Chapter 12, Problem 42AP

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