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Unformatted text preview: 128 Chapt. 14 Gravity The potential energy itself does not depend on the assembly process. This can proven by simple analytic means. The assembly process can be represented by an integral that is easily solved to give: a) PE = − GM 2 R . b) PE = − 3 5 GM 2 R . c) PE = − 1 2 GM 2 R . d) PE = − 1 2 GM 2 R 2 . e) PE = − 1 2 GM R . 014 qmult 00770 2 3 3 mod. math: thin spherical shell PE 34. The gravitational potential energy of infinitely thin spherical shell of mass M and radius R can be calculated easily by imagining a symmetrical assembly process. The shell has all mass at radius R with a uniform surface density. You start with no mass at the shell radius R and bring a differential masses dm from infinity to add to the shell to grow it to its full mass. The trick is to imagine that as you bring the differential masses to the shell radius you spread them uniformly over the shell. There is only a potential energy addition for bringing them up to the shell. The spreading does not changeshell....
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This note was uploaded on 11/16/2011 for the course PHY 2053 taught by Professor Buchler during the Fall '06 term at University of Florida.
 Fall '06
 Buchler
 Physics, Energy, Gravity, Potential Energy

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