Physics · KS3 and GCSE · Interactive lesson
Springs, extension and Hooke’s law
Compare extra length with total length, change force and stiffness, and recognise where force and extension stop being proportional.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Measure extension as the extra length.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- A pulling force can stretch a spring.
- Extension is the extra length: stretched length minus unstretched length.
- In the proportional region, twice the force gives twice the extension for the same spring.
Useful starting points
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What do the words mean?
- Extension
- The increase from the original length, not the whole stretched length.
- Spring constant (k)
- A measure of stiffness: force needed per metre of extension, in N/m.
- Limit of proportionality
- The point beyond which force and extension stop being directly proportional.
- Elastic limit
- The limit beyond which an object will not fully return to its original shape after unloading. It is not the same definition as the limit of proportionality.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the same spring constant. Double the force. Does the extension double? Then compare springs at the same force.
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
A simplified spring stays within its proportional region for all forces in this example. The sketch shows extension rather than a measured drawing scale. Graph axes use fixed scales of 0–12 N and 0–0.6 m, so a stiffer spring gives a steeper line. Changing unstretched length changes the total length, but not F ÷ k. ≈ means approximately; keep full values until the final answer.
More about this diagram
Still picture. Play particle motion in Stage 2.
Extension = 10 cm
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- The unstretched length is 20 cm.
- The extra length is 10 cm.
- Stretched length = original length + extension = 30 cm.
- Subtract the original length from the stretched length to check the extension.
Try on your own
Your turn. No rush.
Question 1
A spring is 26 cm long before stretching and 41 cm long afterwards. Find its extension.
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
A good place to pause
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Can you tell extension from total length and explain what happens when the force doubles?
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
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