Forces, elasticity and Hooke’s law
Physics · GCSE · The School
Elastic deformation is reversible
Stretch a rubber band gently and let go: it snaps back to its original length. That is elastic deformation — the object regains its shape once the force is removed. Bend a metal paperclip and it stays bent even after you let go; that is inelastic (plastic) deformation, and the object has been permanently changed. A spring shows the same split: stretch it gently and it springs back, but stretch it too far and it stays stretched.
Hooke’s law: force is proportional to extension
While deformation stays elastic, force and extension are directly proportional: F = ke, where F is force in newtons, e is extension in metres, and k is the spring constant in newtons per metre. Double the force and the extension doubles too — but only up to the limit of proportionality, the point where this straight-line relationship breaks down.
A worked calculation
A spring has a spring constant of 40 N/m. Find the extension when a force of 6 N is applied. Rearranging F = ke gives e = F ÷ k, so e = 6 ÷ 40 = 0.15 m, or 15 cm. The same rearrangement, e = F ÷ k, answers almost every Hooke’s law calculation the exam asks.
Reading a force–extension graph
A force–extension graph starts as a straight line through the origin: this is the elastic region, and its gradient is the spring constant. Past the limit of proportionality the line curves, extension growing faster than force predicts — the material is starting to deform permanently, and Hooke’s law no longer applies beyond that point.
Elastic potential energy
Stretching or compressing a spring elastically stores energy in it, called elastic potential energy, equal to the area under the force–extension line — for a straight-line region this is ½ × F × e. Release the spring and that stored energy transfers to kinetic energy, which is exactly how a catapult or a wind-up toy works.
The limit of proportionality is not the elastic limit
These two points are often confused. The limit of proportionality is where the straight-line graph ends — beyond it, force and extension are no longer proportional, but the material can still return to its original shape if the force is small enough. The elastic limit is further along: past it, the deformation becomes permanent. Exam answers that treat the two as identical lose marks.