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.
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