Revision notes · Forces

Forces and elasticity

Forces and elasticity4.5.3

To stretch, compress, or bend an object, more than one force must be applied to it — a single force applied to a free object just makes it move (accelerate) rather than change shape. Deformation means a change of shape.

Type of deformationWhat happens when the load is removedExample
Elastic deformationThe object returns to its original shapeAn elastic band, stretched within its limits
Plastic deformationThe object does NOT return to its original shape — it stays permanently deformedA spring stretched too far
Definition: Hooke's Law: the extension of a spring (or other elastic object) is directly proportional to the force applied to it, provided the limit of proportionality is not exceeded.
EquationUnits
force = spring constant × extension — F = k × xF in newtons (N), k in newtons per metre (N/m), x in metres (m)

On a force–extension graph: while the line is straight (linear) through the origin, the spring is obeying Hooke's Law, and the gradient of the line equals the spring constant k. The point where the line stops being straight is the limit of proportionality — beyond this point the material no longer obeys Hooke's Law, and the extension increases non-linearly (a much bigger extension for the same extra force, if the material is soft, or none at all if it fractures instead).

Force and extension of a spring
⚠️ Common mistake: A material that stays perfectly linear right up until it snaps — with no non-linear region before breaking — is described as brittle: it fractures suddenly rather than stretching plastically first.
EquationUnits
elastic potential energy stored = ½ × spring constant × extension² — Eₑ = ½ × k × x²Eₑ in joules (J), k in N/m, x in m

When a force stretches or compresses a spring, work is done on the spring, storing energy in its elastic potential energy store. Provided the spring deforms elastically (not plastically), the work done on the spring equals the elastic potential energy stored in it.

Feel like you’ve got it?

Practise it now →