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.

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.

When the deflection, x = 2inches, F = 3, so:

k = F/x = 3 lb/2 in. = 1.5 lb/in

Now put this into the work equation, add limits (Remember that the limits represent x, deflection, not total length.), and solve.