problem07_70

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

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7.70: a) In this problem, use of algebra avoids the intermediate calculation of the spring constant k . If the original height is h and the maximum compression of the spring is d , then 2 2 1 ) ( kd d h mg = + . The speed needed is when the spring is compressed 2 d , and from conservation of energy, 2 2 1 2 2 1 ) 2 ( ) 2 ( mv d k d h mg = - + . Substituting for k in terms of d h + , , 2 1 4 ) ( 2 2 mv d h mg d h mg = + - + which simplifies to
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Unformatted text preview: . 4 1 4 3 2 2 + = d h g v Insertion of numerical values gives s m 14 . 6 = v . b) If the spring is compressed a distance x , mgx kx = 2 2 1 , or k mg x 2 = . Using the expression from part (a) that gives k in terms of h and d , m. 0210 . ) ( 2 ) 2 ( 2 2 = + = + = d h d d h mg d mg x...
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