A spring of force constant $k$ is stretched a certain distance. It takes twice as much work to stret

Question

A spring of force constant $k$ is stretched a certain distance. It takes twice as much work to stretch a second spring by half this distance. The force constant of the second spring is

Professor PC Thomas Classes · Answer

$W_1 = \frac{1}{2}kx^2$. $W_2 = \frac{1}{2}k'(\frac{x}{2})^2 = 2W_1 \Rightarrow \frac{1}{8}k'x^2 = kx^2 \Rightarrow k' = 8k$.