Hooke Law

Hooke’s law says that when an elastic object is stretched or compressed a small amount, the force it exerts to return to its original shape increases in direct proportion to the displacement. The minus sign shows the force acts in the opposite direction to the stretch or compression, which is why it is called a restoring force. The constant k measures stiffness: a larger k means a stiffer object that resists deformation more strongly.

Use this when dealing with small deformations of springs, rubber-like elastic materials, or simple oscillation problems where the object behaves linearly. It is especially useful in mechanics questions involving force, extension, compression, and spring energy.

• Forgetting the minus sign and giving the force in the same direction as the displacement
• Mixing up units and using displacement in centimetres instead of metres
• Using Hooke’s law for large stretches where the material no longer behaves linearly