants.
[["Award 0.2 pt if the answer uses the Boltzmann factor $p_i \\propto \\exp(-\\varepsilon_i / k_B T)$, where $\\varepsilon_i$ is the energy of state $i$, $k_B$ is the Boltzmann constant, and $T$ is the temperature. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct Boltzmann factor for the spin-up state, $p_{\\uparrow} \\sim e^{h / k_B T}$, where $h$ is the Zeeman energy. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct Boltzmann factor for the spin-down state, $p_{\\downarrow} \\sim e^{-h / k_B T}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct ratio $\\frac{p_{\\uparrow}}{p_{\\downarrow}} = e^{2h / k_B T}$. Otherwise, award 0 pt."]]
["\\boxed{$p_{\\uparrow} / p_{\\downarrow} = e^{2h/k_B T}$}"]
["Expression"]
[null]
[0.5]
text+illustration figure
Thermodynamics
APhO_2025
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None.
19
APhO_2025_2_C_2
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants.
Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$.
[["Award 0.2 pt if the answer deduces the expression for the average polarization as $\\bar{s} = p_{\\uparrow} - p_{\\downarrow}$, where $p_{\\uparrow}$ and $p_{\\downarrow}$ are the probabilities of spin-up and spin-down states, respectively. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses the normalization condition $p_{\\uparrow} + p_{\\downarrow} = 1$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final result $\\bar{s} = \\tanh\\left( \\frac{h}{k_B T} \\right)$, where $h$ is the Zeeman energy, $k_B$ is the Boltzmann constant, and $T$ is the temperature. Otherwise, award 0 pt.", "Award 0.2 pt if the answer provides a correct sketch of $\\bar{s}$ versus $h/h_0$ in the case $h_0 \\gg k_B T$ (sharp step-like curve approaching $\\pm 1$). Otherwise, award 0 pt.", "Award 0.2 pt if the answer provides a correct sketch of $\\bar{s}$ versus $h/h_0$ in the case $h_0 \\approx k_B T$ (smooth nonlinear S-shaped curve). Otherwise, award 0 pt.", "Award 0.2 pt if the answer provides a correct sketch of $\\bar{s}$ versus $h/h_0$ in the case $h_0 \\ll k_B T$ (almost flat line near zero). Otherwise, award 0 pt."]]
["\\boxed{$\\bar{s} = \\tanh(\\frac{h}{k_B T})$}"]
["Expression"]
[null]
[1.0]
text+illustration figure
Thermodynamics
APhO_2025
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None.
20
APhO_2025_2_C_3
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants. (C.2) Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$. In the remaining questions, we turn off the magnetic field, so $h = 0$, and set $\tilde{J} > 0$.
What is the energy $E_{g}$ of the ground state (the lowest energy state)? Express your answer in terms of $\tilde{J}$ and $N$.
[["Award 0.1 pt if the answer recognizes that the energy of the system is minimized when all spins align in the same direction. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct ground state energy as $E_g = -\\tilde{J}(N-1) \\approx -\\tilde{J}N$, where $\\tilde{J}$ is the effective exchange coupling and $N$ is the number of spins (both $N-1$ and $N$ are acceptable). Otherwise, award 0 pt."]]
["\\boxed{$E_g \\simeq -\\tilde{J} N$}"]
["Expression"]
[null]
[0.2]
text+illustration figure
Modern Physics
APhO_2025
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None.
21
APhO_2025_2_C_4
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants. (C.2) Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$. In the remaining questions, we turn off the magnetic field, so $h = 0$, and set $\tilde{J} > 0$. (C.3) What is the energy $E_{g}$ of the ground state (the lowest energy state)? Express your answer in terms of $\tilde{J}$ and $N$. Instead of considering the interactions between each spin and its neighbors, we assume that each spin sees an average polarization $\bar{s}$ from its nearest-neighbors.
Approximate the energy of the system as a sum over all spins $E = -\tilde{J}_{\text{eff}} \sum_i s_i$ and express $\tilde{J}_{\text{eff}}$ in terms of $\tilde{J}$ and $\bar{s}$.
[["Award 0.1 pt if the answer realizes that $s_{i+1}$ can be replaced with the average polarization $\\bar{s}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final result $E = -\\tilde{J}_{\\text{eff}} \\sum_i s_i = -\\tilde{J} \\sum_i s_i \\bar{s}$, where $\\tilde{J}_{\\text{eff}} = \\tilde{J} \\bar{s}$ is the effective coupling constant. Otherwise, award 0 pt."]]
["\\boxed{$\\tilde{J}_{\\text{eff}} = \\tilde{J} \\bar{s}$}"]
["Expression"]
[null]
[0.2]
text+illustration figure
Modern Physics
APhO_2025
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None.
22
APhO_2025_2_C_5
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants. (C.2) Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$. In the remaining questions, we turn off the magnetic field, so $h = 0$, and set $\tilde{J} > 0$. (C.3) What is the energy $E_{g}$ of the ground state (the lowest energy state)? Express your answer in terms of $\tilde{J}$ and $N$. Instead of considering the interactions between each spin and its neighbors, we assume that each spin sees an average polarization $\bar{s}$ from its nearest-neighbors. (C.4) Approximate the energy of the system as a sum over all spins $E = -\tilde{J}_{\text{eff}} \sum_i s_i$ and express $\tilde{J}_{\text{eff}}$ in terms of $\tilde{J}$ and $\bar{s}$.
(1) Using your result from C.2, find an equation that the average polarization $\bar{s}$ must satisfy. (2) The number of solutions to this equation depends on $T$. Find the critical temperature $T_{c}$ at which the number of solutions changes. Express your answer in terms of $\tilde{J}$ and fundamental constants.
[["Award 0.1 pt if the answer correctly states the self-consistent equation for the polarization as $\\bar{s} = \\tanh\\left( \\frac{\\tilde{J}_{\\text{eff}}}{k_B T} \\right)$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer replaces $\\tilde{J}_{\\text{eff}} = \\tilde{J} \\bar{s}$ into the result from C.2, leading to $\\bar{s} = \\tanh\\left( \\frac{\\tilde{J} \\bar{s}}{k_B T} \\right)$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer realizes that for $\\tilde{J} \\ll k_B T$, there exists only one trivial solution $\\bar{s} = 0$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer realizes that for $\\tilde{J} \\gg k_B T$, there exist two non-trivial solutions for $\\bar{s}$. Otherwise, award 0 pt.", "Award 0.3 pt if the answer clearly states the condition when the number of solutions changes, namely when the slope condition at $\\bar{s}=0$ is satisfied: $\\frac{d}{d \\bar{s}} \\tanh\\left( \\frac{\\tilde{J} \\bar{s}}{k_B T_c} \\right) \\right|_{\\bar{s}=0} = \\frac{d}{d \\bar{s}} \\bar{s} \\right|_{\\bar{s}=0}$, which simplifies to $\\frac{\\tilde{J}}{k_B T_c} = 1$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer gives the correct final critical temperature $T_c = \\frac{\\tilde{J}}{k_B}$. Otherwise, award 0 pt."]]
["\\boxed{$\\bar{s} = \\tanh\\left(\\frac{\\tilde{J} \\bar{s}}{k_B T}\\right)$}", "\\boxed{$T_c = \\frac{\\tilde{J}}{k_B}$}"]
["Equation", "Expression"]
[null, null]
[0.3, 0.9]
text+illustration figure
Thermodynamics
APhO_2025
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None.
23
APhO_2025_2_C_6
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants. (C.2) Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$. In the remaining questions, we turn off the magnetic field, so $h = 0$, and set $\tilde{J} > 0$. (C.3) What is the energy $E_{g}$ of the ground state (the lowest energy state)? Express your answer in terms of $\tilde{J}$ and $N$. Instead of considering the interactions between each spin and its neighbors, we assume that each spin sees an average polarization $\bar{s}$ from its nearest-neighbors. (C.4) Approximate the energy of the system as a sum over all spins $E = -\tilde{J}_{\text{eff}} \sum_i s_i$ and express $\tilde{J}_{\text{eff}}$ in terms of $\tilde{J}$ and $\bar{s}$. (C.5) Using your result from C.2, find an equation that the average polarization $\bar{s}$ must satisfy. The number of solutions to this equation depends on $T$. Find the critical temperature $T_{c}$ at which the number of solutions changes. Express your answer in terms of $\tilde{J}$ and fundamental constants.
Find all possible values of $\bar{s}$ when $T < T_{c}$ and $T_{c} - T \ll T_{c}$. Express your answers in terms of $T$ and $T_{c}$. Sketch all possible values of $\bar{s}$ for the temperature $T$ in the range $0 \leq T \leq 2 T_{c}$.
[["Award 0.1 pt if the answer uses the proper approximation $\\tanh(x) \\approx x - \\frac{1}{3}x^3$ for small $x$, leading to $\\bar{s} = \\frac{T_c}{T} \\bar{s} - \\frac{1}{3}\\left( \\frac{T_c}{T} \\bar{s} \\right)^3$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer derives a correct non-trivial solution for $\\bar{s}$, i.e., $\\bar{s} = \\sqrt{3 \\left[ \\left(\\frac{T}{T_c}\\right)^2 - \\left(\\frac{T}{T_c}\\right)^3 \\right]} = \\sqrt{3 \\left(\\frac{T}{T_c}\\right)^2 \\cdot \\left(1 - \\frac{T}{T_c}\\right) } \\approx \\sqrt{3 \\frac{T_c - T}{T_c}}$, even if not fully simplified. Otherwise, award 0 pt.", "Award 0.1 pt if the answer derives a correct non-trivial solution for $\\bar{s}$, i.e., $\\bar{s} = - \\sqrt{3 \\left[ \\left(\\frac{T}{T_c}\\right)^2 - \\left(\\frac{T}{T_c}\\right)^3 \\right]} = - \\sqrt{3 \\left(\\frac{T}{T_c}\\right)^2 \\cdot \\left(1 - \\frac{T}{T_c}\\right) } \\approx - \\sqrt{3 \\frac{T_c - T}{T_c}}$, even if not fully simplified. Otherwise, award 0 pt.", "Award 0.1 pt if the answer sketches $\\bar{s} = 0$ as the only solution for $T > T_c$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer shows that the two non-trivial solutions $\\bar{s}$ emerge vertically at $T = T_c$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer sketches $\\bar{s} = 0$ as a valid solution also for $T < T_c$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer shows that the two non-trivial solutions monotonically increase in magnitude and approach $\\pm 1$ as $T \\to 0$ (award 0.1 pt each). Otherwise, award 0 pt.", "Award 0.1 pt if the answer states that either of the non-trivial solutions has zero slope as $T \\to 0$. Otherwise, award 0 pt."]]
["\\boxed{$\\bar{s} = 0$}", "\\boxed{$\\bar{s} = \\sqrt{3 \\cdot \\frac{T_c - T}{T_c}}$}", "\\boxed{$\\bar{s} = -\\sqrt{3 \\cdot \\frac{T_c - T}{T_c}}$}"]
["Numerical Value", "Expression", "Expression"]
[null, null, null]
[0.2, 0.4, 0.4]
text+illustration figure
Thermodynamics
APhO_2025
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None.
24
APhO_2025_2_C_7
[Waves and Phase Transitions in Spin Systems] [Introduction] In classical physics, angular momentum arises from the motion of an object around an axis - whether it be a spinning top, a rotating planet, or an orbiting electron in the atom. However, in quantum physics, fundamental particles possess an intrinsic and quantized form of angular momentum called spin. This property plays a crucial role in various physical phenomena, ranging from materials properties, such as magnetism, to modern applications, such as quantum computing. In this problem we will treat spin classically, which will lead to some qualitatively correct results. You will explore the physics of spin systems through spin-spin interactions, evolution under magnetic fields, and statistical physics to understand the emergence of spin waves and phase transitions in magnets. Useful information: $\cosh(x) \equiv \frac{e^x + e^{-x}}{2}, \sinh(x) \equiv \frac{e^x - e^{-x}}{2}, $\tanh(x) \equiv \frac{\sinh(x)}{\cosh(x)} \approx x - \frac{1}{3} x^3$ for $|x| \ll 1$. The magnetic field due to a magnetic dipole of moment $\vec{\mu}$ at a position $\vec{r}$ away from it is given by ($\mu_{0}$ is is the vacuum permeability): $\vec{B} = \frac{\mu_0}{4\pi} \left( \frac{3(\vec{\mu} \cdot \vec{r})\vec{r}}{r^5} - \frac{\vec{\mu}}{r^3} \right)$ [Part C: Phase transitions in spin chains] Next we consider the same chain made of $N$ spins from Part B, except the spin vectors are now restricted to point either up or down along the $z$-axis, so that the spin component along $z$ can be written as $S_{i, z} = s_{i} S$, where $s_{i} = \pm 1$, see Figure C.1. In addition to the nearest neighbor interactions, we could have an external magnetic field pointing along the $z$-axis so that the total energy of the system is given by $E = -\tilde{J} \sum_i s_i s_{i+1} - h \sum_i s_i$ We assume $\tilde{J} \geq 0$, and $h$ is a constant dependent on the magnetic field. The spin system is at equilibrium with a heat bath at temperature $T$. Ignore the edges of the chain. [figure1] Figure C.1. (C.1) Assume first that $\tilde{J} = 0$, what is the ratio between the probability to find an arbitrary spin aligned to the magnetic field $p_{\uparrow}$ to being anti-aligned to the magnetic field $p_{\downarrow}$? Express $p_{\uparrow} / p_{\downarrow}$ in terms of $h, T$ and fundamental constants. (C.2) Find the average polarization of the system $\bar{s} \equiv \frac{1}{N} \sum_{i} s_{i}$ for $N \gg 1$ in terms of $h, T$ and fundamental constants. If the magnetic field $h$ can range from $-h_{0}$ to $h_{0}$, make a sketch of $\bar{s}$ as a function of $h$ for the cases $h_{o} \gg k_{B} T$, $h_{o} \approx k_{B} T$ and $h_{o} \ll k_{B} T$. In the remaining questions, we turn off the magnetic field, so $h = 0$, and set $\tilde{J} > 0$. (C.3) What is the energy $E_{g}$ of the ground state (the lowest energy state)? Express your answer in terms of $\tilde{J}$ and $N$. Instead of considering the interactions between each spin and its neighbors, we assume that each spin sees an average polarization $\bar{s}$ from its nearest-neighbors. (C.4) Approximate the energy of the system as a sum over all spins $E = -\tilde{J}_{\text{eff}} \sum_i s_i$ and express $\tilde{J}_{\text{eff}}$ in terms of $\tilde{J}$ and $\bar{s}$. (C.5) Using your result from C.2, find an equation that the average polarization $\bar{s}$ must satisfy. The number of solutions to this equation depends on $T$. Find the critical temperature $T_{c}$ at which the number of solutions changes. Express your answer in terms of $\tilde{J}$ and fundamental constants. (C.6) Find all possible values of $\bar{s}$ when $T < T_{c}$ and $T_{c} - T \ll T_{c}$. Express your answers in terms of $T$ and $T_{c}$. Sketch all possible values of $\bar{s}$ for the temperature $T$ in the range $0 \leq T \leq 2 T_{c}$.
Write the option letter (A or B) in your answer. (1) What magnetic phase of matter does $T > T_{c}$ correspond to? (A) Paramagnetic (B) Ferromagnetic. (2) What magnetic phase of matter does $T < T_{c}$ correspond to? (A) Paramagnetic (B) Ferromagnetic.
[["Award 0.1 pt if the answer correctly classifies the phase for $T > T_c$ as paramagnetic (option A). Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly classifies the phase for $T < T_c$ as ferromagnetic (option B). Otherwise, award 0 pt."]]
["\\boxed{A}", "\\boxed{B}"]
["Multiple Choice", "Multiple Choice"]
[null, null]
[0.1, 0.1]
text+illustration figure
Thermodynamics
APhO_2025
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None.
25
APhO_2025_3_A_1
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part A: Surface Temperature of the Earth] In this section, we study the effect of the atmosphere on the Earth surface's temperature. Assume that Earth and its atmosphere have an albedo $a = 0.3$ for solar radiation, which is the reflected fraction of the total incident radiation. You may use this value in all parts of this problem. In addition, assume the Earth radiates as a black body.
Express the average net solar power received by the Earth and atmosphere system $P_{0}$ in terms of $F_{s}$, $a$ and $R_{E}$, the radius of the Earth.
[["Award 0.1 pt if the answer identifies the correct effective cross-sectional area as $A = \\pi R_E^2$, where $R_E$ is the Earth's radius. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final absorbed power expression $P_0 = (1 - a) \\pi R_E^2 F_s$, where $a$ is the albedo and $F_s$ is the solar flux. Otherwise, award 0 pt."]]
["\\boxed{$P_0 = (1 - a) \\pi R_E^2 F_s$}"]
["Expression"]
[null]
[0.2]
text-only
Thermodynamics
APhO_2025
None.
26
APhO_2025_3_A_2
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part A: Surface Temperature of the Earth] In this section, we study the effect of the atmosphere on the Earth surface's temperature. Assume that Earth and its atmosphere have an albedo $a = 0.3$ for solar radiation, which is the reflected fraction of the total incident radiation. You may use this value in all parts of this problem. In addition, assume the Earth radiates as a black body. (A.1) Express the average net solar power received by the Earth and atmosphere system $P_{0}$ in terms of $F_{s}$, $a$ and $R_{E}$, the radius of the Earth.
Estimate the temperature of the Earth's surface $T_{g 0}$ assuming that it is at a steady state. Ignore the atmosphere. Express your answer in $K$.
[["Award 0.1 pt if the answer sets up the energy balance condition $P_{bd} = P_0$, where $P_{bd}$ is the blackbody radiation power and $P_0$ is the absorbed solar power. Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes the correct explicit blackbody radiation formula $P_{bd} = \\sigma A T^4$ with $A = 4 \\pi R_E^2$, where $\\sigma$ is the Stefan\u2013Boltzmann constant, $T$ is the temperature, and $R_E$ is the Earth's radius. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct numerical value for the temperature, $T_{g0} \\approx 255 \\text{K} \\approx -18^{\\circ}\\text{C}$. Otherwise, award 0 pt."]]
["\\boxed{255}"]
["Numerical Value"]
["K"]
[0.3]
text-only
Thermodynamics
APhO_2025
None.
27
APhO_2025_3_A_3
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part A: Surface Temperature of the Earth] In this section, we study the effect of the atmosphere on the Earth surface's temperature. Assume that Earth and its atmosphere have an albedo $a = 0.3$ for solar radiation, which is the reflected fraction of the total incident radiation. You may use this value in all parts of this problem. In addition, assume the Earth radiates as a black body. (A.1) Express the average net solar power received by the Earth and atmosphere system $P_{0}$ in terms of $F_{s}$, $a$ and $R_{E}$, the radius of the Earth. (A.2) Estimate the temperature of the Earth's surface $T_{g 0}$ assuming that it is at a steady state. Ignore the atmosphere. Your answer for (A.2) should be lower than what you would expect. We now consider adding a thin atmospheric layer at temperature $T_{a}$, see Figure A.1. The atmospheric layer transmits a net fraction $t_{\mathrm{sw}}$ of the incident solar radiation and a net fraction $t_{\text{lw}}$ of the Earth's thermal radiation. Otherwise, you may treat the atmosphere as a black body. [figure1] Figure A.1
Assuming the system is in a steady state, calculate $T_{g}$, the temperature of the ground. Use $t_{\mathrm{sw}} = 0.9$ and $t_{\mathrm{lw}} = 0.2$. Express your answer in $K$.
[["Award 0.1 pt if the answer includes a correct statement of radiation balance in the region outside the atmosphere, e.g., $t_{lw} P_E + P_{atmo} = P_0$, where $t_{lw}$ is the longwave transmission coefficient, $P_E$ is the Earth's emitted power, $P_{atmo}$ is the atmospheric radiation, and $P_0$ is the absorbed solar power. Otherwise, award 0 pt.", "Award 0.2 pt if the answer includes a correct statement of radiation balance in the region between the Earth's surface and the atmosphere, e.g., $P_E = P_{atmo} + t_{sw} P_0$, where $t_{sw}$ is the shortwave transmission coefficient. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses $t_{sw}$ correctly in the equation $P_E = P_{atmo} + t_{sw} P_0$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses $t_{lw}$ correctly in the equation $t_{lw} P_E + P_{atmo} = P_0$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer gives the correct numerical result for the ground temperature, $T_g = \\left( \\frac{1+t_{sw}}{1+t_{lw}} \\right)^{1/4} T_{g0} \\approx 286 \\text{K} \\approx 13^{\\circ}\\text{C}$, where $T_{g0}$ is the temperature of the Earth's surface. Partial points: award 0.1 pt if only the analytic form is given in the answer. Otherwise, award 0 pt."]]
["\\boxed{286}"]
["Numerical Value"]
["K"]
[0.7]
text+illustration figure
Thermodynamics
APhO_2025
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
None.
28
APhO_2025_3_B_1
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules.
Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$?
[["Award 0.1 pt if the answer writes the correct equation of motion for particle A: $\\frac{d^2 x_A}{dt^2} = +\\frac{k}{m_A}(\\ell - \\ell_0)$, where $x_A$ is the position of particle A, $m_A$ is its mass, $k$ is the spring constant, $\\ell$ is the instantaneous spring length, and $\\ell_0$ is the natural spring length. Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes the correct equation of motion for particle B: $\\frac{d^2 x_B}{dt^2} = -\\frac{k}{m_B}(\\ell - \\ell_0)$, where $x_B$ is the position of particle B and $m_B$ is its mass. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly derives the equation of motion for the relative coordinate $\\ell = x_B - x_A$, namely $\\frac{d^2 \\ell}{dt^2} = -k\\left( \\frac{1}{m_A} + \\frac{1}{m_B} \\right)(\\ell - \\ell_0)$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer provides the correct final angular frequency of oscillation: $\\omega_d = \\sqrt{\\frac{k}{\\mu}} = \\sqrt{ k \\frac{m_A + m_B}{m_A m_B}}$, where $\\mu = \\frac{m_A m_B}{m_A + m_B}$ is the reduced mass. Otherwise, award 0 pt."]]
["\\boxed{$\\omega_d = \\sqrt{k \\frac{m_A + m_B}{m_A m_B}}$}"]
["Expression"]
[null]
[0.5]
text-only
Mechanics
APhO_2025
None.
29
APhO_2025_3_B_2
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules. (B.1) Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$?
Quantum mechanics dictates that vibrational excitations due to absorbing a photon can only raise the quantum energy level by one. What is the energy of the photon $E_{p}$ that can excite the vibration in B.1? Neglect recoil effects.
[["Award 0.2 pt if the answer gives the correct photon energy as $E = \\hbar \\omega_d$ (where $\\hbar$ is the reduced Planck constant and $\\omega_d$ is the angular frequency). Partial points: only award 0.1 pt if $h$ is used instead of $\\hbar$; no other numerical factors receive credit."]]
["\\boxed{$E_p = \\hbar \\omega_d$}"]
["Expression"]
[null]
[0.2]
text-only
Modern Physics
APhO_2025
None.
30
APhO_2025_3_B_3
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules. (B.1) Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$? (B.2) Quantum mechanics dictates that vibrational excitations due to absorbing a photon can only raise the quantum energy level by one. What is the energy of the photon $E_{p}$ that can excite the vibration in B.1? Neglect recoil effects. Quantum mechanics forbids the vibrational modes of symmetric diatomic molecules, such as nitrogen and oxygen (the most abundant gasses in the Earth's atmosphere) to be excited by light. This explains why $N_{2}$ and $O_{2}$ do not contribute to the green house effect. In general, the absorption of light by molecules is governed by the allowed energy transitions in them. However, the energy of the light absorbed does not have to exactly match the energy gap in the molecule. Suppose that a molecule at rest has a spectral line (an allowed transition) at frequency $f_{0}$.
What is the shift in the spectral line $f - f_{0}$ if the molecule is moving with velocity $v$ towards the emitter such that $|v| \ll c$, where $c$ is the speed of light.
[["Award 0.1 pt if the answer writes down an expression for the Doppler effect, even if it is incorrect. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct frequency shift as $f - f_0 = \\frac{v}{c} f_0$, where $f$ is the observed frequency, $f_0$ is the source frequency, $v$ is the velocity of the source, and $c$ is the speed of light. Otherwise, award 0 pt."]]
["\\boxed{$f - f_0 = \\frac{v}{c} f_0$}"]
["Expression"]
[null]
[0.2]
text-only
Optics
APhO_2025
None.
31
APhO_2025_3_B_4
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules. (B.1) Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$? (B.2) Quantum mechanics dictates that vibrational excitations due to absorbing a photon can only raise the quantum energy level by one. What is the energy of the photon $E_{p}$ that can excite the vibration in B.1? Neglect recoil effects. Quantum mechanics forbids the vibrational modes of symmetric diatomic molecules, such as nitrogen and oxygen (the most abundant gasses in the Earth's atmosphere) to be excited by light. This explains why $N_{2}$ and $O_{2}$ do not contribute to the green house effect. In general, the absorption of light by molecules is governed by the allowed energy transitions in them. However, the energy of the light absorbed does not have to exactly match the energy gap in the molecule. Suppose that a molecule at rest has a spectral line (an allowed transition) at frequency $f_{0}$. (B.3) What is the shift in the spectral line $f - f_{0}$ if the molecule is moving with velocity $v$ towards the emitter such that $|v| \ll c$, where $c$ is the speed of light. For a gas at temperature $T$, the velocity of its molecules is distributed according to Maxwell's distribution. For a molecule of mass $m$, the probability to find a molecule's velocity along one dimension to be between $v$ and $v + dv$ is $p_{1}(v) d v$, where $p_{1}(v)$ is a probability distribution function given by $p_{1}(v) = C \exp\left( -\frac{mv^{2}}{2k_{B}T} \right)$ $C$ is a normalization constant ensuring the probabilities add up to one, and $k_{B}$ is the Boltzmann constant.
Find the normalization constant $C$, assuming that the velocity $v$ could range from $-\infty$ to $\infty$.
[["Award 0.1 pt if the answer writes down the normalization condition $\\int_{-\\infty}^{\\infty} p(v) dv = 1$, even if it is incorrectly applied from 0 to $\\infty$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct result for the normalization constant as $C = \\sqrt{ \\frac{m}{2 \\pi k_B T} }$, where $m$ is the particle mass, $k_B$ is the Boltzmann constant, and $T$ is the temperature. Otherwise, award 0 pt."]]
["\\boxed{$C = \\sqrt{\\frac{m}{2 \\pi k_B T}}$}"]
["Expression"]
[null]
[0.2]
text-only
Thermodynamics
APhO_2025
None.
32
APhO_2025_3_B_5
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules. (B.1) Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$? (B.2) Quantum mechanics dictates that vibrational excitations due to absorbing a photon can only raise the quantum energy level by one. What is the energy of the photon $E_{p}$ that can excite the vibration in B.1? Neglect recoil effects. Quantum mechanics forbids the vibrational modes of symmetric diatomic molecules, such as nitrogen and oxygen (the most abundant gasses in the Earth's atmosphere) to be excited by light. This explains why $N_{2}$ and $O_{2}$ do not contribute to the green house effect. In general, the absorption of light by molecules is governed by the allowed energy transitions in them. However, the energy of the light absorbed does not have to exactly match the energy gap in the molecule. Suppose that a molecule at rest has a spectral line (an allowed transition) at frequency $f_{0}$. (B.3) What is the shift in the spectral line $f - f_{0}$ if the molecule is moving with velocity $v$ towards the emitter such that $|v| \ll c$, where $c$ is the speed of light. For a gas at temperature $T$, the velocity of its molecules is distributed according to Maxwell's distribution. For a molecule of mass $m$, the probability to find a molecule's velocity along one dimension to be between $v$ and $v + dv$ is $p_{1}(v) d v$, where $p_{1}(v)$ is a probability distribution function given by $p_{1}(v) = C \exp\left( -\frac{mv^{2}}{2k_{B}T} \right)$ $C$ is a normalization constant ensuring the probabilities add up to one, and $k_{B}$ is the Boltzmann constant. (B.4) Find the normalization constant $C$, assuming that the velocity $v$ could range from $-\infty$ to $\infty$.
Find the probability distribution function $p_{2}(f)$ to find a molecule with a spectral line $f_{0}$ shifted to $f$ due to thermal motion, up to a normalization factor, in terms of $f, f_{0}, T, m$ and fundamental constants. Use $C$ to represent the normalization factor.
[["Award 0.1 pt if the answer correctly replaces the velocity $v$ in the distribution using the Doppler effect relation $v = \\frac{f - f_0}{f_0} c$, where $f$ is the observed frequency, $f_0$ is the source frequency, and $c$ is the speed of light. Otherwise, award 0 pt.", "Award 0.2 pt if the answer writes the correct exponential dependence for the probability distribution as $p(f) \\propto \\exp \\left[ - \\frac{m c^2}{2 k_B T} \\left( \\frac{f - f_0}{f_0} \\right)^2 \\right]$, where $m$ is the particle mass, $k_B$ is the Boltzmann constant, and $T$ is the temperature. Otherwise, award 0 pt."]]
["\\boxed{$p_2(f) = C \\exp\\left[-\\frac{mc^2}{2k_B T} \\left(\\frac{f - f_0}{f_0}\\right)^2\\right]$}"]
["Expression"]
[null]
[0.3]
text-only
Thermodynamics
APhO_2025
None.
33
APhO_2025_3_B_6
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part B: The absorption spectrum of atmospheric gases] The infrared radiation emitted by Earth has low energy, incapable of exciting electrons within the molecules, but it has the ability to excite the vibrational and rotational modes of the molecules. (B.1) Consider a simple diatomic molecule modeled as two point masses $m_{A}$ and $m_{B}$ connected by a spring with spring constant $k$. What is the angular frequency of vibrations $\omega_{d}$? (B.2) Quantum mechanics dictates that vibrational excitations due to absorbing a photon can only raise the quantum energy level by one. What is the energy of the photon $E_{p}$ that can excite the vibration in B.1? Neglect recoil effects. Quantum mechanics forbids the vibrational modes of symmetric diatomic molecules, such as nitrogen and oxygen (the most abundant gasses in the Earth's atmosphere) to be excited by light. This explains why $N_{2}$ and $O_{2}$ do not contribute to the green house effect. In general, the absorption of light by molecules is governed by the allowed energy transitions in them. However, the energy of the light absorbed does not have to exactly match the energy gap in the molecule. Suppose that a molecule at rest has a spectral line (an allowed transition) at frequency $f_{0}$. (B.3) What is the shift in the spectral line $f - f_{0}$ if the molecule is moving with velocity $v$ towards the emitter such that $|v| \ll c$, where $c$ is the speed of light. For a gas at temperature $T$, the velocity of its molecules is distributed according to Maxwell's distribution. For a molecule of mass $m$, the probability to find a molecule's velocity along one dimension to be between $v$ and $v + dv$ is $p_{1}(v) d v$, where $p_{1}(v)$ is a probability distribution function given by $p_{1}(v) = C \exp\left( -\frac{mv^{2}}{2k_{B}T} \right)$ $C$ is a normalization constant ensuring the probabilities add up to one, and $k_{B}$ is the Boltzmann constant. (B.4) Find the normalization constant $C$, assuming that the velocity $v$ could range from $-\infty$ to $\infty$. (B.5) Find the probability distribution function $p_{2}(f)$ to find a molecule with a spectral line $f_{0}$ shifted to $f$ due to thermal motion, up to a normalization factor, in terms of $f, f_{0}, T, m$ and fundamental constants. Use $C$ to represent the normalization factor.
Sketch $p_{2}(f)$ as a function of $f - f_{0}$, and determine the shift $f^{\star} - f_{0}$ at which $p_{2}(f^{\star})$ is a fraction $1 / e$ of its peak value, where $e$ is the natural number.
[["Award 0.1 pt if the answer states that the probability distribution $p(f)$ has a single peak at zero frequency shift ($f - f_0 = 0$). Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly identifies that the distribution is symmetric about $f - f_0 = 0$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer states that the probability distribution decays to zero as $f - f_0 \\to \\pm \\infty$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct condition for the $1/e$ point of the distribution as $f^* - f_0 = f_0 \\sqrt{ \\frac{2 k_B T}{m c^2} }$, where $m$ is the particle mass, $k_B$ is the Boltzmann constant, $T$ is the temperature, and $c$ is the speed of light. Otherwise, award 0 pt."]]
["\\boxed{$f^{\\star} - f_0 = f_0 \\sqrt{\\frac{2k_B T}{mc^2}}$}"]
["Expression"]
[null]
[0.4]
text-only
Thermodynamics
APhO_2025
None.
34
APhO_2025_3_C_1
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part C: Stability of air in the atmosphere] Consider a small cylindrical mass of air at height $z$ above the ground. The pressure and mass density of air at that height are $p(z)$ and $\rho(z)$, respectively, see Figure C.1. Assume a uniform downward gravitational field $g$ and that the pressure on the Earth's surface is $p_{o}$. [figure1] Figure C.1
Assuming that the small air mass is at hydrostatic equilibrium, derive an expression of the rate of change of pressure with respect to height, $d p / d z$ in terms of $g$ and $\rho(z)$.
[["Award 0.1 pt if the answer states that the sum of forces equals zero in hydrostatic equilibrium. Otherwise, award 0 pt.", "Award 0.1 pt if the answer correctly identifies the pressure force contributions above and below the thin layer, i.e. $p(z)S = p(z + \\mathrm{d}z)S + \\rho(z) g S \\mathrm{d}z$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final hydrostatic equilibrium equation $\\frac{dp}{dz} = - \\rho(z) g$, where $\\rho(z)$ is the density and $g$ is the gravitational acceleration. Otherwise, award 0 pt."]]
["\\boxed{$\\frac{dp}{dz} = -\\rho(z) g$}"]
["Expression"]
[null]
[0.3]
text+illustration figure
Mechanics
APhO_2025
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None.
35
APhO_2025_3_C_2
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part C: Stability of air in the atmosphere] Consider a small cylindrical mass of air at height $z$ above the ground. The pressure and mass density of air at that height are $p(z)$ and $\rho(z)$, respectively, see Figure C.1. Assume a uniform downward gravitational field $g$ and that the pressure on the Earth's surface is $p_{o}$. [figure1] Figure C.1 (C.1) Assuming that the small air mass is at hydrostatic equilibrium, derive an expression of the rate of change of pressure with respect to height, $d p / d z$ in terms of $g$ and $\rho(z)$.
Express $d p / d z$ in terms of $\mu_{\text{air}}, g, p(z)$ and $T(z)$, the temperature at height $z$ and fundamental constants.
[["Award 0.1 pt if the answer correctly uses the ideal gas law $pV = nRT$ and rewrites it as $\\rho(z) = \\frac{p(z) \\mu_{air}}{R T(z)}$, where $\\mu_{air}$ is the molar mass of air and $R$ is the gas constant. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final hydrostatic equilibrium expression $\\frac{dp}{dz} = - \\frac{\\mu_{air} p(z)}{R T(z)} g$. Otherwise, award 0 pt."]]
["\\boxed{$\\frac{dp}{dz} = -\\frac{\\mu_{\\text{air}} p(z)}{R T(z)} g$}"]
["Expression"]
[null]
[0.2]
text+illustration figure
Thermodynamics
APhO_2025
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None.
36
APhO_2025_3_C_3
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part C: Stability of air in the atmosphere] Consider a small cylindrical mass of air at height $z$ above the ground. The pressure and mass density of air at that height are $p(z)$ and $\rho(z)$, respectively, see Figure C.1. Assume a uniform downward gravitational field $g$ and that the pressure on the Earth's surface is $p_{o}$. [figure1] Figure C.1 (C.1) Assuming that the small air mass is at hydrostatic equilibrium, derive an expression of the rate of change of pressure with respect to height, $d p / d z$ in terms of $g$ and $\rho(z)$. (C.2) Express $d p / d z$ in terms of $\mu_{\text{air}}, g, p(z)$ and $T(z)$, the temperature at height $z$ and fundamental constants.
Assuming an isothermal atmosphere, $T(z) = T$, find an expression for $p(z)$ in terms of $z, \mu_{\text{air}}, g, p_{o}, T$ and fundamental constants.
[["Award 0.1 pt if the answer recognizes and correctly rewrites the equation as a separable differential equation $\\frac{dp}{p} = - \\frac{\\mu_{air}}{R T} g dz$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer gives the correct final solution $p(z) = p_0 \\exp \\left( - \\frac{\\mu_{air}}{R T} g z \\right)$, where $p_0$ is the pressure at $z=0$. Otherwise, award 0 pt."]]
["\\boxed{$p(z) = p_0 \\exp\\left(-\\frac{\\mu_{\\text{air}}}{RT} gz\\right)$}"]
["Expression"]
[null]
[0.2]
text+illustration figure
Thermodynamics
APhO_2025
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None.
37
APhO_2025_3_C_4
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part C: Stability of air in the atmosphere] Consider a small cylindrical mass of air at height $z$ above the ground. The pressure and mass density of air at that height are $p(z)$ and $\rho(z)$, respectively, see Figure C.1. Assume a uniform downward gravitational field $g$ and that the pressure on the Earth's surface is $p_{o}$. [figure1] Figure C.1 (C.1) Assuming that the small air mass is at hydrostatic equilibrium, derive an expression of the rate of change of pressure with respect to height, $d p / d z$ in terms of $g$ and $\rho(z)$. (C.2) Express $d p / d z$ in terms of $\mu_{\text{air}}, g, p(z)$ and $T(z)$, the temperature at height $z$ and fundamental constants. (C.3) Assuming an isothermal atmosphere, $T(z) = T$, find an expression for $p(z)$ in terms of $z, \mu_{\text{air}}, g, p_{o}, T$ and fundamental constants. In a real atmosphere, the temperature is not constant but changes with height. The rate of decrease of temperature with height $\Gamma(z) = -d T / d z$ is called the lapse rate. Consider a small mass of air rising adiabatically in the atmosphere such that it remains at mechanical equilibrium with its surrounding.
For the adiabatically rising air mass, find the adiabatic lapse rate $\Gamma_{a}$ in terms of $c_{p}$, the molar specific heat at constant pressure, $\mu_{\text{air}}$ and $g$.
[["Award 0.1 pt if the answer writes the adiabatic relation in any correct form for an ideal gas, e.g., $p V^{\\gamma} = \\text{const.}$ or equivalently $p^{1-\\gamma} T^{\\gamma} = \\text{const.}$ where $\\gamma = c_p/c_v$, $c_p$ and $c_v$ are the molar specific heats at constant pressure and volume. Otherwise, award 0 pt.", "Award 0.3 pt if the answer differentiates the adiabatic relation with respect to height $z$ to relate temperature and pressure gradients as $\\frac{dT}{dz} = -\\frac{1-\\gamma}{\\gamma} \\frac{T(z)}{p(z)} \\frac{dp}{dz}$, where $T(z)$ is temperature and $p(z)$ is pressure. Otherwise, award 0 pt.", "Award 0.2 pt if the answer obtains the correct adiabatic lapse rate $\\Gamma_a = \\frac{\\mu_{\\text{air}}}{c_p} g$. Otherwise, award 0 pt."]]
["\\boxed{$\\Gamma_a = \\frac{\\mu_{\\text{air}}}{c_p} g$}"]
["Expression"]
[null]
[0.6]
text+illustration figure
Thermodynamics
APhO_2025
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None.
38
APhO_2025_3_C_5
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part C: Stability of air in the atmosphere] Consider a small cylindrical mass of air at height $z$ above the ground. The pressure and mass density of air at that height are $p(z)$ and $\rho(z)$, respectively, see Figure C.1. Assume a uniform downward gravitational field $g$ and that the pressure on the Earth's surface is $p_{o}$. [figure1] Figure C.1 (C.1) Assuming that the small air mass is at hydrostatic equilibrium, derive an expression of the rate of change of pressure with respect to height, $d p / d z$ in terms of $g$ and $\rho(z)$. (C.2) Express $d p / d z$ in terms of $\mu_{\text{air}}, g, p(z)$ and $T(z)$, the temperature at height $z$ and fundamental constants. (C.3) Assuming an isothermal atmosphere, $T(z) = T$, find an expression for $p(z)$ in terms of $z, \mu_{\text{air}}, g, p_{o}, T$ and fundamental constants. In a real atmosphere, the temperature is not constant but changes with height. The rate of decrease of temperature with height $\Gamma(z) = -d T / d z$ is called the lapse rate. Consider a small mass of air rising adiabatically in the atmosphere such that it remains at mechanical equilibrium with its surrounding. (C.4) For the adiabatically rising air mass, find the adiabatic lapse rate $\Gamma_{a}$ in terms of $c_{p}$, the molar specific heat at constant pressure, $\mu_{\text{air}}$ and $g$. To analyze the stability of an atmosphere, we imagine starting from an equilibrium state, and then perturbing a small mass of air and analyze its response. Consider a small air mass initially in equilibrium with the surrounding air at height $z$ and temperature $T$. It is then adiabatically displaced vertically by a displacement $\delta z_{0}$. Assume that throughout the motion, the air parcel always has the same pressure as the surrounding air at the same height. The surrounding atmosphere is unaltered and has a different lapse rate $\Gamma$. Neglect viscosity.
(1) Find the equation of motion for $\delta z$, the instantaneous vertical displacement. (2) Under what condition is the equilibrium at $z$ stable? (3) What is the angular frequency $\omega$ of small oscillation? Express your answers in terms of $T, \Gamma, g, \mu_{\text{air}}$ and $c_{p}$.
[["Award 0.2 pt if the answer obtains the gravitational force with parcel density correctly as $\\delta m g = \\rho_p \\delta V g$, where $\\delta m$ is the mass of the parcel, $\\rho_p$ is the density of the parcel, and $\\delta V$ is its volume. Otherwise, award 0 pt.", "Award 0.3 pt if the answer obtains the buoyancy force with air density correctly as $\\rho_a(z) g \\delta V$, where $\\rho_a$ is the surrounding air density. Otherwise, award 0 pt.", "Award 0.2 pt if the answer writes the correct equation of motion as $\\delta m \\frac{d^2 z}{dt^2} = \\rho_a(z) g \\delta V - \\delta m g$, and after substitution simplifies to $\\frac{d^2 z}{dt^2} = \\frac{\\rho_a(z+\\delta z) - \\rho_p(z+\\delta z)}{\\rho_p(z+\\delta z)} g$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly relates density to inverse temperature as $\\rho \\propto \\frac{1}{T}$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer uses the appropriate approximation $T(z+\\delta z) = T(z) + \\Gamma \\delta z$, and simplifies to $\\frac{d^2 z}{dt^2} = \\frac{T(z) + \\Gamma \\delta z - T(z) - \\Gamma_a \\delta z}{T(z) + \\Gamma_a \\delta z} g$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer provides the correct stability requirement that motion is stable whenever $\\Gamma_a > \\Gamma$, where $\\Gamma_a = \\mu_{air} g / c_p$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer obtains the correct angular frequency of small oscillation as $\\omega = \\sqrt{\\frac{\\Gamma_a - \\Gamma}{T} g} = \\sqrt{\\frac{\\mu_{air} g / c_p - \\Gamma}{T} g}$. Otherwise, award 0 pt."]]
["\\boxed{$\\frac{d^2 z}{d t^2} = \\frac{\\Gamma - \\mu_{\\text{air}} g/c_p}{T} g \\delta_z$}", "\\boxed{$\\mu_{\\text{air}} g/c_p > \\Gamma$}", "\\boxed{$\\omega = \\sqrt{\\frac{\\mu_{\\text{air}} g/c_p - \\Gamma}{T} g}$}"]
["Equation", "Inequality", "Expression"]
[null, null, null]
[1.1, 0.1, 0.2]
text+illustration figure
Mechanics
APhO_2025
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None.
39
APhO_2025_3_D_1
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part D: Moisture] Even though water constitutes a small portion of the atmosphere, it has a significant role in climate science. It is responsible for precipitation, and it is the most significant greenhouse gas. The phase of water depends on what temperature and pressure the water system is at, depicted on a $p-T$ phase diagram, see Figure D.1. When the pressure and temperature lie on the coexistence curve, both liquid and vapor water can be present in the system. The slope of the coexistence curve is given by the ClausiusClapeyron equation: $\frac{d p_s}{d T} = \frac{\Delta S}{\Delta V}$ where $p_{s}$ is the saturation pressure, the pressure at the phase transition, $\Delta S$ and $\Delta V$ are the changes in entropy and volume across the phase transitions, respectively. Treat water vapor as an ideal gas. [figure1] Figure D.1
Express $d p_{s} / d T$ for the water liquid-vapor coexistence curve in terms of the water latent heat of evaporation $L, \mu_{\text{H_2O}}, p_{s}, T$ and fundamental constants.
[["Award 0.2 pt if the answer obtains the correct entropy change as $\\Delta S = \\frac{L m}{T}$, where $L$ is the latent heat of evaporation, $m$ is the mass of liquid water, and $T$ is the temperature. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly states that $V_{vapor} \\gg V_{liquid}$ and therefore approximates $\\Delta V \\approx V_{vapor}$, with $V_{vapor} = \\frac{nRT}{p_s(T)}$, where $n$ is the number of moles, $R$ is the gas constant, and $p_s(T)$ is the saturation vapor pressure. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct final relation $\\frac{dp_s}{dT} = \\frac{\\mu_{H_2O} L p_s}{R T^2}$, where $\\mu_{H_2O}$ is the molar mass of water. Otherwise, award 0 pt."]]
["\\boxed{$\\frac{d p_s}{d T} = \\frac{\\mu_{\\text{H_2O}} L p_s}{R T^2}$}"]
["Expression"]
[null]
[0.5]
text+illustration figure
Thermodynamics
APhO_2025
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None.
40
APhO_2025_3_D_2
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part D: Moisture] Even though water constitutes a small portion of the atmosphere, it has a significant role in climate science. It is responsible for precipitation, and it is the most significant greenhouse gas. The phase of water depends on what temperature and pressure the water system is at, depicted on a $p-T$ phase diagram, see Figure D.1. When the pressure and temperature lie on the coexistence curve, both liquid and vapor water can be present in the system. The slope of the coexistence curve is given by the ClausiusClapeyron equation: $\frac{d p_s}{d T} = \frac{\Delta S}{\Delta V}$ where $p_{s}$ is the saturation pressure, the pressure at the phase transition, $\Delta S$ and $\Delta V$ are the changes in entropy and volume across the phase transitions, respectively. Treat water vapor as an ideal gas. [figure1] Figure D.1 (D.1) Express $d p_{s} / d T$ for the water liquid-vapor coexistence curve in terms of the water latent heat of evaporation $L, \mu_{\text{H_2O}}, p_{s}, T$ and fundamental constants.
If for some reference temperature $T_{o}$, $p_{s} = p_{s o}$, find an expression for $p_{s}(T)$ in terms of $p_{s o}, \mu_{\text{H_2O}}, L, T, T_{o}$ and fundamental constants.
[["Award 0.1 pt if the answer recognizes a separable differential equation and obtains $\\ln [\\frac{p_s(T)}{p_{so}}] = -\\frac{\\mu_{\\text{H_2O}} L}{R} (\\frac{1}{T} - \\frac{1}{T_o})$, where $p_s$ is the saturation vapor pressure, $\\mu_{\\text{H_2O}}$ is the molar mass of water, $L$ is latent heat, $R$ is the gas constant, and $T$ is the temperature. Otherwise, award 0 pt.", "Award 0.1 pt if the answer obtains the correct final solution $p_s(T) = p_{so} \\exp \\left[- \\frac{\\mu_{\\text{H_2O}} L}{R} \\left( \\frac{1}{T} - \\frac{1}{T_0} \\right) \\right]$, where $p_{so}$ is the reference saturation vapor pressure at $T_0$. Otherwise, award 0 pt."]]
["\\boxed{$p_s(T) = p_{s0} \\exp\\left[-\\frac{\\mu_{\\text{H_2O}} L}{R} \\left(\\frac{1}{T} - \\frac{1}{T_0}\\right)\\right]$}"]
["Expression"]
[null]
[0.2]
text+illustration figure
Thermodynamics
APhO_2025
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None.
41
APhO_2025_3_D_3
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part D: Moisture] Even though water constitutes a small portion of the atmosphere, it has a significant role in climate science. It is responsible for precipitation, and it is the most significant greenhouse gas. The phase of water depends on what temperature and pressure the water system is at, depicted on a $p-T$ phase diagram, see Figure D.1. When the pressure and temperature lie on the coexistence curve, both liquid and vapor water can be present in the system. The slope of the coexistence curve is given by the ClausiusClapeyron equation: $\frac{d p_s}{d T} = \frac{\Delta S}{\Delta V}$ where $p_{s}$ is the saturation pressure, the pressure at the phase transition, $\Delta S$ and $\Delta V$ are the changes in entropy and volume across the phase transitions, respectively. Treat water vapor as an ideal gas. [figure1] Figure D.1 (D.1) Express $d p_{s} / d T$ for the water liquid-vapor coexistence curve in terms of the water latent heat of evaporation $L, \mu_{\text{H_2O}}, p_{s}, T$ and fundamental constants. (D.2) If for some reference temperature $T_{o}$, $p_{s} = p_{s o}$, find an expression for $p_{s}(T)$ in terms of $p_{s o}, \mu_{\text{H_2O}}, L, T, T_{o}$ and fundamental constants. Now we consider a `moist' air mass that rises adiabatically starting from a temperature $T_{i}$. The mass mixing ratio of water vapor (the mass of water vapor relative to the total mass) is $\phi$. Take the air mass to have a specific molar heat at constant pressure $c_{p}$. The universal gas constant is $R = 8.31 \mathrm{J} /(\mathrm{mol} \mathrm{K})$.
Assuming that the air mass starts at $T_{i} = 17.0^{\circ} \mathrm{C}$ and $p_{i} = 10^{5} \mathrm{Pa}$. Find the temperature $T_{l}$ at which liquid water starts forming in it if $\phi = 10^{-2}$. Assume that the water content in the air mass stays constant during the rise. Use $L = 2460 \mathrm{kJ} / \mathrm{kg}$ and $p_{s o} = 1.94 \times 10^{3} \mathrm{Pa}$ at $T_{i} = 17.0^{\circ} \mathrm{C}$. Express your answer in $K$.
[["Award 0.4 pt if the answer uses Dalton's law to correctly express the partial pressure of water vapor as $p_w = \\frac{n_{H_2O}}{n_{air}} p = \\frac{m_{H_2O}/\\mu_{H_2O}}{m_{air}/\\mu_{air}} p = \\phi \\frac{\\mu_{air}}{\\mu_{H_2O}} p$, where $n$ is number of moles, $m$ is mass, $\\mu$ is molar mass, $p$ is total pressure, and $\\phi$ is mixing ratio. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly relates the mole ratio to the mass ratio via $\\frac{n_{H_2O}}{n_{air}} = \\frac{m_{H_2O}/\\mu_{H_2O}}{m_{air}/\\mu_{air}}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer states the correct adiabatic process relation for pressure: $p(T) = p_i \\left( \\frac{T}{T_i} \\right)^{c_p/R}$, where $p_i$ is the initial pressure, $T_i$ is the initial temperature, $c_p$ is the specific heat at constant pressure, and $R$ is the gas constant. Otherwise, award 0 pt.", "Award 0.5 pt if the answer shows that partial pressure of water needs to reach saturation for condensation to start. Otherwise, award 0 pt.", "Award 0.4 pt if the answer attempts to solve the transcendental equation iteratively by isolating $T$ on one side, such as rearranging to $T_l = \\frac{1}{\\frac{1}{T_i} - \\frac{R}{\\mu_{H_2O} L} \\ln \\left[ \\phi \\frac{\\mu_{air}}{\\mu_{H_2O}} \\frac{p_i}{p_{so}} \\left( \\frac{T_l}{T_i} \\right)^{c_p/R} \\right]}$. Otherwise, award 0 pt.", "Award 0.4 pt if the answer provides the correct numerical solution $T \\approx 286.8 \\text{K} \\approx 13.7^{\\circ}\\text{C}$. Otherwise, award 0 pt."]]
["\\boxed{286.8}"]
["Numerical Value"]
["K"]
[2.0]
text+illustration figure
Thermodynamics
APhO_2025
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None.
42
APhO_2025_3_E_1
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part E: Sun halo] Under suitable atmospheric conditions, a bright ring appears around the Sun which is called a halo. Halos are caused by ice crystals present in the upper troposphere. One interesting feature about halos is that they always appear at a specific angle relative to the direction of the Sun. [figure1] Figure E.1. On the left: A photograph showing a halo around the Sun. On the right: The path of a light ray passing through the prism.
Consider a simple prism with an apex angle of $\varphi$ and direct a light ray onto it at an incidence angle $\alpha$, as shown in Figure E.1. Let the refractive index of the prism be $n$. Express the angle of deviation $\delta$ of the light ray after passing through the prism in terms of $\alpha, n$ and $\varphi$.
[["Award 0.1 pt if the answer writes Snell's law correctly for the first refraction as $\\frac{\\sin \\alpha}{\\sin \\alpha'} = n$, where $\\alpha$ is the angle of incidence, $\\alpha'$ is the refracted angle, and $n$ is the refractive index. Otherwise, award 0 pt.", "Award 0.1 pt if the answer writes Snell's law correctly for the second refraction as $\\frac{\\sin \\beta}{\\sin \\beta'} = n$, where $\\beta$ is the angle of incidence inside the prism, $\\beta'$ is the refracted angle on exit, and $n$ is the refractive index. Otherwise, award 0 pt.", "Award 0.2 pt if the answer expresses the deviation angle as $\\delta = \\alpha + \\beta - \\varphi$, where $\\varphi$ is the prism angle. Otherwise, award 0 pt.", "Award 0.1 pt if the answer uses the geometric relation $\\alpha' + \\beta' = \\varphi$. Otherwise, award 0 pt.", "Award 0.2 pt if the answer performs the correct calculation steps, including substituting $\\alpha' = \\arcsin \\left( \\frac{\\sin \\alpha}{n} \\right)$ and $\\beta = \\arcsin \\left\\{ n \\sin \\left[ \\varphi - \\arcsin \\left( \\frac{\\sin \\alpha}{n} \\right) \\right] \\right\\}$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer provides the correct final formula for $\\delta$, such as $\\delta = \\alpha + \\arcsin \\left\\{ n \\sin \\left[ \\varphi - \\arcsin \\left( \\frac{\\sin \\alpha}{n} \\right) \\right] \\right\\} - \\varphi$, or any other equivalent expression. Otherwise, award 0 pt."]]
["\\boxed{$\\delta = \\alpha + \\arcsin\\{n \\sin[\\varphi - \\arcsin(\\frac{\\sin\\alpha}{n})]\\} - \\varphi$}"]
["Expression"]
[null]
[0.8]
text+variable figure
Optics
APhO_2025
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None.
43
APhO_2025_3_E_2
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part E: Sun halo] Under suitable atmospheric conditions, a bright ring appears around the Sun which is called a halo. Halos are caused by ice crystals present in the upper troposphere. One interesting feature about halos is that they always appear at a specific angle relative to the direction of the Sun. [figure1] Figure E.1. On the left: A photograph showing a halo around the Sun. On the right: The path of a light ray passing through the prism. (E.1) Consider a simple prism with an apex angle of $\varphi$ and direct a light ray onto it at an incidence angle $\alpha$, as shown in Figure E.1. Let the refractive index of the prism be $n$. Express the angle of deviation $\delta$ of the light ray after passing through the prism in terms of $\alpha, n$ and $\varphi$. The most common type of halo forms when tiny ice crystals take the shape of regular hexagonal prisms. Light from the Sun falls onto randomly oriented ice crystals drifting in the atmosphere and scatters into various directions. However, in certain specific directions, the intensity of the refracted light is maximal, and this determines the angle at which the bright ring appears. [figure2] Figure E.2. Consider a hexagonal ice prism whose six-fold symmetry axis is perpendicular to the direction of the Sun's rays. Investigate a light ray that refracts through two rectangular faces of the prism indicated in Figure E.2. Due to the random orientation of the ice crystals, the light strikes the crystal faces at varying incidence angles $\alpha$.
Calculate the deviation angle $\delta$ for incidence angles $\alpha = 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 60^{\circ}, 70^{\circ}$, in that order. Output the six values in degrees ($^{\circ}$), each with three significant figures, listed sequentially and separately. The refractive index of ice is $n = 1.31$.
[["Award 0.2 pt if the answer gives all six correct values (when \\alpha = 20^{\\circ}, \\delta = 27.5^{\\circ}; when \\alpha = 30^{\\circ}, \\delta = 23.0^{\\circ}; when \\alpha = 40^{\\circ}, \\delta = 21.8^{\\circ}; when \\alpha = 50^{\\circ}, \\delta = 22.5^{\\circ}; when \\alpha = 60^{\\circ}, \\delta = 24.7^{\\circ}; when \\alpha = 70^{\\circ}, \\delta = 28.7^{\\circ}). Partial points: award 0.1 pt if 3-5 values are correct; otherwise, award 0 pt.", "Award 0.2 pt if the calculated data points for $\\delta$ are correctly plotted against $\\alpha$ on the graph, with $\\alpha$ on the horizontal axis and $\\delta$ on the vertical axis. Otherwise, award 0 pt.", "Award 0.2 pt if the answer correctly identifies and shows that $\\delta$ has a local minimum (around $\\alpha \\approx 40^\\circ$). Otherwise, award 0 pt."]]
["\\boxed{$\\delta = 27.5^{\\circ}$ when $\\alpha = 20^{\\circ}$}", "\\boxed{$\\delta = 23.0^{\\circ}$ when $\\alpha = 30^{\\circ}$}", "\\boxed{$\\delta = 21.8^{\\circ}$ when $\\alpha = 40^{\\circ}$}", "\\boxed{$\\delta = 22.5^{\\circ}$ when $\\alpha = 50^{\\circ}$}", "\\boxed{$\\delta = 24.7^{\\circ}$ when $\\alpha = 60^{\\circ}$}", "\\boxed{$\\delta = 28.7^{\\circ}$ when $\\alpha = 70^{\\circ}$}"]
["Numerical Value", "Numerical Value", "Numerical Value", "Numerical Value", "Numerical Value", "Numerical Value"]
["degrees", "degrees", "degrees", "degrees", "degrees", "degrees"]
[0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
text+variable figure
Optics
APhO_2025
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None.
44
APhO_2025_3_E_3
[Atmospheric Physics] The Earth's atmosphere is a complex physical system, and predicting its behavior is crucial for environmental and meteorological purposes. However, even the best theoretical models run on modern computers are insufficient to make precise predictions. In this problem, we will attempt to understand some of the basic atmospheric phenomena based on simple models. You might need the following constants: the mean solar power per unit area at Earth, the total solar irradiance $F_{s} = 1370 \mathrm{W} / \mathrm{m}^{2}$, molar mass of water $\mu_{\text{H_2O}} \approx 18 \mathrm{g} / \mathrm{mol}$ and average molar mass of air $\mu_{\text {air }} \approx 29 \mathrm{g} / \mathrm{mol}$, The Stefan-Boltzmann constant $\sigma=5.67 \times 10^{-8} \mathrm{W} /\left(\mathrm{m}^{2} \mathrm{K}^{4}\right)$. All gases in this problem can be treated as ideal gases. Assume that all air molecules have 5 degrees of freedom. You may need the following integral: $\int_{-\infty}^{\infty} e^{-a x^2/2} dx = \sqrt{2 \pi/a}$, $a > 0$. [Part E: Sun halo] Under suitable atmospheric conditions, a bright ring appears around the Sun which is called a halo. Halos are caused by ice crystals present in the upper troposphere. One interesting feature about halos is that they always appear at a specific angle relative to the direction of the Sun. [figure1] Figure E.1. On the left: A photograph showing a halo around the Sun. On the right: The path of a light ray passing through the prism. (E.1) Consider a simple prism with an apex angle of $\varphi$ and direct a light ray onto it at an incidence angle $\alpha$, as shown in Figure E.1. Let the refractive index of the prism be $n$. Express the angle of deviation $\delta$ of the light ray after passing through the prism in terms of $\alpha, n$ and $\varphi$. The most common type of halo forms when tiny ice crystals take the shape of regular hexagonal prisms. Light from the Sun falls onto randomly oriented ice crystals drifting in the atmosphere and scatters into various directions. However, in certain specific directions, the intensity of the refracted light is maximal, and this determines the angle at which the bright ring appears. [figure2] Figure E.2. Consider a hexagonal ice prism whose six-fold symmetry axis is perpendicular to the direction of the Sun's rays. Investigate a light ray that refracts through two rectangular faces of the prism indicated in Figure E.2. Due to the random orientation of the ice crystals, the light strikes the crystal faces at varying incidence angles $\alpha$. (E.2) Calculate the deviation angle $\delta$ for incidence angles $\alpha = 20^{\circ}, 30^{\circ}, 40^{\circ}, 50^{\circ}, 60^{\circ}, 70^{\circ}$, in that order. Output the six values in degrees ($^{\circ}$), each with three significant figures, listed sequentially and separately. The refractive index of ice is $n = 1.31$.
Using the numerical results from the previous question (E.2), determine at what angle the halo appears the brightest relative to the direction of the Sun. Express your answer in degrees ($^{\circ}$) with three significant figures.
[["Award 0.1 pt if the answer correctly reads and states the minimal value of $\\delta$ as approximately $21.8^\\circ$. Otherwise, award 0 pt.", "Award 0.1 pt if the answer concludes that the angular size of the halo corresponds to this minimal value of $\\delta$, i.e. about $21.8^\\circ$. Otherwise, award 0 pt."]]
["\\boxed{21.8}"]
["Numerical Value"]
["degrees"]
[0.2]
text+variable figure
Optics
APhO_2025
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None.