2.1.11Interactions Over Small and Large Distances
Energy Stored In A Stretched Spring — AQA GCSE Combined Science Synergy 8465 - Physical Sciences Revision Notes & Topical Questions
5 min read 9 parts Lesson 12 of 26
Part 1 of 7Work done on a spring
Stretching transfers energy
- Stretching transfers energy When a force stretches a spring, work is done on it and energy is transferred to the spring's elastic potential energy store.
Released on return
- Released on return If the spring is elastic and returns to its original length, this stored energy is released again.
- It may be transferred to the kinetic energy store of a moving object, as in a catapult or a pogo stick.
Linear region
- Linear region The equation below works only while the force is proportional to the extension.
- Beyond the limit of proportionality the relationship no longer applies.
Part 2 of 7The equation
| Quantity | Symbol | Unit |
|---|---|---|
| Elastic potential energy | Ee | joules (J) |
| Spring constant | k | N/m |
| Extension | e | metres (m) |
| Equation | Ee = ½ × k × e2 | J |
Part 3 of 7Worked calculation
1
A spring has k = 50 N/m and is stretched by 12 cm.
2
Convert the extension to metres: 0.12 m.
3
Square the extension: 0.12 × 0.12 = 0.0144 m2.
4
Multiply: ½ × 50 × 0.0144 = 0.36 J.
5
State the unit: joules.
Part 4 of 7More practice
| Spring constant | Extension | Working | Energy stored |
|---|---|---|---|
| 20 N/m | 0.10 m | ½ × 20 × 0.01 | 0.10 J |
| 100 N/m | 0.05 m | ½ × 100 × 0.0025 | 0.125 J |
| 200 N/m | 0.20 m | ½ × 200 × 0.04 | 4.0 J |
| 40 N/m | 5.0 cm = 0.05 m | ½ × 40 × 0.0025 | 0.050 J |
Part 5 of 7Link to the graph
1Force against extension
- Force against extension A straight line from the origin forms a triangle with the axis.
2Area is work done
- Area is work done Area = ½ × base × height = ½ × e × F.
3Substitute F = k × e
- Substitute F = k × e This gives ½ × k × e2, the same equation.
Part 6 of 7Effect of changing extension
E = ½ k e2
Doubling the extension
- Doubling the extension Energy stored becomes four times larger, since extension is squared.
Stiffer spring
- Stiffer spring A larger k stores more energy at the same extension.
Rearranging
- Rearranging To find extension, rearrange to e = √(2E ÷ k) once energy and spring constant are known.
Energy transfer
- Energy transfer When a stretched spring is released, the elastic energy it stores is transferred to kinetic energy,
- and some is wasted as heat and sound.
Part 7 of 7Everyday examples
Catapult or bow
- Catapult or bow Pulling back the elastic stores energy that is released as kinetic energy of the projectile,
- and a bigger pull stores much more energy.
Trampoline
- Trampoline The springs stretch as a person lands, storing energy that is then given back to push the person upwards again.
Vehicle suspension
- Vehicle suspension Springs compress over bumps and store energy, which is dissipated by dampers so the car does not keep bouncing.
Energy conservation
- Energy conservation If the stretched spring is released and no energy is wasted, the elastic energy stored equals the kinetic energy gained,
- so ½ × k × e² = ½ × m × v²,
- which lets you find the speed of an object launched by a spring.
Compression
- Compression The same equation applies to a compressed spring, with e as the amount by which its length has decreased.
Key terms
| Term | Meaning |
|---|---|
| Elastic potential energy | Energy stored in a stretched or compressed elastic object. |
| Work done | Energy transferred when a force moves through a distance. |
| Spring constant | The force required per metre of extension. |
| Extension | The increase in length of a stretched spring. |
| Joule | The unit of energy, equal to one newton metre. |
Avoid these mistakes
1
Forgetting to square the extension.
2
Leaving out the half.
3
Using extension in centimetres, giving an answer 10 000 times too large.
4
Using the total length of the spring in place of the extension.
5
Using the equation for a spring that has been stretched past its limit of proportionality.
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