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ps11 - separated by a distance D what is the period of the...

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Assignment 11, Phys1112 Spring 2010 Due April 19 Y&F: 12.30, 12.34, 12.35, 12.36, 12.47 Problem 6 A building reaches a total height h and has mass m . (a) Treating the building as a thin, uniform rod, calculate the gravitational force the Earth exerts on it. (b) In the limit that h R E , show that this force reduces to mg . Problem 7 A mass above the earth has potential energy U = - GM E m/r 2 . (a) Calculate the change in potential energy when an object moves from the surface of the Earth to a height h above it. (b) Show that when h R E , this change is approximately mgh . (c) At what value of h do your answers in parts (a) and (b) di ff er by 1%? Problem 8 Two identical masses M are in orbit around their center of mass. If the masses are always
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Unformatted text preview: separated by a distance D , what is the period of the orbit as a function of M and D ? Problem 9 A satellite of the Earth has an elliptical orbit with semi-major and semi-minor axes related by b = a/ 2, where a is the semi-major axis. Imagine drawing this ellipse in the x-y plane, with the center of the ellipse (not the foci) at the orgin, and the semi-major axis along the x-axix. Calculate the ratio of the speed at perihelion (closest point of the orbit to earth) to the speed at the point of the orbit that intersects the y-axis, i.e. just above the center of the ellipse. 1...
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