A 764 g block is released from rest at height h0 above a vertical spring with sp

Question

A 764 g block is released from rest at height h0 above a vertical spring with spring constant k = 540 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 18.9 cm. How much work is done (a) by the block on the spring and (b) by the spring on the block? (c) What is the value of h0? (d) If the block were released from height 5h0 above the spring, what would be the maximum compression of the spring? (a) Number Units j (b) Number Units j (c) Number Units m (d) Number Units m

Explanation / Answer

take the topmost point of the spring as reference ..A point .....i.e, potential of that point is assumed to be zero....

the energy of the block till it reaches the top point of spring = mgh0 =1/2 mv2 ............(1)

                                                                                 where v is the velocity of the block at point A

now since the block compresses the spring by a distance of 18.9 cm ,

                                                         1/2mv2 =k(0.189)-mg(0.189)...............(2)

(A) the work done by the block on the spring is = 1/2k(0.189)2 = 9.65 J

(B)the work done by the spring on the block =(-)1/2 k(0.189)2 =   -9.65 J

(C) using equation 1 and 2 we get,

                                    mgh0 = k(0.189)-mg(0.189)

                                        h0 =13.43m

        so the height h0 =13.43m

(D)so if the block were to fall from a hieght of 5h0 the compression in the spring will be =

                                                     ( 5mgh0)/(k-mg)

                                     =0.95m

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