Question

A 540 g block is released from rest at height h0 above a vertical spring with spring constant k = 320 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 19.8 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 3h0 above the spring, what would be the maximum compression of the spring?


I just need help with d). I got for a) is 6.27 J, b) is -6.27, and c) is 0.987. All of these are correct, but I am having trouble with d).

Answer 1

distance block moves down = h0 + .198
loss of potential energy by block =
.540 ( 9.81 ) (h0+.198)

gain of potential energy by spring = (1/2)(320)(.198). This is energy gained by spring and lost by block.

so
.540(9.81)(h0+.198) = (1/2)(320)(.198)
solve for h0

then do it for 3 h0

Answer 2

I got the complete equation
1/2*k*y^2 - m*g*y - m*g*3h0 and solved for y, and got 0.330 and its correct. Thanks.