AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Changes in energy: spring constant, k, in newtons per metre, N/m
The spring constant, k, is a measure of the stiffness of a spring or elastic object.
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The spring constant, k, is a measure of the stiffness of a spring or elastic object. It is defined as the force needed to extend or compress the object by one metre, and its unit is newtons per metre, N/m. A larger k means a stiffer spring that needs a greater force for the same extension. For a linear spring that obeys Hooke's law, force is directly proportional to extension, so F = k x, where F is in newtons, N, and x is the extension in metres, m. Rearranging gives k = F ÷ x. The spring constant also appears in the elastic potential energy equation E_e = ½ k x². In an experiment, a student hangs masses on a spring, records the extension for each force, and plots a force-extension graph; the gradient of the straight-line region equals k.
What earns the marks
- State that the spring constant k is measured in newtons per metre, N/m, and describes the stiffness of a spring.
- Use F = k x and rearrange to k = F ÷ x, substituting force in N and extension in m.
- Interpret a force-extension graph: the gradient of the linear region gives the spring constant.
- Explain that a larger k means a stiffer spring requiring a greater force for the same extension.
- Recognise that k is also used in E_e = ½ k x² to calculate stored elastic potential energy.
Common mistakes and how to put them right
Using the total length of the spring instead of the extension.
Put it right by subtracting the original length to find the extension.
Giving the unit as N/m² or N m.
Put it right by using N/m, since k is force per unit extension.
Reading the gradient of a force-extension graph as extension divided by force.
Put it right by dividing the change in force by the change in extension.
Exam tips
- Show the rearrangement k = F ÷ x clearly before substituting numbers.
- Check that extension is in metres and force is in newtons so the unit comes out as N/m.
- On a graph question, choose two points on the straight line and calculate gradient as change in y divided by change in x.
Try the lesson
The start of the Changes in energy: spring constant, k, in newtons per metre, N/m lesson, made from checked teaching notes for this specification point.
Have a go first
A spring has a spring constant of 50 N/m. What is the elastic potential energy stored when it is stretched by an extension of 0.20 m?
Listen
The spring constant, k, is a measure of the stiffness of a spring or elastic object. It is defined as the force needed to extend or compress the object by one metre, and its unit is newtons per metre, N/m. A larger k means a stiffer spring that needs a greater force for the same extension. For a linear spring that obeys Hooke's law, force is directly proportional to extension, so F = k x, where F is in newtons, N, and x is the extension in metres, m. Rearranging gives k = F ÷ x. The spring constant also appears in the elastic potential energy equation E_e = ½ k x². In an experiment, a student hangs masses on a spring, records the extension for each force, and plots a force-extension graph; the gradient of the straight-line region equals k. A strong answer earns marks for these points. State that the spring constant k is measured in newtons per metre, N/m, and describes the stiffness of a spring. Use F = k x and rearrange to k = F ÷ x, substituting force in N and extension in m. Interpret a force-extension graph: the gradient of the linear region gives the spring constant. Explain that a larger k means a stiffer spring requiring a greater force for the same extension. A common slip: Using the total length of the spring instead of the extension. Instead, subtracting the original length to find the extension. Exam tip: Show the rearrangement k = F ÷ x clearly before substituting numbers.
Key words
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spring constant, k
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Hooke's law
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force-extension graph
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elastic potential energy
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See every definition
- spring constant, k
- A measure of the stiffness of a spring or elastic object, measured in newtons per metre, N/m.
- Hooke's law
- For a linear spring, force is directly proportional to extension, so F = k x.
- force-extension graph
- A plot of force against extension whose gradient in the straight-line region equals k.
- elastic potential energy
- Energy stored in a spring, calculated using E_e = ½ k x².
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