This might be better suited for a physics forum. If you can set up the integral, I or someone else can help you, but other than that you might not get the help you're looking for.
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
Hello mmattson07Two 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
Hello mmattson07My 'method', as you describe it, is simply the result of applying Hooke's Law, which states that the tension in an elastic spring (or string) is proportional to the extension. In other words, with and defined as before:
, for some constant .
Now if we define the modulus (or modulus of elasticity), , to be the force required to double the length of the spring, then when . So , which in turn gives the first of the two formulae that I quoted, namely
The second formula is derived by integration, as follows:
Suppose the spring is extended from to . Then the work done is given by
, where is the work done extending the spring from to .
So there's nothing other than Hooke's Law here. However, it's much easier to learn and apply these two well-known formulae, than to derive the answers from first principles each time!
Grandad