Question #126a1

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Answer 1 · 2015-11-28T18:17:34

You can do it like this:

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

$:.F=-kx$

$k$ 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:

$W=intF.dx$

$:.W=-int_0^xkx.dx$

$:.W=1/2kx^2$

This gives us the stored elastic potential energy.