CIE AS Physics (9702) exams from 2022

Revision Notes

6.1.2 Hooke's Law

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

Worked example - hooke's law (1), downloadable AS & A Level Physics revision notes

Worked example - hooke's law (2), downloadable AS & A Level Physics revision notes

Exam 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

Worked example - combination of springs (1), downloadable AS & A Level Physics revision notes

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

Exam 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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