problem06_p101

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

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6.101: a) Denote the position of a piece of the spring by l ; 0 = l is the fixed point and L l = is the moving end of the spring. Then the velocity of the point corresponding to l , denoted u , is L v l u 1 ) ( = (when the spring is moving, l will be a function of time, and so u is an implicit function of time). The mass of a piece of length dl is , dl dm L M = and so , 2 1 2 1 2 3 2 2 dl l L Mv dmu dK = = and = = = L Mv dl l L Mv dK K 0 2 2 3 2 . 6 2 b) , 2 2 1 2 2 1 mv kx = so s. m 6.1 m) 10 50 . 2 ( kg) 053 . 0 ( m) N 3200 ( ) ( 2 = × = = - x m k v . c) With the mass of the spring included, the work that the spring does goes into the
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Unformatted text preview: kinetic energies of both the ball and the spring, so . 2 6 1 2 2 1 2 2 1 Mv mv kx + = Solving for v , s. m 3.9 m) 10 50 . 2 ( 3 kg) (0.243 kg) 053 . ( m) N 3200 ( 3 2 = × + = + =-x M m k v d) Algebraically, J 40 . ) 3 1 ( ) 2 1 ( 2 1 2 2 = + = m M kx mv and J. 60 . ) 3 1 ( ) 2 1 ( 6 1 2 2 = + = M m kx Mv...
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