AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
The extension of an elastic object, such as a spring, is directly…
Full specification wording
Forces and elasticity: The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
For an elastic object such as a spring, extension means the increase in length from its original length.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 4 of 19
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
For an elastic object such as a spring, extension means the increase in length from its original length. If the force applied is doubled, the extension doubles, provided the force stays below the limit of proportionality. This straight-line relationship is written as F = k × e, where F is the force in newtons, e is the extension in metres and k is the spring constant in newtons per metre. The spring constant measures stiffness: a stiffer spring has a larger k and stretches less for the same force. On a force-extension graph, the directly proportional region is a straight line through the origin. Beyond the limit of proportionality the line curves and the relationship is no longer directly proportional, so F = k × e cannot be used. A spring stretched past this limit may also show inelastic deformation.
What earns the marks
- Extension is the increase in length of the object from its original length, measured in metres.
- Directly proportional means extension is proportional to force, so doubling the force doubles the extension while the limit of proportionality is not exceeded.
- The relationship is written as F = k × e, where F is force in newtons, e is extension in metres and k is the spring constant in newtons per metre.
- On a force-extension graph, the proportional region is a straight line through the origin; the limit of proportionality is the point where the line starts to curve.
- The spring constant k is a measure of stiffness: a larger k means a stiffer spring and a smaller extension for the same force.
- Beyond the limit of proportionality the graph curves and the extension is no longer directly proportional to the force.
Common mistakes and how to put them right
Using the total length of the spring instead of the extension.
Put it right: Extension = current length − original length.
Treating the limit of proportionality as the same as the elastic limit.
Put it right: The limit of proportionality is where proportionality ends; the elastic limit is where elastic behaviour ends.
Forgetting to convert extension from centimetres to metres before using F = k × e.
Put it right: Convert cm to m by dividing by 100.
Exam tips
- Write the equation as F = k × e and rearrange it only after substituting known values, so units stay clear.
- On a graph question, identify the limit of proportionality as the point where the straight line through the origin begins to curve.
- Check that extension is in metres and force is in newtons before calculating the spring constant.
Try the lesson
The start of the Forces and elasticity: The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided that the limit of proportionality is not exceeded. lesson, made from checked teaching notes for this specification point.
Have a go first
A spring stretches by 4 cm when a 2 N force is applied to it. The limit of proportionality is not exceeded. What is the extension of the spring when a 6 N force is applied?
Listen
For an elastic object such as a spring, extension means the increase in length from its original length. If the force applied is doubled, the extension doubles, provided the force stays below the limit of proportionality. This straight-line relationship is written as F = k × e, where F is the force in newtons, e is the extension in metres and k is the spring constant in newtons per metre. The spring constant measures stiffness: a stiffer spring has a larger k and stretches less for the same force. On a force-extension graph, the directly proportional region is a straight line through the origin. Beyond the limit of proportionality the line curves and the relationship is no longer directly proportional, so F = k × e cannot be used. A spring stretched past this limit may also show inelastic deformation. A strong answer earns marks for these points. Extension is the increase in length of the object from its original length, measured in metres. Directly proportional means extension is proportional to force, so doubling the force doubles the extension while the limit of proportionality is not exceeded. The relationship is written as F = k × e, where F is force in newtons, e is extension in metres and k is the spring constant in newtons per metre. On a force-extension graph, the proportional region is a straight line through the origin; the limit of proportionality is the point where the line starts to curve. A common slip: Using the total length of the spring instead of the extension. Instead, extension = current length − original length. Exam tip: Write the equation as F = k × e and rearrange it only after substituting known values, so units stay clear.
See it
Key words
Say what each word means before you turn the card.
Extension
Try answering aloud or in your head before turning the card.
Directly proportional
Try answering aloud or in your head before turning the card.
Spring constant
Try answering aloud or in your head before turning the card.
Limit of proportionality
Try answering aloud or in your head before turning the card.
See every definition
- Extension
- The increase in length of an elastic object from its original length, measured in metres.
- Directly proportional
- Extension is proportional to force, so doubling the force doubles the extension while the limit of proportionality is not exceeded.
- Spring constant
- A measure of stiffness in newtons per metre, where a larger value means a stiffer spring and a smaller extension for the same force.
- Limit of proportionality
- The point on a force-extension graph where the straight line through the origin starts to curve, after which the relationship is no longer directly proportional.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Forces and elasticity: The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge