Energy stored in the wire

Whenever a force is applied on a body it produces a change in the shape of the body but due to the elastic nature,the particles tries to come back to their original position. As no body is perfectly elastic there will be a permanent change in the shape of the body which is called as extension or elongation. For producing this elongation we must have done some work and after the job was done, this work and cannot disappear all of a sudden. That is against the law conservation of energy.

This work done hence stored in the format of energy and that is called the energy stored in your wire. It depends on the applied force as well as the extension. Here for producing a small elongation, with respect to the applied force the corresponding work done is also small. The total elongation is the sum of all this kind of small elongation is and the total work done is the sum of all the works done together. To calculate the total amount of the work done therefore we have to add all that works together and that kind of adding is mathematically called integration. In the following diagram we have shown how to derive the equation for the work done.