Question

A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch [see Menz, P.G. “The Physics of Bungee Jumping.” The Physics Teacher (November 1993) 31: 483-487]. Suppose an unstretched bungee cord has a length l₀ = 23.3 m and during a bungee jump it stretches so that its maximum total length is l = 53.7 m. Suppose that bungee cord behaves like an ideal spring, but with two spring constants, depending on the amount of stretch (relative to its unstretched length). When the amount of stretch is less than s = 9.7 m then the spring constant is k₁ = 116 N/m, but when the amount of stretch is more than s the spring constant is k₂ = 166 N/m. The interpretation here is that the tension in the cord increases by k₁ = 116 N/m for the first s = 9.7 m of stretch, and there is an additional k₂ = 166 N/m of tension for any stretch beyond s = 9.7 m of stretch.

d)  What is the magnitude of work done on the cord, in joules, in order to stretch it to a total length l = 53.7 m?

Answer 1