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5.3.3Forces

Force–Extension Graphs — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions

5 min read 7 parts Lesson 15 of 44

📚 AQA GCSE Combined Science Trilogy 8464 - Physics Hub / Topical Revision
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Part 1 of 5Hooke's law

Statement
  • Statement Within the limit of proportionality, the extension of a spring is directly proportional to the force applied.
  • F = k × e, where F is force in N, e is extension in m and k is the spring constant in N/m.
Linear region
  • Linear region On a force–extension graph, Hooke's law is shown by a straight line through the origin.
Non-linear region
  • Non-linear region Beyond the limit of proportionality the graph curves, so force and extension are no longer proportional.

Part 2 of 5The spring constant

k = F ÷ e
Meaning
  • Meaning It is the force needed per metre of extension, in newtons per metre (N/m).
Stiffness
  • Stiffness A stiffer spring has a larger k, because it needs more force to extend by the same amount.
On the graph
  • On the graph k is the gradient of the straight part of a graph of force against extension.

Part 3 of 5Calculating k

1
A 0.6 kg mass hangs from a spring and produces an extension of 2 cm.
2
Find the force, which equals the weight: F = m × g = 0.6 × 9.8 = 5.88 N.
3
Convert the extension to metres: 2 cm = 0.02 m.
4
Rearrange F = k × e to give k = F ÷ e.
5
Substitute: k = 5.88 ÷ 0.02 = 294 N/m.

Part 4 of 5Reading the graph

Part of graphWhat it showsWhat to do
Straight line through originForce proportional to extensionCalculate k from the gradient
Point where the line starts to curveLimit of proportionalityDo not use F = k × e beyond it
Steeper lineLarger spring constantThe spring is stiffer
Curved regionNon-linear behaviourUse the graph values, not Hooke's law

Part 5 of 5Maths words that are often confused

1Linear
  • Linear A graph that is a straight line, whether or not it passes through the origin.
2Proportional
  • Proportional A straight line that passes through the origin.
3Non-linear
  • Non-linear A graph that is a curve, not a straight line.
4Gradient
  • Gradient Change in force divided by change in extension on the straight section gives k.

Key terms

TermMeaning
Hooke's lawThe extension of a spring is directly proportional to the force applied, up to the limit of proportionality.
Spring constantA measure of the stiffness of a spring: the force needed per unit extension.
ExtensionThe increase in length of a spring from its original length.
Limit of proportionalityThe point beyond which force and extension are no longer directly proportional.
GradientHow steep a line is, found by the change in y divided by the change in x.

Avoid these mistakes

1
Using the total length of the spring as the extension; extension is the increase over the original length.
2
Leaving the extension in centimetres when the spring constant is wanted in N/m.
3
Applying F = k × e to the curved part of the graph.
4
Describing a straight line as always proportional; it must also pass through the origin.

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