Hooke's Law (DP IB Physics) : Revision Note

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Hooke's Law

  • When a force is applied to each end of a spring, it stretches

    • This phenomenon occurs for any material with elasticity, such as a wire or a bungee rope 

  • A material obeys Hooke’s Law if:

    The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality

  • This linear relationship is represented by the Hooke’s law equation:

F subscript straight H space equals space minus k x 

  • Where:

    • FH = elastic restoring force (N)

    • k = spring constant (N m–1)

    • x = extension (m)

  • The spring constant, k is a property of the material being stretched and measures the stiffness of a material

    • The larger the spring constant, the stiffer the material

  • Hooke's Law applies to both extensions and compressions:

    • The extension of an object is determined by how much it has increased in length

    • The compression of an object is determined by how much it has decreased in length

  • The extension x is the difference between the unstretched and stretched length 

extension = stretched length − unstretched length

Load extension and force, downloadable AS & A Level Physics revision notes

Stretching a spring with a load produces a force that leads to an extension

Force–Extension Graphs

  • The way a material responds to a given force can be shown on a force-extension graph

  • Every material will have a unique force-extension graph depending on how brittle or ductile it is

  • A material may obey Hooke's Law up to a point

    • This is shown on its force-extension graph by a straight line through the origin

  • As more force is added, the graph starts to curve slightly as Hooke's law no longer applies

1-2-8-force-extension-graph-ib-2025-physics

The Hooke's Law region of a force-extension graph is a straight line. The spring constant is the gradient of that region

  • The gradient of the linear portion of this graph is equal to the spring constant k

Worked Example

A spring was stretched with increasing load.

The graph of the results is shown below.

WE - hookes law question image, downloadable AS & A Level Physics revision notes

Determine the spring constant.

Answer:

Worked example hookes law - 2, downloadable AS & A Level Physics revision notes
Worked example hookes law - 3, downloadable AS & A Level Physics revision notes
Worked example hookes law - 4, downloadable AS & A Level Physics revision notes

Examiner Tips and Tricks

Always double check the axes before finding the spring constant as the gradient of a force-extension graph.

Exam questions often swap the force (or load) onto the x-axis and extension (or length) on the y-axis. In this case, the gradient is not the spring constant, it is 1 over k instead.

Make sure that you put the extension of the object into the equation for x and not just the length.

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Ashika

Author: Ashika

Expertise: Physics Content Creator

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.

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