The Energy Stored in a Stretched Spring

Work must be done to stretch a spring. This work is stored in the spring as elastic potential energy and is released when the spring returns to its original length.The energy stored is the area under the force-extension graph. The force is not constant during stretching: it increases steadily from zero to F, so the average force is ½F.For a spring that obeys Hooke's law, the graph is a straight line and the area is a triangle, so the energy stored is E = ½FΔL. Since F = kΔL, this can also be written E = ½kΔL².Because the energy depends on the square of the extension, doubling the extension stores four times as much energy. If the spring is stretched beyond its limit of proportionality, the energy is still the area under the curve, but the simple formulae no longer apply.