AQA A Level Physics

Revision Notes

4.7.2 Hooke's Law

Hooke's Law

  • When a force F is added to the bottom of a vertical metal wire of length L, the wire stretches
  • 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 = kΔL

  • Where:
    • F = force (N)
    • k = spring constant (N m–1)
    • ΔL = extension (m)

 

  • The spring constant 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

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 may start to curve slightly

Force Extension Graph, downloadable AS & A Level Physics revision notes

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

  • The key features of the graph are:
    • The limit of proportionality: The point beyond which Hooke’s law is no longer true when stretching a material i.e. the extension is no longer proportional to the applied force
      • The point is identified on the graph where the line starts to curve (flattens out)
    • Elastic limit: The maximum amount a material can be stretched and still return to its original length (above which the material will no longer be elastic). This point is always after the limit of proportionality
      • The gradient 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

What is the spring constant?

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

Exam Tip

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 ÷ gradient instead.

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