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AQA GCSE Physics · Topic 4.5 Forces · Combined and Triple · Required practical
Forces and Elasticity: Hooke's Law, the Spring Practical and Elastic Potential Energy
In this lesson you'll learn to: do the force and extension required practical and plot the graph; use it to
show Hooke's law, read off the limit of proportionality and find the spring constant; calculate with
F = k e and Ee = ½ k e², converting to metres; and say whether a deformation is elastic or
inelastic.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. Hang masses on the spring one at a time and watch the graph build. Keep going past 400 g, then take them all off again. Does the spring get back to where it started?
Spring:
Your results · g = 9.8 N/kg
| mass / g | force / N | length / cm | extension / cm |
|---|
Analyse the graph
Limit of proportionality ≈ N
Graph:
The spring
Your turn
Elastic: the object returns to its original length once the
deforming force is removed. Inelastic: it does not return to its original length once the deforming
force is removed: it is permanently deformed.
Hooke’s law: the extension is directly proportional to the force (a straight line through the origin) up to the limit of proportionality. F = k e and Ee = ½ k e², with e in metres. Energy stored = area under the force–extension line.
Physics With Kate · physicswithkate.com — AQA GCSE Physics 4.5.3
Straight line through the origin = Hooke's law. Where it starts to curve = the limit of proportionality.
Straight line through the origin? The extension is proportional to the force.
Past the limit of proportionality it curves, and the spring may not go back. The notes show you the method, the graph and the calculations.
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Revision notes
Changing shape: elastic and inelastic
To stretch, bend or compress an object you need more than one force. Hang a spring from a clamp and pull it down: the clamp pulls up as you pull down. With only one force, the object would just move.
⭐ Learn these definitions
Elastic deformation: the object returns to its original length once the deforming force is removed.
Inelastic deformation: the object does not return to its original length once the deforming force is removed. It is permanently deformed.
Hooke's law
⭐ The equation
force = spring constant × extension F = k e
F in newtons (N), k in newtons per metre (N/m), e in metres (m). It works for compression too: then e is how much shorter the spring gets.
- Extension = stretched length − original length.
- Hooke's law: the extension is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
- You know it's directly proportional because the graph is a straight line through the origin. That's a linear relationship.
- Past the limit of proportionality the graph curves: a non-linear relationship. The extension grows much faster than the force, Hooke's law no longer applies, and the spring may not go back to its original length.
- A bigger k means a stiffer spring: it takes more force to stretch it each metre.
Required practical: force and extension of a spring
1
Set up
Hang the spring from a boss and clamp on a clamp stand. Fix a metre ruler beside it, its zero level with the top of the spring. Measure the original length.
2
Add a mass
Hang a 50 g mass on the spring. Force = weight: F = m g = 0.050 × 9.8 = 0.49 N.
3
Measure
Read the new length with a set square at eye level, so you read the scale straight on. Extension = stretched length − original length.
4
Repeat
Add 50 g at a time and repeat, for at least six readings. Then take the masses off one at a time to check whether it returns to its original length.
5
Plot the graph
Extension up the side (y-axis), force along the bottom (x-axis). Draw a line of best fit.
| Variable | In this practical |
|---|---|
| Independent (you change it) | the force (the weight of the masses) |
| Dependent (you measure it) | the extension |
| Control (keep it the same) | the same spring; add the masses gently and wait until the spring is still |
| Safety | wear eye protection in case the spring snaps or flies off; keep feet clear and clamp the stand so it can't tip |
Reading the graph
- Limit of proportionality: the point where the line stops being straight. Read the force at that point off the x-axis. In the workbook's results it's about 3.9 N.
- Spring constant: work out the gradient of the straight part. With extension on the y-axis, the gradient is extension ÷ force, which is 1 ÷ k. So k = 1 ÷ gradient, with the gradient in m/N.
- If the graph had force on the y-axis instead, the gradient would be force ÷ extension = k itself. Always check which way round the axes are.
- Unloading: if the points come back down the same line to the origin, the spring was elastic. If they finish above it, it's permanently stretched: inelastic.
Elastic potential energy
⭐ The equation
elastic potential energy = ½ × spring constant × (extension)² Ee = ½ k e²
Ee in joules (J), k in N/m, e in metres. It's on the equation sheet, but you have to choose it.
- Stretching or compressing a spring means doing work on it. The work done is stored as elastic potential energy, as long as the spring is not inelastically deformed.
- The energy stored is the area under the force–extension graph. Up to the limit of proportionality that area is a triangle: E = ½ × base × height = ½ × e × F. That's the same as ½ k e², because F = k e.
⚠ Trap — millimetres and centimetres
F = k e and E = ½ k e² need e in metres. Divide mm by 1000 and cm by 100 first: 70 mm = 0.070 m. Leaving it in mm makes F a thousand times too big, and E a million times too big. Force must be in newtons: convert kN or a mass in grams (via W = m g) first.
The answer that gets the marks
The extension is directly proportional to the force because the graph is a
straight line through the origin, up to the limit of proportionality at ___ N.
the relationship the evidence where it stops
🗣 Words to use in a written answer
Tick each one off as you use it.
How to write it in the exam
A graph of extension (y-axis) against force (x-axis) for a spring passes through F = 14 N, e = 70 mm. Calculate the spring constant.
e = 70 ÷ 1000 = 0.070 m. k = F ÷ e = 14 ÷ 0.070 = 200 N/m
Calculate the energy stored in the same spring when it is stretched by 70 mm.
Area of the triangle = ½ × base × height = ½ × 0.070 m × 14 N = 0.49 J. Check: ½ k e² = ½ × 200 × 0.070² = 0.49 J.
In the required practical, the straight part of the graph of extension against force rises 7.5 cm for every 3.0 N. Calculate the spring constant.
Gradient = 7.5 ÷ 3.0 = 2.5 cm/N = 0.025 m/N. Extension is on the y-axis, so k = 1 ÷ gradient = 1 ÷ 0.025 = 40 N/m
State Hooke's law. (2 marks)
The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
A spring's force–extension line begins to curve at point P. Name point P and explain what happens to the spring beyond it. (3 marks)
P is the limit of proportionality. Beyond P the extension is no longer directly proportional to the force, so Hooke's law no longer applies, and the spring may be inelastically deformed: it won't return to its original length.
✅ Check your answer
Extension = stretched − original · e in metres, F in newtons · which way round are the axes (k = gradient or 1 ÷ gradient)? · energy = area under the line = ½ F e = ½ k e² · units: N/m for k, J for energy.
📘 Now do it in your workbook
Page 6: draw the set-up, fill in the method, then plot the results and find the limit of proportionality and k. Page 7: F = k e and ½ k e² from a graph, elastic or inelastic, and two exam-style questions.
AQA GCSE Physics Workbook · FORCES · pages 6–7✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this topic.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
The spring practical, the graph, and both workbook pages explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
The spring practical, the graph, and both workbook pages explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook pages above cover every mark.
Now put it into practice
Pages 6–7 of the Forces workbook are free: the required practical with its graph, then the calculations and elastic potential energy.
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