AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Changes in energy: extension, e, in metres, m
Extension, e, is the increase in length of a spring or elastic object when a force stretches it, measured in metres (m).
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Extension, e, is the increase in length of a spring or elastic object when a force stretches it, measured in metres (m). It is not the total stretched length: if a spring hangs at 12 cm and stretches to 20 cm, the extension is 8 cm, which must be converted to 0.08 m before substitution. Extension is a change in length, so it is found by subtracting the original length from the stretched length. In elasticity calculations, e is squared in the equation for elastic potential energy, Ee = ½ke², so the unit must be metres. A metre rule or tape measure can measure lengths, and the difference gives e. Extension increases linearly with force up to the limit of proportionality.
What earns the marks
- State that extension is the increase in length of a spring or elastic object when a stretching force is applied.
- Give the unit of extension as metres, symbol m, and convert centimetre measurements by dividing by 100.
- Calculate extension by subtracting the original length from the stretched length, for example 20 cm − 12 cm = 8 cm = 0.08 m.
- Explain that extension is not the same as the total stretched length of the spring.
- Use extension in the elastic potential energy equation Ee = ½ke², ensuring e is in metres before squaring.
- Describe how to measure extension in a practical using a ruler and a known mass or force.
Common mistakes and how to put them right
Using the total stretched length as the extension.
Put it right by subtracting the original length first.
Substituting centimetres directly into Ee = ½ke².
Put it right by converting to metres, for example 8 cm = 0.08 m.
Forgetting to square the extension in Ee = ½ke².
Put it right by writing e² explicitly before multiplying by ½k.
Exam tips
- Underline the words original length and stretched length in the question before calculating extension.
- Show the subtraction and the unit conversion as separate steps so the examiner can award method marks.
- Check that your final extension is smaller than the stretched length; if it is larger, you have subtracted the wrong way round.
Try the lesson
The start of the Changes in energy: extension, e, in metres, m lesson, made from checked teaching notes for this specification point.
Have a go first
A spring has a natural length of 0.20 m. It is stretched until its total length is 0.32 m. Calculate the extension, e, of the spring in metres.
Listen
Extension, e, is the increase in length of a spring or elastic object when a force stretches it, measured in metres (m). It is not the total stretched length: if a spring hangs at 12 cm and stretches to 20 cm, the extension is 8 cm, which must be converted to 0.08 m before substitution. Extension is a change in length, so it is found by subtracting the original length from the stretched length. In elasticity calculations, e is squared in the equation for elastic potential energy, Ee = ½ke², so the unit must be metres. A metre rule or tape measure can measure lengths, and the difference gives e. Extension increases linearly with force up to the limit of proportionality. A strong answer earns marks for these points. State that extension is the increase in length of a spring or elastic object when a stretching force is applied. Give the unit of extension as metres, symbol m, and convert centimetre measurements by dividing by 100. Calculate extension by subtracting the original length from the stretched length, for example 20 cm − 12 cm = 8 cm = 0.08 m. Explain that extension is not the same as the total stretched length of the spring. A common slip: Using the total stretched length as the extension. Instead, subtracting the original length first. Exam tip: Underline the words original length and stretched length in the question before calculating extension.
Key words
Say what each word means before you turn the card.
Extension
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Metres
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Elastic potential energy equation
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Limit of proportionality
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See every definition
- Extension
- The increase in length of a spring or elastic object when a force stretches it, measured in metres (m).
- Metres
- The unit of extension, symbol m, with centimetre measurements converted by dividing by 100.
- Elastic potential energy equation
- Ee = ½ke², in which e is squared, so the unit must be metres before substitution.
- Limit of proportionality
- The point up to which extension increases linearly with force.
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