## Hooke's Law

Hookes law states that the extension of a spring is proportional to the applied force. If the force doubles, the extension doubles. If the force triples, the extension triples and so on. In general we can write

whereis the applied force

is the extension produced by that force

is a constant of proportionality called the force constant.

A graph of extension against applied force is then a straight line through the origin.

Hookes law is actually not only applicable to springs. A wide range of materials and objects display the property that the amount of stretch (or even compression) is directly proportional to the applied force. This proportionality only applies up to a limit however, called the elastic limit. If a material is deformed past it's elastic limit it can be permanently deformed or even break.

The amount of energythat must be used to stretch a spring is equal to the area under the force – extension graph. If Hooke's law is obeyed, then the area is that of a triangle so

Hooke's law then saysso