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Work done in stretching a wire

In stretching a wire, work is done against internal restoring forces. This work is stored in the wire as elastic potential energy or strain energy.
 
If a force F acts along the length L of the wire of cross section A and stretches it by x, then
48365.png  48358.png
 
So, the work done for an additional small increase dx in length,
48350.png
 
Hence, the total work done in increasing the length by l,
48344.png
 
This work done is stored in the wire.
 
∴ Energy stored in wire, 48338.png
48332.png
 
Dividing both sides by volume of the wire, we get energy stored in per unit volume of wire.
48326.png
48320.png
[as AL = volume of wire]




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