As shown in Fig. P2.45, a spring having an initial

Chapter 2, Problem 2.45

(choose chapter or problem)

As shown in Fig. P2.45, a spring having an initial unstretched length of \(\ell_{0}\) is stretched by a force F applied at its end. The stretched length is \(\ell\). By Hooke’s law, the force is linearly related to the spring extension by \(F=k\left(\ell-\ell_{0}\right)\) where k is the stiffness. If stiffness is constant,

(a) obtain an expression for the work done in changing the spring’s length from \(\ell_{1} \text { to } \ell_{2}\).

(b) evaluate the work done, in J, if \(\ell_{0}=3 \mathrm{~cm}, \ell_{1}=6 \mathrm{~cm}\), \(\ell_{2}=10 \mathrm{~cm}\), and the stiffness is \(k=10^{4} \mathrm{~N} / \mathrm{m}\).