A wire of length $L,$ Young's modulus $Y$, and cross-sectional area $A$ is stretched elastically by an amount A $L$. By Hooke's law, the restoring force is $-k \Delta L$. (a) Show that $k=Y A / L$. (b) Show that the work done in stretching the wire by an amount $\Delta L$ is $W=\frac{1}{2} Y A(\Delta L)^{2} / L$.