- Stress is the applied force per unit cross sectional area of a material
- Forces can be;
- Tensile forces, which pull on an object and extend it
- Compressive forces, which push onto an object and compress (or squash) it
- The equation for stress is the force per unit area, and so the units are N m−2, or Pascals, the same unit as pressure
- The ultimate tensile stress is the maximum force per original cross-sectional area a wire is able to support until it breaks
- Strain is the extension per unit length
Strain is the ratio of the extension (or compression) and the original length
- This is a deformation of a solid due to stress in the form of elongation or contraction
- Note that strain is a dimensionless unit because it’s the ratio of lengths
- The Young modulus (sometimes called Young's Modulus) is the measure of the ability of a material to withstand changes in length with an added load ie. how stiff a material is
- This gives information about the elasticity of a material
- The Young Modulus is defined as the ratio of stress and strain
Young Modulus equation
- 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-stress graph when it is linear is the Young Modulus
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.