Chapter 6, Problem 83P

You’re an engineer for a company that makes bungee-jump cords, and you’re asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force-distance relations described by F = − (kx + bx² + cx³ + dx⁴), where k, b, c, and d are constants. (a) Given a cord with un-stretched length L₀, what’s your formula? (b) Evaluate the work done in doubling the stretch of a 10-m cord with k = 420 N/m, b = −86 N/m², c = 12 N/m³, and d = −0.50 N/m⁴.