AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
F orce = spring constant × extension F = k e force, F, in newtons, N…
Full specification wording
Forces and elasticity: f orce = spring constant × extension F = k e force, F, in newtons, N spring constant, k, in newtons per metre, N/m extension, e, in metres, m This relationship also applies to the compression of an elastic object, where ‘e’ would be the compression of the object.
This equation links the force applied to a spring, the spring constant in newtons per metre and the extension in metres.
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 3 of 7
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
This equation links the force applied to a spring, the spring constant in newtons per metre and the extension in metres. The spring constant is a property of that particular spring: a large value means a stiff spring that extends very little. Rearranged, k = F/e and e = F/k. A 3.0 N load on a spring of 25 N/m gives e = 3.0/25 = 0.12 m. Almost every lost mark here is a unit. Extensions are usually measured in centimetres or millimetres and must be converted to metres first, and a mass in grams has to be turned into a weight in newtons before it can be used as the force. The same relationship covers compression, where e is how much shorter the spring has become, which is why car suspension springs and bathroom scales obey it too.
What earns the marks
- The equation force = spring constant × extension, or a correct rearrangement.
- Converting the extension to metres, and a mass to a weight in newtons where needed.
- The answer with its unit, N/m for a spring constant or m for an extension.
Common mistakes and how to put them right
Substituting the total length of the spring instead of its extension.
Leaving the extension in centimetres, so the spring constant comes out a hundred times too small.
Using a mass in kilograms as the force instead of its weight in newtons.
Assuming the equation fails for compression, when e is simply the compression.
Exam tips
- Underline whether the question has given you a length or an extension before substituting.
- If the question gives a mass, convert it to a weight first; the value of g is printed on the paper.
Try the lesson
The start of the Forces and elasticity: f orce = spring constant × extension F = k e force, F, in newtons, N spring constant, k, in newtons per metre, N/m extension, e, in metres, m This relationship also applies to the compression of an elastic object, where ‘e’ would be the compression of the object. 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 force is needed to extend the spring by 0.2 m, below its limit of proportionality?
Listen
This equation links the force applied to a spring, the spring constant in newtons per metre and the extension in metres. The spring constant is a property of that particular spring: a large value means a stiff spring that extends very little. Rearranged, k = F/e and e = F/k. A 3.0 N load on a spring of 25 N/m gives e = 3.0/25 = 0.12 m. Almost every lost mark here is a unit. Extensions are usually measured in centimetres or millimetres and must be converted to metres first, and a mass in grams has to be turned into a weight in newtons before it can be used as the force. The same relationship covers compression, where e is how much shorter the spring has become, which is why car suspension springs and bathroom scales obey it too. A strong answer earns marks for these points. the equation force = spring constant × extension, or a correct rearrangement. converting the extension to metres, and a mass to a weight in newtons where needed. the correct substitution. the answer with its unit, N/m for a spring constant or m for an extension. Exam tip: Underline whether the question has given you a length or an extension before substituting.
Key words
Say what each word means before you turn the card.
spring constant
Try answering aloud or in your head before turning the card.
extension and compression
Try answering aloud or in your head before turning the card.
weight from mass
Try answering aloud or in your head before turning the card.
See every definition
- spring constant
- A property of that particular spring, measured in newtons per metre, where a large value means a stiff spring that extends very little.
- extension and compression
- The amount by which an elastic object gets longer, or how much shorter it has become, measured in metres and given the symbol e.
- weight from mass
- A mass in kilograms must not be used as the force; it has to be turned into its weight in newtons first.
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Test your understanding of Forces and elasticity: f orce = spring constant × extension F = k e force, F, in newtons, N spring constant, k, in newtons per metre, N/m extension, e, in metres, m This relationship also applies to the compression of an elastic object, where ‘e’ would be the compression of the object.
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