Elasticity · Physics

Springs that stretch and spring back

Pull a rubber band and it gets longer. Let go and it returns to its first length. A material that does this is elastic. Springs, rulers and trampolines all use elasticity.

Hooke's law

Hooke's law: The extension of a spring is directly proportional to the force applied, as long as the elastic limit is not passed.

Force equals spring constant times extension.

force on the spring (newtons, N)
spring constant (how stiff the spring is) (N/m)
extension (new length minus original length) (metres, m)

A spring hanging from a stand with a mass attached and a ruler beside it — A spring, mass and ruler: the set-up for measuring extension.

See it move

Pull the mass down and release it. It moves up and down about the rest position while energy swaps between movement and stored stretch.

Try it yourself

Try itHang a mass on a spring

Change the mass and the stiffness of the spring. Watch the extension and the graph. Weight is with N/kg.

Worked exampleForce needed to stretch a spring

A spring has a spring constant of . What force stretches it by ?

Write the formula.
Change the extension to metres: .
Put in the numbers.
Calculate.

Answer: The force is 10 N.

Where Hooke's law stops working

Small forcesExtension is proportional to force. The spring returns to its first length.
Elastic limitThe most force the spring can take and still return to its first length.
Too much forceThe spring is stretched past its limit and stays longer. Hooke's law no longer applies.

Elastic

Returns to its first shape
Spring, rubber band, steel ruler

Plastic

Keeps its new shape
Clay, a bent paper clip

Spring constants of three springs
Spring	k (N/m)	Force for 0.1 m
Soft	20	2 N
Medium	50	5 N
Stiff	100	10 N

Check yourself A spring stretches 2 cm when a 4 N force acts on it. What force gives 6 cm, if the limit is not passed?

Check yourself What does a large spring constant tell you?

Open the Hooke's law lab
Add masses, measure extensions and find from the gradient of your graph.

Key terms

Elasticity: The ability of a material to return to its shape after a force is removed.
Extension: How much longer a spring becomes: new length minus original length.
Spring constant: The force needed per metre of extension, in N/m.
Elastic limit: The largest force after which the spring still returns to its first length.

Summary

Elastic materials return to their shape when the force is removed.
Hooke's law: while the elastic limit is not passed.
A force–extension graph is a straight line through the origin; its gradient is .
Past the elastic limit the spring is permanently stretched.