# Stress, Strain & The Young Modulus(Edexcel International A Level Physics)

Expertise

Physics

## Stress & Strain

#### Stress

• 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

Stress equation

• The ultimate tensile stress is the maximum force per original cross-sectional area a wire is able to support until it breaks

#### Strain

• 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

Strain equation

## The Young Modulus

#### Young Modulus

• 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-strain graph when it is linear is 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

#### 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.

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