problem12_38

University Physics with Modern Physics with Mastering Physics (11th Edition)

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12.38: a) Divide the rod into differential masses dm at position l, measured from the right end of the rod. Then , dm = dl ( L M ), and dU = . x l dl L GmM x l dm Gm + - = + - Integrating, U = + - = + - L O x L L GmM x l dl L GmM . 1 ln For x >> L, the natural logarithm is ( 29 x L ~ , and U . x M Gm - b) The x -component of the gravitational force on the sphere is , ) ( )) ( 1 ( ) ( 2 2 Lx x GmM x L x L L GmM δx δU F x + - = + - = - = with the minus sign indicating an attractive force. As
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Unformatted text preview: x >> L, the denominator in the above expression approaches 2 x , and x F 2 x M Gm , as expected. The derivative may also be taken by expressing x L x x L ln ) ln( 1 ln-+ = + at the cost of a little more algebra....
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