AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Describe the difference between a linear and non-linear relationship…
Full specification wording
Forces and elasticity: describe the difference between a linear and non-linear relationship between force and extension
A force–extension graph shows force on the vertical axis and extension on the horizontal axis.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 12 of 19
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A force–extension graph shows force on the vertical axis and extension on the horizontal axis. A linear relationship is a straight line: equal increases in force produce equal increases in extension. If this straight line passes through the origin, force is directly proportional to extension, so the spring obeys Hooke's law, F = ke, and the gradient is the spring constant k. A non-linear relationship is a curved line: the gradient changes as extension increases. For a metal spring, the graph is linear up to the limit of proportionality, then curves. To describe the difference, state the shape, whether the line passes through the origin, whether the gradient is constant, and what that means for proportionality.
What earns the marks
- States that a linear force–extension graph is a straight line, which has a constant gradient.
- Explains that if a linear graph passes through the origin, force is directly proportional to extension (F = ke).
- States that a non-linear force–extension graph is curved, so the gradient changes as force or extension changes.
- Explains that in a non-linear relationship force is not directly proportional to extension.
- Identifies the limit of proportionality as the point where a metal spring's graph stops being linear.
- Uses the gradient of the linear region passing through the origin to find the spring constant, with units N/m.
Common mistakes and how to put them right
Conflating a linear relationship with direct proportionality.
Put it right: State that direct proportionality requires a straight line that passes through the origin.
Confusing the limit of proportionality with the elastic limit.
Put it right: State that the limit of proportionality is where the graph stops being linear, while the elastic limit is where permanent deformation begins.
Describing a curve as 'going up faster' without linking it to gradient or proportionality.
Put it right: State that the gradient increases or decreases and that force is not directly proportional to extension.
Exam tips
- Refer to both axes when describing a graph, for example 'force on the y-axis and extension on the x-axis'.
- Use the phrase 'directly proportional' only when the graph is a straight line through the origin.
- Quote gradient values with units, such as N/m, and show how you read coordinates from the graph.
Try the lesson
The start of the Forces and elasticity: describe the difference between a linear and non-linear relationship between force and extension lesson, made from checked teaching notes for this specification point.
Have a go first
A student investigates the extension of a spring. Which statement correctly describes a non-linear relationship between force and extension?
Listen
A force–extension graph shows force on the vertical axis and extension on the horizontal axis. A linear relationship is a straight line: equal increases in force produce equal increases in extension. If this straight line passes through the origin, force is directly proportional to extension, so the spring obeys Hooke's law, F = ke, and the gradient is the spring constant k. A non-linear relationship is a curved line: the gradient changes as extension increases. For a metal spring, the graph is linear up to the limit of proportionality, then curves. To describe the difference, state the shape, whether the line passes through the origin, whether the gradient is constant, and what that means for proportionality. A strong answer earns marks for these points. States that a linear force–extension graph is a straight line, which has a constant gradient. Explains that if a linear graph passes through the origin, force is directly proportional to extension (F = ke). States that a non-linear force–extension graph is curved, so the gradient changes as force or extension changes. Explains that in a non-linear relationship force is not directly proportional to extension. A common slip: Conflating a linear relationship with direct proportionality: the error is assuming any straight line means direct proportionality. Instead, state that direct proportionality requires a straight line that passes through the origin. Exam tip: Refer to both axes when describing a graph, for example 'force on the y-axis and extension on the x-axis'.
Key words
Say what each word means before you turn the card.
Hooke's law
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Force–extension graphs
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Limit of proportionality
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See every definition
- Hooke's law
- A spring obeys this when force is directly proportional to extension, so that F = ke.
- Force–extension graphs
- A graph with force on the vertical axis and extension on the horizontal axis, showing a linear or non-linear relationship.
- Limit of proportionality
- The point where a metal spring's graph stops being linear and begins to curve.
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