OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Describe the difference between linear and non-linear relationships…
Full specification wording
Forces in action: describe the difference between linear and non-linear relationships between force and extension
A linear force–extension relationship gives a straight-line graph through the origin: equal increases in force produce equal increases in extension, so the ratio of force to extension is constant.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 10 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A linear force–extension relationship gives a straight-line graph through the origin: equal increases in force produce equal increases in extension, so the ratio of force to extension is constant. A non-linear relationship gives a curved graph, so equal force steps produce unequal extension steps and the ratio changes as force rises. For a spring, the linear region holds below the elastic limit; beyond it the graph curves and the spring deforms permanently. Learners should distinguish the two by inspecting the shape of the graph, by testing whether the ratio stays constant, and by explaining what the curvature means physically rather than merely calling it 'not straight'.
What earns the marks
- Describes a linear relationship as a straight-line graph through the origin with a constant force-to-extension ratio.
- Describes a non-linear relationship as a curved graph in which the ratio of force to extension changes.
- Explains that equal force increases give equal extension increases only in the linear region.
- Links the onset of non-linearity in a spring to passing the elastic limit and permanent deformation.
- Tests linearity by checking whether force divided by extension stays constant across readings.
Common mistakes and how to put them right
Calls any graph with a positive gradient linear.
Put it right: Require a straight line through the origin.
Treats a curve as linear because it still rises.
Put it right: Identify the changing ratio instead.
Confuses non-linearity with a negative gradient.
Put it right: The two features are independent.
Ignores the origin when judging linearity.
Put it right: A straight line not through the origin is not proportional.
Exam tips
- Compare successive ratios of force to extension to test for linearity quickly.
- Describe the shape of the graph explicitly, using terms such as straight line through the origin or curve.
- Link any curvature to the elastic limit to gain the explanation mark.
Try the lesson
The start of the Forces in action: describe the difference between linear and non-linear relationships between force and extension lesson, made from checked teaching notes for this specification point.
Have a go first
A student plots force on the vertical axis against extension on the horizontal axis for a stretched spring. Which description matches a linear relationship between force and extension?
Listen
A linear force–extension relationship gives a straight-line graph through the origin: equal increases in force produce equal increases in extension, so the ratio of force to extension is constant. A non-linear relationship gives a curved graph, so equal force steps produce unequal extension steps and the ratio changes as force rises. For a spring, the linear region holds below the elastic limit; beyond it the graph curves and the spring deforms permanently. Learners should distinguish the two by inspecting the shape of the graph, by testing whether the ratio stays constant, and by explaining what the curvature means physically rather than merely calling it 'not straight'. A strong answer earns marks for these points. Describes a linear relationship as a straight-line graph through the origin with a constant force-to-extension ratio. Describes a non-linear relationship as a curved graph in which the ratio of force to extension changes. Explains that equal force increases give equal extension increases only in the linear region. Links the onset of non-linearity in a spring to passing the elastic limit and permanent deformation. Exam tip: Compare successive ratios of force to extension to test for linearity quickly.
See it
Key words
Say what each word means before you turn the card.
Linear versus non-linear graphs
Try answering aloud or in your head before turning the card.
Constant versus changing ratio
Try answering aloud or in your head before turning the card.
Elastic limit
Try answering aloud or in your head before turning the card.
Interpreting graph shape physically
Try answering aloud or in your head before turning the card.
See every definition
- Linear versus non-linear graphs
- A linear relationship gives a straight-line graph through the origin, while a non-linear relationship gives a curved graph.
- Constant versus changing ratio
- In a linear relationship the ratio of force to extension is constant, whereas in a non-linear relationship the ratio changes as force rises.
- Elastic limit
- The linear region holds below this point; beyond it the graph curves and the spring deforms permanently.
- Interpreting graph shape physically
- Explaining what the curvature means physically rather than merely calling it 'not straight'.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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