Question

When you stretch a rubber band, the force applied is not constant. Assuming it follows Hooke’s...

When you stretch a rubber band, the force applied is not constant. Assuming it follows Hooke’s Law, and using the definition of work (W = Fd), derive the equation for the work done in stretching the rubber band.

The answer is 1/2kx2 but how do I get it?

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Answer #1

From Hooke's law

Where x is the stretch in the rubber band.

The work done by this force for a small displacement dx around the distance x can be given by

Integrating the above equation from 0 to x we get

So, the work done in stretching the rubber band by a distance x is given by

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