Work done stretching a spring

Hello mmattson07 Quote:

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**mmattson07** A spring has a natural length of 28 cm. If a 28 N force is required to keep it stretched to a length of 31 cm, how much work W is required to stretch it from 28 cm to 38 cm?

W= ___ J

I know Work= Force * Distance but i dont know how to go about solving this i know it will be an integration of some sort

Two formulae you need to know about an elastic spring with natural length and modulus :

- When the extension in the spring is , the tension, , is given by

- When the spring is stretched from an extension to an extension , the work done, , is given by

So here, m. And when (because the total length is m), .

So, using the first of the two formulae above:

And we need to find when and

So

Joules

Grandad