- 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
- 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
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
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 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
A stress-strain graph is a straight line with its gradient equal to the Young modulus
The graph below shows the stress-strain graph for a copper wire.
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
Step 2: Calculate the gradient of the graph in this region