Elastic and inelastic deformation, Hooke's law and the spring constant, the equation F = ke, the limit of proportionality, and the energy stored in a stretched spring.

What this dot point is asking

Edexcel wants you to distinguish elastic and inelastic deformation, state Hooke's law and use the equation $F = ke$, explain the limit of proportionality, and describe the energy stored in a stretched spring.

Elastic and inelastic deformation

Hooke's law

The limit of proportionality

A graph of force against extension for a spring is a straight line through the origin while Hooke's law holds. The limit of proportionality is the point beyond which the line begins to curve, because the extension is no longer proportional to the force. Beyond this, stretching the spring further may also cause inelastic deformation, so it does not return to its original length.

Energy stored in a spring

When a force does work stretching a spring, energy is transferred to the elastic potential energy store of the spring. For a spring obeying Hooke's law, this stored energy equals the area under the force-extension graph. The energy is released when the spring returns to its original shape, which is how catapults, trampolines and clockwork devices work.

The core practical for this topic investigates how the extension of a spring depends on the force. You hang the spring from a clamp stand, measure its original length, then add masses one at a time. Each mass adds a known weight (force = mass times $g$), and you measure the new length to find the extension. Plotting force against extension gives a straight line through the origin while the spring obeys Hooke's law, and the gradient of this line is the spring constant. The line begins to curve at the limit of proportionality.

The same ideas apply to compressing a spring, not just stretching it: a spring squashed by a force also stores elastic potential energy and obeys Hooke's law up to its limit. This is why springs are used in car suspensions and weighing scales, where a known force produces a predictable, reversible change in length. If a spring is stretched beyond its limit it deforms inelastically and no longer returns to its original length, so it can no longer be used to measure force reliably.

Try this

Q1. State Hooke's law. [1 mark]

• Cue. The extension of a spring is directly proportional to the force applied (up to the limit of proportionality).

Q2. A spring with a spring constant of $50\,N/m$ is stretched by a force of $10\,N$. Calculate the extension. [2 marks]

• Cue. $e = F / k = 10 / 50 = 0.2\,m$.