Forces and Elasticity (Hooke's Law)
Learn Forces and Elasticity (Hooke's Law) for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Hooke's law states that extension is proportional to force, F = ke, up to the limit of proportionality.
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Topic overview
To change the shape of a stationary object, more than one force has to be applied. A single force would simply make the object move.
An object may be deformed elastically or inelastically. Elastic deformation means the object returns to its original shape when the forces are removed. Inelastic deformation means it does not.
Hooke's law states that the extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded. The equation is force = spring constant × extension. A stiffer spring has a larger spring constant, so a greater force is needed for the same extension.
Revision notes
Changing shape
More than one force must be applied to change the shape of a stationary object.
A single force would cause the object to move rather than deform. The forces may stretch, compress or bend the object.
Elastic and inelastic deformation
Elastic deformation: the object returns to its original shape when the forces are removed.
Inelastic deformation: the object does not return to its original shape. A spring stretched beyond its limit is inelastically deformed.
Hooke's law
Force = spring constant × extension, F = ke.
Force in newtons, spring constant in N/m, extension in metres. Extension is directly proportional to force up to the limit of proportionality. A stiffer spring has a larger spring constant.
Key points
- More than one force is needed to change shape.
- Elastic deformation returns to the original shape.
- Inelastic deformation does not.
- Force = spring constant × extension.
- Extension is proportional to force up to the limit.
- A stiffer spring has a larger spring constant.
Worked examples
Example 1
A spring has a spring constant of 25 N/m and is extended by 0.4 m. Calculate the force applied. [2 marks]
Model answer
Force = spring constant × extension = 25 × 0.4 (1 mark) = 10 N (1 mark).
Example 2
Explain the difference between elastic and inelastic deformation. [2 marks]
Model answer
In elastic deformation the object returns to its original shape once the forces are removed (1 mark). In inelastic deformation it does not return to its original shape (1 mark).
Example 3
Explain why more than one force is needed to stretch a spring. [2 marks]
Model answer
A single force acting on the spring would simply make it move (1 mark). Two forces acting in opposite directions are needed to change its shape rather than its position (1 mark).
Common mistakes
Using the total length instead of the extension.
Extension is the increase in length from the natural length.
Saying one force can deform an object.
More than one force is needed, otherwise the object just moves.
Applying Hooke's law beyond the limit of proportionality.
The relationship only holds up to that limit.
Confusing elastic and inelastic.
Elastic returns to the original shape; inelastic does not.
Exam tips
- Work out the extension before using the equation.
- State the limit of proportionality condition.
- Explain why two forces are needed to deform.
- Use N/m as the unit for spring constant.
Key terms
- Hooke's law
- Extension is proportional to force up to the limit of proportionality.
- Elastic deformation
- Deformation from which an object recovers.
- Inelastic deformation
- Deformation from which an object does not recover.
- Spring constant
- The stiffness of a spring, in newtons per metre.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.