GCSE Physics resources

AQA GCSE Forces

Forces, Elasticity and Springs

For a spring obeying Hooke’s law, extension is proportional to force. The limit of proportionality is where the graph stops being straight; beyond the elastic limit the spring may not return to its original length.

AQA 8463AQA 8464 GCSE PhysicsCombined Science: Trilogy FoundationHigher

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The revision snapshot

For a spring obeying Hooke’s law, extension is proportional to force. The limit of proportionality is where the graph stops being straight; beyond the elastic limit the spring may not return to its original length.

By the end, you should be able to:

  • Read force-extension behaviour.
  • Apply the forces model, evidence or method to an unfamiliar exam context.
  • Recognise and correct this wrong turn: Using total length as extension.

Before you revise

Diagnostic question

Choose an answer from memory. Your result tells you what to watch for in the guide.

Which statement correctly summarises forces, elasticity and springs?

Core revision guide

Learn the model, then use it

Forces, Elasticity and Springs questions become manageable when the central model, evidence and exam method are kept together. Read the explanation, test the misconception and then apply the idea without looking back.

Read force-extension behaviour

For a spring obeying Hooke’s law, extension is proportional to force. The limit of proportionality is where the graph stops being straight; beyond the elastic limit the spring may not return to its original length.

Build the physics picture

Extension is the increase in length, not the total length. In the straight-line region, force and extension are proportional. Beyond the limit of proportionality the graph curves; beyond the elastic limit, removing the load leaves the spring permanently stretched.

Relationships used in this guide

Hooke’s law: F = ke (N, N/m, m). Elastic potential energy: Eₑ = ½ke² (J, N/m, m). Choose each relationship from the physical change described, convert quantities into compatible units and keep the unit beside the final answer.

A force-extension graph is linear through the origin before curving beyond the limit of proportionality.
Use the straight section for Hooke's law; beyond the labelled limit, extension is no longer proportional to force.Open the full-size exam diagram
Hooke’s lawF = keN, N/m, m
Elastic potential energyEₑ = ½ke²J, N/m, m

Misconception clinic

Replace the tempting answer

Read each belief, say what is wrong with it, then compare your correction.

Tempting idea: Using total length as extension.

Use instead: For a spring obeying Hooke’s law, extension is proportional to force. The limit of proportionality is where the graph stops being straight; beyond the elastic limit the spring may not return to its original length.

Tempting idea: Confusing proportional and elastic limits.

Use instead: Extension is the increase in length, not the total length. In the straight-line region, force and extension are proportional. Beyond the limit of proportionality the graph curves; beyond the elastic limit, removing the load leaves the spring permanently stretched.

Tempting idea: Using cm with N/m.

Use instead: Distinguish extension from total length, identify the straight-line region and describe the graph before and after proportionality.

Retrieval practice

Quick checks

1. Which exam method is most reliable for forces, elasticity and springs?

2. Which statement correctly applies forces, elasticity and springs to a question?

3. A pupil writes: “Using total length as extension.” Which replacement is accurate?

Explore the relationship

Force-extension explorer

Change the force or extension, then calculate spring constant in the proportional region using F = ke.

What to notice: use the readout to describe how one variable changes when the other is controlled.

Worked examples

See the method being built

These examples expose the difference between a secure read force-extension behaviour method and the common error “Using total length as extension.”.

Example 1 · Calculate extension

A spring is 8.0 cm unloaded and 13.5 cm loaded. Find extension.

  1. Use loaded minus unloaded length.
  2. Calculate 13.5 − 8.0.
  3. Keep cm or convert consistently.
Show the answer

Extension = 5.5 cm.

Example 2 · Use Hooke’s law

A spring constant is 40 N/m and extension 0.15 m in the proportional region. Find force.

  1. Use F = ke.
  2. Substitute 40 × 0.15.
  3. Give newtons.
Show the answer

F = 6.0 N.

Example 3 · Read graph region

A force-extension graph begins to curve after 7 N. State the limit of proportionality.

  1. Find the first departure from straight line.
  2. Quote force.
  3. Do not confuse with elastic limit.
Show the answer

The limit of proportionality is about 7 N.

Exam precision

Exam technique: Read force-extension behaviour

Do this: Distinguish extension from total length, identify the straight-line region and describe the graph before and after proportionality.

Independent practice

Exam-style questions

Write an answer before opening the marking guidance. Then edit the exact phrase or step that would gain the next mark.

1. Define extension.

[2 marks]
Show marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: The increase in length from the unloaded/original length.

2. State Hooke’s law.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: Extension is proportional to force up to the limit of proportionality.

3. A spring extends 0.20 m under 10 N. Calculate k.

[3 marks]
Show marking guidance and model answer

Marking guidance: Award one mark for the correct relationship, one for a valid substitution and one for the final answer with its unit.

Model answer: k = F/e = 10 ÷ 0.20 = 50 N/m.

4. Describe a force-extension graph beyond the limit of proportionality.

[2 marks]
Show marking guidance and model answer

Marking guidance: 2 marks are available for relevant, linked physics points that match the model answer.

Model answer: It curves because extension is no longer proportional to force.

5. State what can happen beyond the elastic limit.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: The spring may not return to its original length.

6. Give one reason to wait before reading a spring length.

[1 mark]
Show marking guidance and model answer

Marking guidance: Award one mark for the precise statement shown in the model answer.

Model answer: Allow oscillations to stop so the reading is stable.

Questions pupils ask

Forces, Elasticity and Springs FAQs

What is the main idea in Forces, Elasticity and Springs?

For a spring obeying Hooke’s law, extension is proportional to force. The limit of proportionality is where the graph stops being straight; beyond the elastic limit the spring may not return to its original length.

What mistake should I avoid in Forces, Elasticity and Springs?

Using total length as extension. Extension is the increase in length, not the total length. In the straight-line region, force and extension are proportional. Beyond the limit of proportionality the graph curves; beyond the elastic limit, removing the load leaves the spring permanently stretched.

Useful next steps

Connect this guide to your next task

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