Work Done by the Force of a Spring

Example: A spring has a free length of 10 inches. (Free length is it’s unstretched length.) It takes 3-lb of force in order to stretch the spring 2 inches. Find the work needed to stretch the spring to a total length of 15 inches.

Solution: The general equation for the work is:

We need an equation F(x) to describe the spring force. We know that F(x) = k x for a spring, but we done yet know the spring constant, k.

We do have the information we need to calculate it.