Young's Modulus
- The Young modulus is defined as
The measure of the ability of a material to withstand changes in length with an added load
- This gives information about the elasticity of a material ie. how stiff a material is
- The Young Modulus, E, can be calculated from the ratio of stress and strain
- Its unit is the same as stress: Pa (since strain is unitless)
- Just like the Force-Extension graph, stress and strain are directly proportional to one another for a material exhibiting elastic behaviour
A stress-strain graph is a straight line with its gradient equal to Young modulus
- The gradient of a stress-strain graph when it is linear is equal to the Young Modulus
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
Examiner 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’ ie. Stress ÷ strain.