Question

A 615 g block is released from rest at height h0 above a vertical spring with spring constant k = 310 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 6h0 above the spring, what would be the maximum compression of the spring? Please Help. I worked out the first two 5.54 & -5.54. Had no idea to do the rest.

Answer 1

By conservation of energy:
\[mgh_0 = 0.5*k*\Delta l\]
and from here work out c and d

Answer 2

actually, the potential energy should be written:
\[mg(h_0 + 0.189)\]
since in compresses the spring by falling downwards and thus the total energy of the block at it's momentary rest is:
\[0.5*k*\Delta l -m*g*0.189\]
(the minus sign is due to it being lower than the relax length of the spring which is defined as the zero potential energy reference point)