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

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8.69: (This problem involves solving a quadratic. The method presented here formulates the answer in terms of the parameters, and avoids intermediate calculations, including that of the spring constant.) Let the mass of the frame be M and the mass putty be m . Denote the distance that the frame streteches the spring by x 0 , the height above the frame from which the putty is dropped as h , and the maximum distance the frame moves from its initial position (with the frame attached) as d . The collision between the putty and the frame is completely inelastic, and the common speed after the collision is . 2 0 M m m gh v + = After the collision, energy is conserved, so that or , ) ((
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Unformatted text preview: ) ( ) ( 2 1 2 2 2 x x d k gd M m v M m-+ = + + + , ) (( 2 1 ) ( ) 2 ( 2 1 2 2 2 x x d x mg gd M m gh M m m-+ = + + + where the above expression for v , and x mg k = have been used. In this form, it is seen that a factor of g cancels from all terms. After performing the algebra, the quadratic for d becomes which has as its positive root For this situation, m = 4/3 M and h/x 0 = 6, so d = 0.232 m. , 2 2 2 2 = +- -M m m hx M m x d d . ) ( 2 2 2 + + + = M m M m x h M m M m x d...
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