OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Springs: (i) force–extension (or compression) graphs for springs and wires
A force–extension graph plots applied force F on the y-axis against extension x on the x-axis.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A force–extension graph plots applied force F on the y-axis against extension x on the x-axis. For a spring or wire obeying Hooke's law, the initial region is a straight line through the origin; its gradient equals the force constant k, since F = kx. The straight region ends at the limit of proportionality. Beyond it the line curves, and eventually the elastic limit is passed so the material no longer returns to its original length. For a wire, the same shape appears but the gradient is much steeper because a wire is stiffer. Compression graphs for springs show the same linear behaviour for small compressions. The area under the graph represents the work done in stretching the spring.
What earns the marks
- Plots force on the y-axis and extension (or compression) on the x-axis.
- Identifies the straight-line region through the origin as Hooke's law behaviour.
- Relates the gradient of the linear region to the force constant k.
- Describes the curve beyond the limit of proportionality and the loss of elastic behaviour.
Common mistakes and how to put them right
Plotting total length on the x-axis instead of extension.
Put it right: Plot the change in length so the line passes through the origin.
Reading the gradient as the reciprocal of k.
Put it right: Gradient = k because F = kx.
Assuming the graph stays straight for all forces.
Put it right: It curves beyond the limit of proportionality.
Exam tips
- Label both axes with quantity and unit before plotting any points.
- Draw a straight line of best fit through the origin for the linear region and read the gradient from it.
- State clearly where the straight region ends when describing the graph.
Try the lesson
The start of the Springs: (i) force–extension (or compression) graphs for springs and wires lesson, made from checked teaching notes for this specification point.
Listen
A force–extension graph plots applied force F on the y-axis against extension x on the x-axis. For a spring or wire obeying Hooke's law, the initial region is a straight line through the origin; its gradient equals the force constant k, since F = kx. The straight region ends at the limit of proportionality. Beyond it the line curves, and eventually the elastic limit is passed so the material no longer returns to its original length. For a wire, the same shape appears but the gradient is much steeper because a wire is stiffer. Compression graphs for springs show the same linear behaviour for small compressions. The area under the graph represents the work done in stretching the spring. A strong answer earns marks for these points. Plots force on the y-axis and extension (or compression) on the x-axis. Identifies the straight-line region through the origin as Hooke's law behaviour. Relates the gradient of the linear region to the force constant k. Describes the curve beyond the limit of proportionality and the loss of elastic behaviour. A common slip: Plotting total length on the x-axis instead of extension. Instead, plot the change in length so the line passes through the origin. Exam tip: Label both axes with quantity and unit before plotting any points.
Key words
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Force–extension graphs
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Hooke's law
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Gradient and force constant
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Elastic limit
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See every definition
- Force–extension graphs
- A graph that plots applied force F on the y-axis against extension x on the x-axis for springs and wires.
- Hooke's law
- Behaviour shown by the initial straight-line region through the origin of a force–extension graph, where F = kx.
- Gradient and force constant
- The gradient of the linear region equals the force constant k, since F = kx.
- Elastic limit
- The point beyond which the material no longer returns to its original length.
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