(a)[4]
A metal wire has spring constant $k$. Forces are applied to the ends of the wire so that it extends while remaining within Hooke’s law. Show that, for an extension $x$, the strain energy $E$ stored in the wire is $E = \frac{1}{2}kx^2$.
(b(i))[1]
The wire in (a) is now stretched beyond its elastic limit. The forces responsible for the extension are then taken away. The way the tension $F$ in the wire changes with extension $x$ is shown in Fig. 4.1. Energy $E_s$ is used to produce a permanent extension of the wire. On Fig. 4.1, shade the region that represents the energy $E_s$.
(b(ii))[3]
Use Fig. 4.1 to work out the energy $E_s$.
(b(iii))[1]
Suggest the structural change in the wire that is caused by the energy $E_s$.