A solid cylindrical bar of 5-mm diameter is slowly stretched from an initial length

Chapter 1, Problem 1.56

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A solid cylindrical bar of 5-mm diameter is slowly stretched from an initial length of 100 mm to a final length of 101 mm. The normal stress acting at the end of the bar varies according to \(\sigma = E(x - x_1)/x_1\), where x is the position of the end of the bar, \(x_1\) is the initial length, and E is a material constant (Young’s modulus). For \(E = 2 \times 10^7 \ \mathrm{kPa}\), determine the work done on the bar (J).

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