Show, using the force-extension graph, that the work done in stretching a spring by x is ½kx².

1. 1 · State Hooke's law. The restoring force of a spring is proportional to its extension: Fₛ = −kx, where k is the spring constant.
2. 2 · Draw the graph. [F on the y-axis, x on the x-axis; a straight line from the origin; mark xₘ and kxₘ; shade the triangle under the line]
3. 3 · Use the area rule. The work done by a varying force = the area under its F-x graph.
4. 4 · Find the area. Area of the triangle = ½ × base × height = ½ × xₘ × kxₘ = ½kxₘ².
5. 5 · Give the signs. The external force does +½kxₘ²; the spring force does −½kxₘ². This work is stored as elastic potential energy.
6. 6 · Real-life link. A spring balance works by Hooke's law, and the springs in a motorcycle's shock absorbers store this energy when they are pressed.
7. 7 · Close in one line. So the work done in stretching a spring by x is ½kx².

Scoring tip: Draw and shade the triangle. Writing 'area under the F-x graph = work done' earns a mark on its own.