500
Using our spring force equation:
82 = -k * (-0.03)
Solve for k:
k = 82 / 0.03 = 2733 N/m
Now we apply force on the block, such that it does work on the spring.
The potential energy stored in a spring is given by:
U = 1/2 * k * x^2
Work = - (change in potential energy) = U1 - U2
6.0 = 1/2 * k * (x^2 - (-0.03)^2)
Now solving for x:
12 / k = x^2 - .0009
x^2 = 0.0053
x = +/- sqrt[ 0.0053 ] = +/- 0.073 m = +/- 7.3 cm
We must apply a force of magnitude 82.0 N to hold the block stationary at x=-3.0 cm. From that position, we then slowly move the block so that our force does +6.0 J of work on the spring–block system; the block is then again stationary. What are the block's positions, in cm? (two answers-(a) positive and (b) negative)