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

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13.67: a) The quantity l is the amount that the origin of coordinates has been moved from the unstretched length of the spring, so the spring is stretched a distance x l - (see Fig. (13.16 ( c ))) and the elastic potential energy is 2 el ) ( ) 2 1 ( x l k U - = . b) ( 29 ( 29 . 2 1 2 1 0 2 2 0 el mgx mgx lx k l kx x x mg U U - + - + = - + = Since , k mg l = the two terms proportional to
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Unformatted text preview: x cancel, and ( 29 . 2 1 2 1 2 2 mgx l k kx U-∆ + = c) An additive constant to the mechanical energy does not change the dependence of the force on , , dx dU x F x-= and so the relations expressing Newton’s laws and the resulting equations of motion are unchanged....
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