OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Springs: (c) force constant k of a spring or wire; F = kx
The force constant k measures stiffness: the force needed per unit extension.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The force constant k measures stiffness: the force needed per unit extension. For a spring or wire obeying Hooke's law, F = kx, where F is the applied force in newtons, x is the extension (or compression) in metres and k is in N m⁻¹. A stiff spring has a large k, so a given force produces only a small extension. Example: a spring with k = 200 N m⁻¹ extends 0.05 m under F = kx = 200 × 0.05 = 10 N. Rearranged, k = F ÷ x. The relationship is linear only up to the limit of proportionality; beyond it the graph curves and F = kx no longer holds. Extension is the change in length, not the total length, so always subtract the original length.
What earns the marks
- States that k is the force per unit extension and has units N m⁻¹.
- Applies F = kx correctly, including rearrangement to k = F ÷ x or x = F ÷ k.
- Uses extension (change in length), not total length, in the calculation.
- Recognises that F = kx applies only within the limit of proportionality for the spring or wire.
Common mistakes and how to put them right
Using the total length of the spring instead of the extension.
Put it right: Subtract the original length to find x.
Treating k as a force rather than force per unit extension.
Put it right: Quote k in N m⁻¹ and remember it describes stiffness.
Assuming F = kx holds for any force.
Put it right: The linear relationship fails beyond the limit of proportionality.
Exam tips
- Write the equation, substitute values with units, then rearrange only after listing known quantities.
- Check that x is in metres before dividing; convert centimetres by dividing by 100.
- Sanity-check the size of k: a very small k means a very stretchy spring.
Try the lesson
The start of the Springs: (c) force constant k of a spring or wire; F = kx lesson, made from checked teaching notes for this specification point.
Listen
The force constant k measures stiffness: the force needed per unit extension. For a spring or wire obeying Hooke's law, F = kx, where F is the applied force in newtons, x is the extension (or compression) in metres and k is in N m⁻¹. A stiff spring has a large k, so a given force produces only a small extension. Example: a spring with k = 200 N m⁻¹ extends 0.05 m under F = kx = 200 × 0.05 = 10 N. Rearranged, k = F ÷ x. The relationship is linear only up to the limit of proportionality; beyond it the graph curves and F = kx no longer holds. Extension is the change in length, not the total length, so always subtract the original length. A strong answer earns marks for these points. States that k is the force per unit extension and has units N m⁻¹. Applies F = kx correctly, including rearrangement to k = F ÷ x or x = F ÷ k. Uses extension (change in length), not total length, in the calculation. Recognises that F = kx applies only within the limit of proportionality for the spring or wire. A common slip: Using the total length of the spring instead of the extension. Instead, subtract the original length to find x. Exam tip: Write the equation, substitute values with units, then rearrange only after listing known quantities.
See it
Key words
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Force constant
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Hooke's law
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Extension
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Limit of proportionality
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See every definition
- Force constant
- The force constant k measures stiffness: the force needed per unit extension, in N m⁻¹.
- Hooke's law
- For a spring or wire obeying this law, F = kx, where F is the applied force in newtons and x is the extension in metres.
- Extension
- The change in length, not the total length, so always subtract the original length.
- Limit of proportionality
- The relationship is linear only up to this point; beyond it the graph curves and F = kx no longer holds.
Label the diagram
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