Cambridge Stage 7 · Physics · 1.7

Elastic potential energy

Pull back a bowstring, squash a mattress, bend a diving board — and you've stored energy just by changing a shape. Let go, and it all comes rushing back.

the big picture

Energy you can hide in a shape

Think about pulling back the string of a bow. Your muscles do work, the bow bends, and now something feels loaded — ready to go. You haven't fired anything yet, but the energy is in there, waiting. The instant you let go, it leaps out and flings the arrow.

That stored, ready-to-go energy is called elastic potential energy — EPE for short. Another way to say it is energy in an elastic store. You build it up whenever you change the shape of something springy: pulling a rubber band, squashing the springs in a mattress when you lie down, bending a ruler over the edge of a desk.

Here's the key idea: changing the shape of a springy object stores energy, and letting it snap back gives that energy out again. People have used this for thousands of years — a bow carved more than 2000 years ago worked on exactly the same trick as a modern trampoline.

what you can see

Elastic, or just squashed?

When you stretch or squash something so its shape changes, we say it has deformed. But not everything that deforms stores useful energy. Press your thumb into modelling clay and it just stays dented — the clay keeps the new shape and gives nothing back. Press a spring and it pushes right back at you.

A material that springs back to its original shape once you stop pushing or pulling is called elastic. Only elastic objects store EPE and hand it back. Clay isn't elastic; a rubber band is.

Which of these are storing elastic potential energy?
What you doWhat happensSprings back?Stores EPE?
Stretch a rubber bandIt gets longer and thinnerYesYes
Lie on a mattressThe springs squash downYesYes
Bend a diving boardIt curves downwardYesYes
Squash modelling clayIt stays dentedNoNo
play with it

Load the slingshot, then let go

behind the scenes

Energy never vanishes — it moves

Energy is never made or destroyed. It just gets passed between stores — like money moving between pockets. Watching where it goes is the whole game.

A bungee jump, store by store

Grace stands on a high bridge with an elastic cord tied to her legs. Up there she has lots of gravitational energy (energy because she is high up). She jumps. As she falls she speeds up: gravitational energy turns into kinetic energy — the energy of moving. Near the bottom the cord stretches tight and slows her down, soaking up that movement and storing it as elastic potential energy. For one instant she stops dead. Then the cord snaps back, pushing her up: EPE becomes kinetic energy again, then gravitational energy as she rises. The energy keeps getting handed around the same little circle.

A bouncing ball loses the game slowly

When a ball hits the ground it squashes — for a moment it deforms and stores EPE, exactly like the bungee cord. Then it springs back to its round shape and pushes off the floor: the EPE becomes kinetic energy and up it goes. So one bounce is the chain movement → elastic → movement → height.

So why does each bounce get lower? Misconception alert: the missing energy hasn't been used up or destroyed — that can't happen. Every time the ball squashes, a little energy is dissipated: it spreads out into the surroundings as heat (the ball and floor warm up the tiniest bit) and sound (that's the bounce you hear). That energy is too spread out to bounce the ball, so each bounce is smaller, until it finally rests and all of it has drifted off into the warmth of the room.

One bungee fall, traced through the energy stores
MomentWhere the energy is
On the bridgeGravitational (she is high up, not moving)
FallingGravitational turning into kinetic (movement)
Cord stretched, stopped at the bottomElastic potential — stored in the stretched cord
Bouncing back upElastic → kinetic → gravitational again
Finally at restDissipated — spread out as heat and sound
try it yourself

The rubber-band ruler launcher

  1. Hook a rubber band over your thumb and first finger to make a little slingshot. Scrunch up a small ball of paper to fire.
  2. Predict first: pull the band back just a little and guess where the paper ball will land. Mark the spot in your head.
  3. Fire it. Then pull the band back twice as far and predict again — a bit further, or a lot further?
  4. Fire it and compare. Try three pull-back distances and notice how the landing spot races away as you stretch more.
What's going on?The further you stretch the band, the more elastic potential energy you store in it. When you let go, all of that stored energy becomes kinetic energy — movement — in the paper ball, so it leaves your hand faster and flies further. It's the same thing the slider showed you: more stretch, more stored energy, a longer flight. This is exactly why an archer who pulls the string back further sends the arrow further.

Use a soft paper ball, never anything hard, and never aim at anyone's face or eyes — point it at a wall or across an empty floor. A loose rubber band can sting, so keep fingers clear of the snap-back.

going further

Four springy surprises

Elastic energy is hiding all over the living world and the sports field — sometimes doing things no rubber band could.

🔥

Stretch it and it warms up

Almost everything cools when you pull it, but a rubber band does the opposite. Stretch one quickly against your lip and you'll feel it go warm; let it relax and it turns cool. It's one of the few materials that breaks this rule.

🦗

Fleas are living catapults

A flea is too small for its muscles to jump fast — so instead it slowly squeezes a tiny rubbery spring, then trips a latch to release it all at once. It launches at about 100 times the force of gravity, far more than any pilot could survive.

🦘

Kangaroos hop on pogo sticks

A kangaroo's long leg tendons stretch and store elastic energy each time it lands, then snap back to power the next hop. By recycling the energy this way, it can bound faster while barely burning any extra fuel.

🏃

A pole that flings you skyward

A pole vaulter sprints, jams a bendy pole into the ground, and their speed bends it into a giant spring. As it un-bends it flings them over 6 metres up — about as high as a two-storey house.

bonus experiment

Feel the warmth in a rubber band

  1. Find a fairly thick rubber band and rest it gently against your top lip — lips notice tiny temperature changes really well.
  2. Predict: when you stretch it, will it feel warmer, cooler, or the same?
  3. Now stretch it out quickly and hold it tight against your lip. Notice the warmth.
  4. Keep it on your lip and let it slowly relax — it cools back down again.
Why does it warm up?A rubber band is made of millions of long, tangled molecule chains. Stretching forces them to line up neatly, and lining them up releases a little heat — so the band warms. Let it relax and the chains tangle up again, pulling heat back in, so it cools. Most materials don't do this, which makes the humble rubber band a tiny rule-breaker.

Completely safe. Just don't let the band snap — keep a firm grip on both ends and stretch gently.

Key points

  • Changing the shape of something springy — stretching, squashing or bending it — stores elastic potential energy (EPE).
  • A material that springs back to its original shape when the force is removed is called elastic; only elastic objects give the stored energy back.
  • The more you stretch or squash an elastic object, the more EPE it stores.
  • Energy is never destroyed — it is passed between stores (gravitational ↔ kinetic ↔ elastic) as things fall, fly and bounce.
  • Some energy is dissipated as heat and sound every time a material deforms, so a bouncing ball never returns to its starting height.
check yourself

Quick questions

A girl stretches an elastic band and then lets it go. Describe how the energy is stored and what happens to it.
As she stretches the band she stores elastic potential energy in it. When she lets go, the band springs back and that stored EPE becomes kinetic energy — the band (and anything it fires) moves.
Explain, in terms of energy, why the band fires something further if she pulls it back more.
Pulling it back further stores more elastic potential energy. When she releases it, all that extra energy turns into extra kinetic energy, so the object leaves faster and travels further.
Name the energy stores in order, from the moment a bungee jumper leaps off the bridge to the instant she is briefly stationary at the bottom.
Gravitational energy (high on the bridge) → kinetic energy (speeding up as she falls) → elastic potential energy (stored in the stretched cord as it stops her at the bottom).
A ball is dropped and bounces. Explain why it never bounces back higher than the height you dropped it from.
Each time the ball squashes against the floor, a little energy is dissipated as heat and sound and spreads into the surroundings. With less energy left to lift it, every bounce is lower than the one before — it can never gain energy, so it can never out-bounce its starting height.