Hooke's Law (Cambridge (CIE) AS Physics)

Revision Note

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on

Hooke's law

  • A material demonstrating elastic behaviour obeys Hooke’s Law if its extension is directly proportional to the applied force (load)

  • The Force-extension graph of an object obeying Hooke's law is a straight line through the origin 

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

F space equals space k x

  • Where:

    • F is force applied in N

    • k is the spring constant in N m−1

    • x is the extension of the spring

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

  • k is defined as the force per unit extension up to the limit of proportionality

  • 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

k space equals space F over m

  • Therefore, the spring constant k is the gradient of the linear part of a force-extension graph

Gradient of force-extension graph

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

Spring constant is the gradient of a force vs extension graph

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 value of the spring constant.

Answer:

Step 1: Rearrange Hooke's Law:

  • Spring constant, k, is:

k space equals space F over x

Step 2: Relate the gradient of this graph to k :

  • The y axis of this graph is length L and the x axis is load F

  • Gradient is change in y over change in x:

gradient space equals space fraction numerator straight capital delta L over denominator straight capital delta F end fraction space equals space x over F

  • The change in length is the extension x

  • Therefore:

gradient space equals space 1 over k

Step 3: Determine the gradient of the graph:

  • Choose a large section of the graph line to determine the changes in the x and y axes

6-1-2-we-hookes-law-cie-new
  • Convert the extension from cm to m

gradient space equals space fraction numerator 0.145 space minus space 0.100 over denominator 0.36 end fraction space equals space 0.125 space straight m space straight N to the power of negative 1 end exponent

Step 4: Calculate the spring constant:

  • The spring constant is

k space equals space 1 over gradient space equals space fraction numerator 1 over denominator 0.125 end fraction space equals space 8.0 space straight N space straight m to the power of negative 1 end exponent

Examiner Tips and Tricks

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 spring constant is 1 over gradient and not the spring constant.

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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.

Caroline Carroll

Author: Caroline Carroll

Expertise: Physics Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.