hw7_3221spring2011

hw7_3221spring2011 - 1 Phy 3221 Due: March 2, 2011 Homework...

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1 Phy 3221 Due: March 2, 2011 Homework set # 7 Problem 1: Imagine that you are at rest relative to the surface of a planet with the same mass and radius as the Earth. What would be the length of a day on that planet if it were rotating so fast that the acceleration of gravity on the equator (at rest relative to the surface of the planet) were zero? hint: The surface is rotating around the axis of the planet, so if you are at rest on the surface then you are subject to a “centrifugal force” which arises from the acceleration of your frame of reference. Problem 2: A commuting scheme involves boring a straight tunnel through the crust of the Earth between New York City and San Francisco. If you were to drop a ball down into the tunnel in NYC then how long does it take for the ball to pop up in SF? Assume that there is no friction or air resistance in the tunnel. Assume that the earth is round and has constant density, and that at the surface of the Earth g = 10 m/s 2 . Finally assume that
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