Explain what is meant by the limit of proportionality and describe how the extension of a steel spring changes as increasing loads are applied, both before and after this limit is reached.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (5 marks)
The limit of proportionality is the point beyond which the extension of a spring is no longer directly proportional to the applied force.
Before this limit the spring obeys Hooke’s law:
1. Extension is directly proportional to the applied force.
2. A force–extension graph is a straight line through the origin.
After the limit the spring behaves non‑linearly:
3. The extension increases more rapidly for the same increase in force.
4. The spring may not return to its original length when the load is removed, indicating permanent deformation.
Before this limit the spring obeys Hooke’s law:
1. Extension is directly proportional to the applied force.
2. A force–extension graph is a straight line through the origin.
After the limit the spring behaves non‑linearly:
3. The extension increases more rapidly for the same increase in force.
4. The spring may not return to its original length when the load is removed, indicating permanent deformation.
Examiner tips
- Use the definition of the limit of proportionality first. Explain Hooke’s law and the straight‑line graph. Describe the change in behaviour after the limit and mention permanent deformation.
Common mistakes
- Confusing the limit of proportionality with the elastic limit. Forgetting to mention the straight‑line graph. Saying the spring always returns to its original length after the limit.
Mark scheme (5 marks)
- The limit of proportionality is the point beyond which extension is no longer proportional to force/load
- Before the limit of proportionality, extension is directly proportional to the force applied (Hooke's law is obeyed)
- A graph of force against extension would be a straight line through the origin before the limit of proportionality
- After the limit of proportionality, extension increases more rapidly / disproportionately for the same increase in force
- After the limit of proportionality the spring may not return to its original length / may be permanently deformed when the load is removed
Key terms in this question
limit of proportionality · extension
Related
- All AQA A-Level Physics (7408) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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