GCSE Physics Forces & Hooke's Law Notes
Hooke's law says the extension of a spring is proportional to the force applied — up to a limit. Learn the equation and the graph and springs become easy marks.
Key concepts
- Hooke's law
- The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
- Spring constant (k)
- How stiff a spring is, measured in N/m. A larger k means a stiffer spring that extends less for the same force.
- Limit of proportionality
- The point beyond which extension is no longer proportional to force — the force–extension graph starts to curve.
- Extension is measured from the spring's natural (unstretched) length.
- On a force–extension graph the straight-line region obeys Hooke's law; the gradient relates to the spring constant.
- Elastic deformation returns to shape; inelastic (plastic) deformation is permanent.
Key formulas
Hooke's law
F = k × e
force (N) = spring constant (N/m) × extension (m).
Required practicals
- Investigate how the extension of a spring varies with the force applied and identify the limit of proportionality.
Worked example
A spring with a spring constant of 25 N/m is stretched by a force of 5 N. Find the extension.
- 1Write the equation: F = k × e.
- 2Rearrange for e: e = F ÷ k.
- 3Substitute: e = 5 ÷ 25.
- 4Calculate: e = 0.2 m (20 cm).
Answer: e = 0.2 m
Common mistakes
✗ Using the total length instead of the extension.
✓ Extension = stretched length − original length.
✗ Applying Hooke's law beyond the limit of proportionality.
✓ The equation only holds while the graph is a straight line.
✗ Leaving extension in cm when the spring constant uses metres.
✓ Convert cm to m before substituting.
Quick check
Try these, then reveal the answers.
What are the units of the spring constant?Reveal answer
Newtons per metre (N/m).
A 10 N force extends a spring 0.5 m. Find k.Reveal answer
k = F ÷ e = 10 ÷ 0.5 = 20 N/m
What does the limit of proportionality mark on the graph?Reveal answer
Where the line stops being straight and Hooke's law no longer applies.
Exam tips
- Always measure extension from the unstretched length.
- For the required practical, plot force (y) against extension (x) and identify where the line curves.
- Convert all lengths to metres before using F = ke.
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Frequently asked questions
What is the spring constant?+
The spring constant k measures stiffness in newtons per metre — a bigger k means the spring needs more force to produce the same extension.
What happens beyond the limit of proportionality?+
Extension is no longer proportional to force, the force–extension graph curves, and the spring may not return to its original shape.
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