AQA A Level Physics

Revision Notes

4.8.1 The Young Modulus

The Young Modulus

  • The Young modulus is the measure of the ability of a material to withstand changes in length with an added load
    • This gives information about the stiffness of a material
    • This is useful for engineers to make sure the materials they are using can withstand sufficient forces
  • The Young Modulus is defined as the ratio of tensile stress and tensile strain

Young Modulus Equation

  • Where:
    • F = force (N)
    • L = original length (m)
    • A = cross-sectional area (m2)
    • ΔL = extension (m)

 

  • Since strain is dimensionless, the units of the Young Modulus is pascals (Pa)
  • The Young Modulus of a material is typically a very large number, in the order of GPa

Table of the Young’s Modulus for Materials

Table of Young’s Modulus for Materials, downloadable AS & A Level Physics revision notes

Worked Example

A metal wire that is supported vertically from a fixed point has a load of 92 N applied to the lower end.
The wire has a cross-sectional area of 0.04 mm2 and obeys Hooke’s law.
The length of the wire increases by 0.50%.

What is the Young modulus of the metal wire?

A.    4.6 × 107Pa              B.    4.6 × 1012 Pa              C.    4.6 × 109 Pa               D.    4.6 × 1011 Pa

WE - Young modulus answer image, downloadable AS & A Level Physics revision notes

Exam Tip

To remember whether stress or strain comes first in the Young modulus equation, try thinking of the phrase ‘When you’re stressed, you show the strain’ i.e. Stress ÷ Strain.

The Young Modulus from Stress-Strain Graphs

  • The Young Modulus is equal to the gradient of a stress-strain graph when it is linear (a straight line)
    • This is the region in which Hooke’s Law is obeyed
  • The area under the graph in this region is equal to the energy stored per unit volume of the material

YM on Stress-Strain Graph, downloadable AS & A Level Physics revision notes

A stress-strain graph is a straight line with its gradient equal to the Young modulus

Worked Example

The graph below shows the stress-strain graph for a copper wire.

Stress-Strain Worked Example, downloadable AS & A Level Physics revision notes

Use the graph to calculate the Young Modulus of copper.

Step 1: Determine the stress and strain where the linear region ends

    The Young Modulus is the gradient of the linear region of a stress-strain graph

Stress-Strain Worked Example Solution

Step 2: Calculate the gradient of the graph in this region

Stress-Strain Worked Example Final Answer

 

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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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