A 700g block is released from rest at height Ho(initial) above a vertical spring with spring constant k=400 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 19.0 cm.
How much work is done
A) by the block on the spring?
B) by the spring on the block?
C) What is the value of Ho?
D) If the block were released from height 2ho above the spring, what would be the maximum compression of the spring?
Conservation of Energy:
Ug(o) + Us(o) + Ko = Ug(f) + Us(f) +Kf
The Attempt at a Solution
mgho + 0 (because the spring is not compressed at the start) + 0 (because the initial velocity is 0) = mg(-0.19m) (setting the top of the spring at y=0) + (kx^2)/2 + 0 (because the final instantaneous velocity is 0)
ΣW = Kf - Ko = Ug(o) - Ug(f) - Us(f) = mgho - mg(-0.19m) - 7.22J
I am mainly struggling with the conceptual part... for (a), the work done is only the compression of the spring, not the total work, right? So, it would be 7.22J. And (b) would be negative because the block is exerting force on the spring, and the spring is experiencing work that it can later convert into its own form of work?
For (c), solving Ug(o) + 0 + Ko = Ug(f) + Us(f) +Kf for ho:
W = mgho - 7.22J - mg(-0.19m) = 0
ho + (0.19m) = 7.22J/6.86N
ho = 0.86meters
W = 2mgho - (k(x^2)/2) - mg(-0.19m) = 0
x^2 = 2(13.10J)/400N/m
x = 0.26meters
If someone could help explain work vs. forces vs. energy as it relates to this problem it'd be much appreciated!