Lesson focus: In the initial linear region, spring extensionHow much longer a spring or elastic band gets when it is stretched. is proportionalWhen two quantities go up together at the same rate, so doubling one doubles the other. to applied force: F = kx.
Investigate force and extension, calculate spring constantA number that tells you how stiff a spring is: the force needed to stretch it by 1 metre. and evaluate data quality.
Build on earlier learning
Squashing and stretching: springsYear 7 explored springs. This lesson uses the force–extension graph quantitatively.
Practical
Hooke’s law
- Clamp a spring next to a ruler and record its original length.
- Add 100 g masses one at a time and record the new length.
- Calculate each extension and plot force against extension.
- Use the model on this page to find the spring constant.
Record: A force–extension graph and the spring constant from its gradient.
Safety: Wear eye protection.
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 extension.
- Use F = kx.
- Find k from a graph.
- Design a controlled spring test.
Words that carry the science
- extension
- Stretched length minus original length.
- Hooke’s law
- In the initial linear region, extension is proportional to force.
- spring constant
- Force per unit extension, k, measured in N m⁻¹.
- proportional
- Two quantities have a constant ratio and a straight-line graph through the origin.
- limit of proportionality
- The point beyond which force and extension are no longer proportional.
- repeatability
- Closeness of repeated results obtained by the same method and operator.
Extension is not total length
01Extension is not total length
Measure the unloaded original length, then calculate extension = loaded length − original length for each force. Convert centimetres to metres before using SI-form equations.
Add loads in safe increments, allow oscillations to settle and read the ruler at eye level from a fixed reference point.
02The linear region obeys Hooke’s law
In the initial straight-line region through the origin, F = kx. On a graph of force on the vertical axis against extensionHow much longer a spring or elastic band gets when it is stretched. on the horizontal axis, gradient equals k.
If axes are reversed, the gradient is 1/k. Always identify axes before interpreting a gradient.
03Evidence needs control variables and uncertainty
Use the same spring, add known forces, repeat measurements and avoid exceeding the safe load. A pointer and set square reduce parallax; repeats reveal random variation.
The limit of proportionalityThe point after which a spring stops stretching by the same amount for each extra weight. is estimated from where the best-fit trend ceases to be linear, not from one slightly scattered point.
Calculate spring constant
A force of 3.0 N produces an extension of 0.060 m in the linear region.
- Use F = kx.
- Rearrange: k = F ÷ x.
- Substitute: k = 3.0 ÷ 0.060.
- Calculate k = 50 N m⁻¹.
How to make the reasoning visible: A spring constantA number that tells you how stiff a spring is: the force needed to stretch it by 1 metre. of 50 N m⁻¹ means 50 N would be required per metre of extension within the proportionalWhen two quantities go up together at the same rate, so doubling one doubles the other. region.
Spring investigation
Analyse force–extension evidence from a spring loaded safely.
| Force / N | Length / cm | Extension / cm | F ÷ x / N m⁻¹ |
|---|---|---|---|
| 0 | 10.0 | 0.0 | — |
| 1 | 12.0 | 2.0 | 50 |
| 2 | 14.1 | 4.1 | 48.8 |
| 3 | 16.0 | 6.0 | 50 |
| 4 | 18.2 | 8.2 | 48.8 |
Graph skills: SLAPUK and choosing a scaleHooke’s law: a ruled line of best fit.
Estimate the spring constant.
Why record the unloaded length?
Check your understanding
Answer from memory, then check against the suggested answer.
Define extension.
State Hooke’s law equation.
What unit measures spring constant?
Why should a student not keep adding masses after obvious curvature appears?
Why can one anomalous point not locate the limit of proportionality securely?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
A student investigates how the extension of a spring varies with the force applied.
Describe how to set up the apparatus and take each reading.
(3)Describe how to process the readings and work safely.
(3)Total for this question: 6 marks
Command word: For describeA command word: say what happens or what something is like, step by step, without needing to give reasons., give a reproducible sequence including measurements, control variables, safety and processing.