Chapter 9, Problem 51EAP

Hook’s law describes an ideal spring. Many real springs are better described by the restoring force (F_sp)_s = -k ?s − q(?s)3, where q is constant. Consider a spring with k = 250 N/m and q = 800 N/m³

1. How much work must you do to compress this spring 15 cm? Note that, by Newton’s third low, the work you do on the spring is the negative of the work done by the spring.

By what percent has the cubic term increased the work over what would be needed to compress an ideal spring?

Hint: Let the spring lie along the s-axis with the equilibrium position of the end of the spring at s = 0, then ?s = s