AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
A force that stretches (or compresses) a spring does work and elastic…
Full specification wording
Forces and elasticity: A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring. Provided the spring is not inelastically deformed, the work done on the spring and the elastic potential energy stored are equal.
When a force stretches or compresses a spring, the force moves the spring's ends, so work is done.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 11 of 19
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When a force stretches or compresses a spring, the force moves the spring's ends, so work is done. That transferred energy is stored as elastic potential energy. For a spring obeying Hooke's law, the force grows steadily from zero to F, so the average force is F/2 and the work done is W = ½Fe, where e is the extension. Because energy is conserved, this work equals the elastic potential energy stored, Ee = ½ke², since F = ke. This equality holds only while the spring is not inelastically deformed: if the force exceeds the elastic limit, the spring is permanently stretched, some energy heats the material and is not recovered, so work done exceeds the elastic energy stored. Example: stretching a spring by 0.20 m with a final force of 10 N stores ½ × 10 × 0.20 = 1.0 J.
What earns the marks
- States that a stretching or compressing force does work because the point of application moves in the direction of the force.
- Explains that the work done on an elastically deformed spring is stored as elastic potential energy.
- Uses W = ½Fe or Ee = ½ke² correctly, recognising that the average force is half the final force for a linear spring.
- States that work done equals elastic potential energy stored only when the spring is not inelastically deformed.
- Explains that inelastic deformation beyond the elastic limit causes permanent extension and energy loss to the surroundings.
- Applies the relationship to a numerical example, keeping units of force in N, extension in m and energy in J.
Common mistakes and how to put them right
Using W = Fe instead of W = ½Fe.
Put it right: Use the average force, which is F/2 for a linear spring.
Assuming all work done is always stored elastically.
Put it right: State that beyond the elastic limit some energy is dissipated, so work done exceeds elastic potential energy stored.
Mixing extension units, for example using cm in ½ke².
Put it right: Convert all lengths to metres before calculating.
Exam tips
- Write the equation, substitute values with units, then give the answer with the correct unit, usually J.
- When asked to compare work done and energy stored, refer explicitly to whether the spring is elastically or inelastically deformed.
- Use a force–extension graph: the area under the straight-line region represents the work done and the elastic potential energy stored.
Try the lesson
The start of the Forces and elasticity: A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring. Provided the spring is not inelastically deformed, the work done on the spring and the elastic potential energy stored are equal. lesson, made from checked teaching notes for this specification point.
Have a go first
A student pulls a spring so that it stretches. The spring is not stretched too far and returns to its original length when released. What type of energy is stored in the stretched spring?
Listen
When a force stretches or compresses a spring, the force moves the spring's ends, so work is done. That transferred energy is stored as elastic potential energy. For a spring obeying Hooke's law, the force grows steadily from zero to F, so the average force is F/2 and the work done is W = ½Fe, where e is the extension. Because energy is conserved, this work equals the elastic potential energy stored, Ee = ½ke², since F = ke. This equality holds only while the spring is not inelastically deformed: if the force exceeds the elastic limit, the spring is permanently stretched, some energy heats the material and is not recovered, so work done exceeds the elastic energy stored. Example: stretching a spring by 0.20 m with a final force of 10 N stores ½ × 10 × 0.20 = 1.0 J. A strong answer earns marks for these points. States that a stretching or compressing force does work because the point of application moves in the direction of the force. Explains that the work done on an elastically deformed spring is stored as elastic potential energy. Uses W = ½Fe or Ee = ½ke² correctly, recognising that the average force is half the final force for a linear spring. States that work done equals elastic potential energy stored only when the spring is not inelastically deformed. A common slip: Using W = Fe instead of W = ½Fe: the error is treating the force as constant at its final value. Instead, use the average force, which is F/2 for a linear spring. Exam tip: Write the equation, substitute values with units, then give the answer with the correct unit, usually J.
Key words
Say what each word means before you turn the card.
Work done by a force
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Elastic potential energy
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Hooke's law and the elastic limit
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See every definition
- Work done by a force
- A stretching or compressing force does work because the point of application moves in the direction of the force.
- Elastic potential energy
- The work done on an elastically deformed spring is stored as this energy in the spring.
- Hooke's law and the elastic limit
- For a spring obeying Hooke's law the force grows steadily from zero to F, so the average force is F/2; beyond the elastic limit the spring is inelastically deformed and permanently stretched.
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