5.3.4Forces
Work Done on a Spring — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions
5 min read 6 parts Lesson 16 of 44
Part 1 of 4Work done and stored energy
1Force applied
- Force applied A force stretches or compresses the spring through a distance.
2Work done
- Work done Work is done on the spring, which means energy is transferred to it.
3Elastic potential store
- Elastic potential store The energy is stored in the elastic potential energy store of the spring.
4Equal amounts
- Equal amounts If the spring has not been permanently deformed, the work done equals the energy stored.
Part 2 of 4The equation
Formula
- Formula elastic potential energy = 0.5 × spring constant × (extension)2.
- Ee = ½ × k × e2What the symbols mean: E = elastic potential energy stored (J) · k = spring constant (N m−1) · x = extension (m) · F = force (N)
Units
- Units Ee in joules (J), k in newtons per metre (N/m), e in metres (m).
Limit
- Limit This only applies to a spring that is still within its limit of proportionality.
Squared extension
- Squared extension Doubling the extension makes the stored energy four times bigger, because 22 = 4.
Part 3 of 4Rearranging to find k
1
A spring is stretched by 4.5 cm and 0.2 J of work is done. Write down Ee = 0.2 J.
2
Convert the extension to metres: 4.5 cm = 0.045 m.
3
Rearrange Ee = ½ k e2 to give k = 2 × Ee ÷ e2.
4
Substitute: k = 2 × 0.2 ÷ (0.045)2 = 0.4 ÷ 0.002025.
5
Calculate: k is about 198 N/m (roughly 200 N/m).
Part 4 of 4Effect of changing quantities
| Change | Effect on stored energy | Reason |
|---|---|---|
| Extension doubled | Four times as much | Energy depends on e2 |
| Extension tripled | Nine times as much | 32 = 9 |
| Spring constant doubled | Twice as much | Energy is proportional to k |
| Stretched beyond limit of proportionality | Equation no longer valid | Spring is permanently deformed |
Key terms
| Term | Meaning |
|---|---|
| Elastic potential energy | The energy stored in an elastic object when work is done to deform it. |
| Spring constant | The force required per unit extension of a spring, in N/m. |
| Extension | How much longer a spring is than its original length. |
| Work done | The energy transferred when a force moves through a distance. |
| Limit of proportionality | The point beyond which the spring no longer obeys Hooke's law. |
Avoid these mistakes
1
Forgetting to square the extension in E = ½ k e2.
2
Using the extension in centimetres, which gives an energy value that is 10 000 times too large.
3
Squaring the whole product ½ k e instead of squaring only e.
4
Using the equation for a spring that has been stretched past its limit of proportionality.
Last updated: