The energy in a stretched wire

A steel wire $1.8\ \text{m}$ long and $0.90\ \text{mm}$ across is stretched slowly by up to $2.0\ \text{mm}$. You will make the program follow the force as the wire stretches, work out the stored energy from $\tfrac12 kx^2$, and check it by adding up thin strips of the area under the force-stretch graph.

The idea. The wire is a spring with $k = \dfrac{YA}{L}$, so $F = kx$. The work done, stored as elastic energy, is the area under the graph of $F$ against $x$: $U = \tfrac12 kx^2$.

Your tasks.

1. Work out the force constant k, and the force F at every stretch in x.
2. Work out the stored energy U at every stretch, from $\tfrac12 kx^2$.
3. Add up the strips under the graph to get the energy at the largest stretch.