Answer to Question #45906 in Mechanics | Relativity for Gideon

Question

A spring of natural length L extends to a new length L' under tensile force. If Hooke's law applies, the work done in stretching the spring is .........?

Answer 1

A spring has a natural length of L. When it is stretched x meters beyond that, Hooke’s Law states that the spring pulls back with a restoring force F = k * x, where x = (L' - L), and the constant k is called the spring constant, and represents the stiffness of the spring.
All the work involved in stretching from L to L', i.e. for the increase in length, we would calculate as W = F * x = k * x^2 / 2 = k * (L' - L)^2 / 2