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.† Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l minus its unstretched length l0; that is, x = l − l0. Suppose a particular bungee cord has a spring constant, for 0 ≤ x ≤ 3.88 m, of k1 = 206 N/m and, for x > 3.88 m, of k2 = 103 N/m.The function of the force F(x) is displayed as a function of its stretch below. (Recall that the spring constant is the slope of the force F(x) versus its stretch x.)F(x) = k1x x ≤ 3.883.88k1 + k2(x − 3.88) x > 3.88 (a) What is the tension (in N) in the cord when the stretch is 17.3 m (the maximum desired for a given jump)? N (b) How much work (in J) must be done against the elastic force of the bungee cord to stretch it 17.3 m? J

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Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter5: Newton's Laws Of Motion

Section: Chapter Questions

Problem 44PQ: A student working on a school project modeled a trampoline as a spring obeying Hookes law and...

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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.† Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l minus its unstretched length l₀; that is, x = l − l₀. Suppose a particular bungee cord has a spring constant, for 0 ≤ x ≤ 3.88 m, of k₁ = 206 N/m and, for x > 3.88 m, of k₂ = 103 N/m.

The function of the force F(x) is displayed as a function of its stretch below. (Recall that the spring constant is the slope of the force F(x) versus its stretch x.)

F(x) =

k₁x		x ≤ 3.88
3.88k₁ + k₂(x − 3.88)		x > 3.88

(a) What is the tension (in N) in the cord when the stretch is 17.3 m (the maximum desired for a given jump)?

(b) How much work (in J) must be done against the elastic force of the bungee cord to stretch it 17.3 m?

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