Answer
The spring stretches by 2x, and the work done increases by a factor of 4, to 4W.
Work Step by Step
Hooke’s Law tells us that the spring’s force is proportional to the distance stretched from equilibrium. If the spring exerts twice the force, it is stretched twice as far as it was originally, a distance 2x.
As seen in equation 6.9, the work done by the force is proportional to the square of the distance stretched, $W=\frac{1}{2}kX^2$.
If the final stretch is 2 times greater than before, then the work done, 4W, is 4 times greater than before.
