Elastic Energy

When we stretch a wire, we store elastic strain energy.  This is represented by the area under the force extension graph.  We will see how this is derived.

Suppose we stretch the wire a very tiny amount dx, we do a tiny job of work dW, since dW = Fdx.

If we stretch the wire more, the job of work we do is represented by more little rectangles.  Therefore the energy is the area under the force extension graph.  For a material that obeys Hooke's Law (i.e. Force µ Extension), the graph is a straight line.  Therefore the area is a triangle.

We can write this as a simple equation:

Hooke's Law states that F = kx.  So we can substitute kx for F to give us: