Lesson focus: Proportional behaviour and elastic behaviour are related but not identical: a material may be non-linear yet still recover its shape.
Distinguish the limit of proportionalityThe point after which a spring stops stretching by the same amount for each extra weight. from the elastic limitThe point after which a stretched object will not go back to its original shape. and compare spring, wire and rubber behaviour.
Build on earlier learning
Hooke’s law: force and extensionThe previous lesson established the initial Hooke’s-law region. This lesson examines unloading and permanent deformation.
Practical
Elastic limit
- Load the spring in steps and unload it after each step.
- Check whether it returns to its original length.
- Use the model on this page to see the line curve beyond the limit of proportionality.
Record: The load at which the spring stops returning to its original length.
Stretching a spring
Add weights one newton at a time and watch the extension. Remove them all to test whether the spring returns to its original length.
Controls
Illustrative spring: 4 cm per newton up to 5 N; it stays stretched if loaded beyond 6 N.
You will be successful when you can…
- Define elastic behaviour.
- Separate two important limits.
- Interpret loading and unloading data.
- Compare materials fairly.
Words that carry the science
- elastic deformation
- A reversible change of shape that disappears when the force is removed.
- plastic deformation
- A permanent change of shape remaining after the force is removed.
- elastic limit
- The greatest load after which the material still returns to its original shape.
- limit of proportionality
- The end of the region where force and extension are proportional.
- loading curve
- Force–extension path while force increases.
- unloading curve
- Force–extension path while force decreases.
Recovery defines elastic behaviour
01Recovery defines elastic behaviour
A material behaves elastically if it returns to its original dimensions after the deforming force is removed. Elastic does not mean “easy to stretch”; steel can be stiff and elastic over a small strain.
plastic deformationWhen a material stays stretched or bent after the force is taken away. leaves a permanent extension because the internal structure has rearranged irreversibly.
02Two limits must not be confused
The limit of proportionalityThe point after which a spring stops stretching by the same amount for each extra weight. ends the straight-line F–x relationship. The elastic limitThe point after which a stretched object will not go back to its original shape. is the greatest force from which full recovery still occurs.
A material can pass the limit of proportionalityThe point after which a spring stops stretching by the same amount for each extra weight. and behave non-linearly while still returning to its original length.
03Loading and unloading reveal energy pathways
If unloading returns to zero extension, deformation was elastic. A non-zero intercept after unloading shows permanent extension.
Rubber can show different loading and unloading paths. The enclosed area represents energy dissipated as heating; it does not by itself prove plastic deformation if original length is recovered.
Interpret unloading evidence
A wire has extension 8 mm under load and still measures 1.5 mm longer after unloading.
- Compare final length with original length.
- A 1.5 mm residual extension remains.
- The deformation was not fully reversible.
- The elastic limitThe point after which a stretched object will not go back to its original shape. was exceeded during loading.
How to make the reasoning visible: Permanent extension is direct evidence of plastic deformation, even if some of the extension recovered.
Elastic-limit investigation
Compare recovery after increasing maximum force.
| Maximum force / N | Maximum extension / mm | Extension after unloading / mm | Interpretation |
|---|---|---|---|
| 2 | 3.0 | 0.0 | elastic |
| 4 | 6.1 | 0.0 | elastic |
| 6 | 9.8 | 0.0 | non-linear but elastic |
| 8 | 14.0 | 1.2 | plastic deformation |
| 10 | 18.5 | 3.6 | greater permanent extension |
Between which tested forces is the elastic limit?
Why is 6 N important even if the graph is non-linear?
Check your understanding
Answer from memory, then check against the suggested answer.
What is elastic deformation?
What is plastic deformation?
Which limit concerns straight-line proportionality?
Why test unloading when selecting a bungee material?
Why can a rubber band dissipate energy without permanent deformation?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
A spring is loaded and then unloaded. A force–extension graph is plotted.
Describe what the loading graph shows.
(2)Explain how the unloading data show elastic or plastic behaviour.
(3)Total for this question: 5 marks
Command word: For explainA command word: say how or why something happens, giving reasons with words like "because" or "so"., use graph evidence and keep proportionality separate from recovery.