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.
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.
Start here
The quick 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…
- Explain read force-extension behaviour using precise physics language.
- Apply the relevant equations, diagrams or practical method to an exam-style situation.
- Use the mini quizzes and practice answers to identify and correct a misconception.
Core learning content
Learn the idea before you practise it
Start with this short teaching sequence for Forces, Elasticity and Springs. Read the model, use the visual, then test your recall before moving into examples and exam practice.
Build the 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.
Use the right relationship
Choose a relationship because of the physical change in the question, not because it is familiar. Weight: W = mg (N, kg, N/kg). Newton’s second law: F = ma (N, kg, m/s²). Momentum: p = mv (kg m/s). Keep the unit next to each value while you substitute.
What a strong answer does
Distinguish extension from total length, identify the straight-line region and describe the graph before and after proportionality. Before writing, underline the command word and identify the information that matters. Keep a calculation as equation, substitution and answer with unit; keep an explanation as a linked chain using because, so or therefore. Finish by checking that the final sentence answers the exact context in the question and that the number, direction or conclusion agrees with the evidence given.
Retrieval practice
Quick checks
Answer without looking back first. The feedback explains the model, so a wrong answer still helps you learn.
Mini quiz 1
Check the core idea
Mini quiz 2
Apply the model
Mini quiz 3
Use exam precision
Try it
Force-extension explorer
Where does a spring stop behaving proportionally?
What to notice: the readout and written explanation remain available if you do not use the controls.
Worked examples
See the method being built
Cover the answer, attempt the method and then compare your physics language as well as the number.
Example 1 · Calculate extension
A spring is 8.0 cm unloaded and 13.5 cm loaded. Find extension.
- Use loaded minus unloaded length.
- Calculate 13.5 − 8.0.
- 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.
- Use F = ke.
- Substitute 40 × 0.15.
- 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.
- Find the first departure from straight line.
- Quote force.
- Do not confuse with elastic limit.
Show the answer
The limit of proportionality is about 7 N.
Misconception clinic
Common wrong turns
Each of these is tempting because it sounds almost right. Replace it with the precise physics before you meet it in a question.
- Using total length as extension.
- Confusing proportional and elastic limits.
- Using cm with N/m.
Independent practice
Exam-style questions
Use the working space first. Reveal the guidance only after you have committed to an answer, then improve the exact part that would gain the next mark.
1. Define extension.
[2 marks]Show answer and marking guidance
The increase in length from the unloaded/original length.
2. State Hooke’s law.
[1 mark]Show answer and marking guidance
Extension is proportional to force up to the limit of proportionality.
3. A spring extends 0.20 m under 10 N. Calculate k.
[2 marks]Show answer and marking guidance
k = F/e = 10 ÷ 0.20 = 50 N/m.
4. Describe a force-extension graph beyond the limit of proportionality.
[2 marks]Show answer and marking guidance
It curves because extension is no longer proportional to force.
5. State what can happen beyond the elastic limit.
[1 mark]Show answer and marking guidance
The spring may not return to its original length.
6. Give one reason to wait before reading a spring length.
[1 mark]Show answer and marking guidance
Allow oscillations to stop so the reading is stable.
Questions pupils ask
GCSE Physics FAQs
What is the key idea in Forces, Elasticity and Springs?
Forces questions often hide a simple model inside a diagram. Draw the forces, find the resultant, then connect the resultant to the motion or deformation.
How should I practise Forces, Elasticity and Springs?
Read the snapshot, attempt the worked examples without looking, complete the mini quizzes and then use the practice questions to check your wording and method.
Next step
Keep your revision moving
Physics sticks when you move between explanation, retrieval and application.