AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
That proportionality, for example between weight and mass of an object or…
Full specification wording
Key ideas: that proportionality, for example between weight and mass of an object or between force and extension in a spring, is an important aspect of many models in science
Proportionality means two quantities are linked by a constant multiplier, so doubling one doubles the other.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 25 of 26
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Proportionality means two quantities are linked by a constant multiplier, so doubling one doubles the other. Weight is proportional to mass: W = m × g, where g is about 9.8 N/kg on Earth, so a 2 kg mass weighs about 19.6 N and a 4 kg mass about 39.2 N. For a spring obeying Hooke's law, force is proportional to extension: F = k × e, so doubling the force doubles the extension, provided the limit of proportionality is not exceeded. A proportional relationship gives a straight-line graph through the origin, and the gradient equals the constant. This lets scientists predict values, calculate the constant from measurements, and test whether a model still holds; a graph that curves or misses the origin shows the simple proportional model has broken down.
What earns the marks
- Defines proportionality as a relationship in which one quantity is a constant multiple of another.
- Applies W = m × g to show weight is proportional to mass, using g ≈ 9.8 N/kg.
- Applies F = k × e to show force is proportional to extension for a spring within its limit of proportionality.
- Recognises that a proportional relationship gives a straight-line graph through the origin, with gradient equal to the constant.
- Uses proportionality to predict a new value, for example doubling mass doubles weight.
- Interprets a curved graph or a non-zero intercept as evidence that the proportional model no longer applies.
Common mistakes and how to put them right
Confusing mass and weight.
Put it right: Mass is measured in kg and weight in N, and weight equals mass multiplied by gravitational field strength.
Treating any straight-line graph as proportional.
Put it right: Proportionality requires the line to pass through the origin.
Assuming Hooke's law always applies to a spring.
Put it right: Force is proportional to extension only up to the limit of proportionality, beyond which the graph curves.
Exam tips
- State the equation you are using, such as W = m × g or F = k × e, before substituting values.
- Check whether a graph passes through the origin before calling the relationship proportional.
- Use the gradient of a straight-line graph through the origin to find the constant, with correct units.
Try the lesson
The start of the Key ideas: that proportionality, for example between weight and mass of an object or between force and extension in a spring, is an important aspect of many models in science lesson, made from checked teaching notes for this specification point.
Have a go first
A student hangs masses on a spring and records the extension each time. The results show that doubling the mass doubles the extension. What does this show about the extension and the mass?
Listen
Proportionality means two quantities are linked by a constant multiplier, so doubling one doubles the other. Weight is proportional to mass: W = m × g, where g is about 9.8 N/kg on Earth, so a 2 kg mass weighs about 19.6 N and a 4 kg mass about 39.2 N. For a spring obeying Hooke's law, force is proportional to extension: F = k × e, so doubling the force doubles the extension, provided the limit of proportionality is not exceeded. A proportional relationship gives a straight-line graph through the origin, and the gradient equals the constant. This lets scientists predict values, calculate the constant from measurements, and test whether a model still holds; a graph that curves or misses the origin shows the simple proportional model has broken down. A strong answer earns marks for these points. Defines proportionality as a relationship in which one quantity is a constant multiple of another. Applies W = m × g to show weight is proportional to mass, using g ≈ 9.8 N/kg. Applies F = k × e to show force is proportional to extension for a spring within its limit of proportionality. Recognises that a proportional relationship gives a straight-line graph through the origin, with gradient equal to the constant. A common slip: Confusing mass and weight. Instead, mass is measured in kg and weight in N, and weight equals mass multiplied by gravitational field strength. Exam tip: State the equation you are using, such as W = m × g or F = k × e, before substituting values.
Key words
Say what each word means before you turn the card.
Proportionality
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Limit of proportionality
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Gradient
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See every definition
- Proportionality
- A relationship in which one quantity is a constant multiple of another, so doubling one doubles the other.
- Limit of proportionality
- The point beyond which force is no longer proportional to extension, and the graph curves.
- Gradient
- For a straight-line graph through the origin, this equals the constant linking the two quantities.
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