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Hooke's Law (CIE AS Physics)

Revision Note

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Katie M

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Hooke's Law

  • A material obeys Hooke’s Law if its extension is directly proportional to the applied force (load)
  • The Force v Extension graph is a straight line through the origin (see “Extension and Compression”)
  • This linear relationship is represented by the Hooke’s law equation

Hooke's law equation, downloadable AS & A Level Physics revision notes

Hooke’s Law

  • The constant of proportionality is known as 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

Examiner Tip

Double check the axes before finding the spring constant as the gradient of a force-extension graph. Exam questions often swap the load onto the x-axis and length on the y-axis. In this case, the gradient is not the spring constant but 1 ÷ gradient is.

The Spring Constant

  • k is the spring constant of the spring and is a measure of the stiffness of a spring
    • A stiffer spring will have a larger value of k

  • It is defined as the force per unit extension up to the limit of proportionality (after which the material will not obey Hooke’s law)
  • The SI unit for the spring constant is N m-1
  • Rearranging the Hooke’s law equation shows the equation for the spring constant is

Spring constant equation, downloadable AS & A Level Physics revision notes

Spring constant equation

  • The spring constant is the force per unit extension up to the limit of proportionality (after which the material will not obey Hooke’s law)
  • Therefore, the spring constant k is the gradient of the linear part of a Force v Extension graph

Spring constant on graph, downloadable AS & A Level Physics revision notes

Spring constant is the gradient of a force v extension graph

Combination of springs

  • Springs can be combined in different ways
    • In series (end-to-end)
    • In parallel (side-by-side)

Series and parallel springs, downloadable AS & A Level Physics revision notes

Spring constants for springs combined in series and parallel

  • This is assuming k1 and k2 are different spring constants
  • The equivalent spring constant for combined springs are summed up in different ways depending on whether they’re connected in parallel or series

Worked example

Three springs are arranged vertically as shown.Springs P,Q and O are identical and have spring constant k. Spring R has spring constant 4k.What is the increase in the overall length of the arrangement when a force W is applied as shown?

Worked example - combination of springs (2), downloadable AS & A Level Physics revision notes

Examiner Tip

The equivalent (or effective) spring constant equations for combined springs work for any number of springs e.g. if there are 3 springs in parallel k1 , k2 and k3 , the equivalent spring constant would be keq = k1 + k2 + k3 .

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.