As shown in Fig.P2.39, a steel wire suspended vertically having a cross-section area A and an initial length X0 is stretched by a downward force F applied to the end of the wire. The normal stress in the wire varies linearly according to σ= C ε, where ε is the strain, given by ε=(X-X0)/X0, and x is the stretched length of the wire, C is a material constant (Young€™s modulus). Assuming the cross-sectional area remains constant. (a) Obtain an expression for the work done on the wire. (b) Evaluate the work done no the wire, in ft.lbf, and the magnitude of the downward force, in lbf, if x=10 ft, x= 10.01 ft, A= 0.1 in2, and C= 2.5 × 107 lbf/in2.

Wire Cross-section area = A