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## Homework Statement

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)

## Homework Equations

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?

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