The big idea: Pull back a catapult, or squash a pogo stick, and you can feel it push back — you've stored elastic potential energy in the spring. Let go and it's released again.
It depends on the spring's stiffness and on the stretch squared: EH = ½kΔx² (in joules).
Two words to know first: Spring constant (k): how stiff a spring is — the force needed per metre of stretch (unit N m⁻¹). A bigger k means a harder spring to pull.
Extension (Δx): how far the spring is stretched or squashed from its natural length (in metres).
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Spot it — the stretch is SQUARED: Because of the Δx², the stretch matters a lot: double the stretch ⇒ four times the stored energy.
A spring pulled twice as far stores 4× the energy — and shoots back with 4× the energy to give away.
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The elastic-energy formula is given in the data booklet. The spring constant k comes from Hooke's law (F = kΔx) — it links the force to the stretch — but for the stored energy you use the ½kΔx² formula directly.
- elastic potential energy — energy stored in the stretched/squashed spring (J, joules)
- spring constant — how stiff the spring is (N m⁻¹: newtons per metre)
- extension or compression — how far the spring is stretched or squashed from its natural length (m)
- the spring's restoring force — it pulls/pushes back toward the natural length (N)
- spring constant — the stiffness (N m⁻¹)
- extension or compression from the natural length (m)
Don't forget to square the stretch — and use metres: The most common slip is forgetting the Δx². Square the extension first, then multiply by k and halve.
And convert any centimetres to metres before squaring (e.g. 4 cm = 0.04 m).
A spring has a spring constant of 250 N m⁻¹. It is stretched by 0.080 m. Find the elastic potential energy stored.
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How this is tested — elastic energy is the link between forces and energy conservation:
Paper 1A
- A quick EH calculation.
- Or average power as a spring releases its energy (power = energy ÷ time).
Paper 2
- The classic spring-coupled collision: a moving cart hits a spring on a second cart.
- At the instant they move together, find the elastic energy stored by energy conservation.
The classic trap: When the carts momentarily move together, the spring stores the kinetic energy that has 'gone missing'. Find the KE before, the KE of the combined motion, and the difference is the elastic energy stored (nothing is destroyed).
Energy conservation with a spring: Energy is never lost — it just changes form. When a spring is squashed during a collision:
EH stored = kinetic energy before − kinetic energy of the combined motion.
Later the spring pushes the carts apart and gives that energy back.
Find momentum first, then energies: At the instant the carts move together they share one common speed. Get it from conservation of momentum (total momentum before = total momentum after), then compare kinetic energies.
A 2.0 kg cart moves at 6.0 m s⁻¹ toward a stationary 4.0 kg cart carrying a spring bumper. At the instant the spring is most compressed, the two move together. (a) Find their common speed. (b) Find the elastic energy stored in the spring at that instant.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.