Question #126a1

1 Answer
Nov 28, 2015

Answer:

You can do it like this:

Explanation:

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.