In the figure below, we must apply a force of magnitude 89 N to hold the block stationary at x = -2.0 cm. From that position we then slowly move the block so that our force does +4.0 J of work on the spring-block system; the block is then again stationary. What is the block's position (x)? (There are two answers.)
---cm (smaller value)
---cm (larger value)
W = .5 * [-k(xfinal^2) + k(xinitial^2)]
k = spring constant = force / distance stretched (or compressed)
The Attempt at a Solution
1. Find the spring constant:
K = 89N / -.02m = -4450 N/m
2. Plug values in
W = 4 J = .5 * -4450N.m * [ -xf^2 - xi^2]
The initial distance from 0 was -.02m so I plugged that in for the initial distance and solved for the final distance, which = .0469 m = 4.69cm.
This was the right answer, but I'm not sure in which direction it was (although it was the larger value) and or how to find the smaller one. Would I add the initial distance instead of subtract it?