# Question #126a1

Nov 28, 2015

You can do it like this:

#### Explanation:

Hooke's Law tells us that force $F$ is proportional to extension $x$:

$\therefore F = - k x$

$k$ is the force constant.

$x$ is the extension.

For a spring the work done in stretching it will be converted to stored elastic potential energy.

Work done = force x distance moved in the direction of the force.

With a spring we cannot use this directly since the force is constantly changing.

We need to use a bit of calculus:

$W = \int F . \mathrm{dx}$

$\therefore W = - {\int}_{0}^{x} k x . \mathrm{dx}$

$\therefore W = \frac{1}{2} k {x}^{2}$

This gives us the stored elastic potential energy.