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Unformatted text preview: Physics 325 homework 9 - Solutions Wednesday 25 October 2006 There are 15 points for each correct question for a total of 45 points. 1. Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perpendicular to the rod. Set the center of the rod as the origin and the rod as the x axis. In this case the potential φ of the point indicated in this problem can be expressed as an integral φ =- Z- l/ 2 l/ 2 Gρdx √ x 2 + R 2 =- 2 GM l ArcSinh( l 2 R ) where ρ = M l is the line density of the rod. 2. Calculate the gravitational field vector due to a homogeneous cylinder ar exterior points on the axis of the cylinder. Perform the calculation a) by computing the force directly First, we consider the radius of the rod as a , the length as l and the mass as M . We calculate the vector field at the point A which has the distance s from the center of the rod, where a > l/ 2....
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