How is the Young modulus defined in terms of stress and strain?

The Young modulus is defined as tensile stress divided by tensile strain.

State the formula for the Young modulus, defining each symbol used.

E = FL/(AΔL), where E is the Young modulus, F is the applied force, L is the original length, A is the cross-sectional area, and ΔL is the extension.

Write the equation for tensile stress and identify each quantity in the formula.

σ = F/A, where σ is tensile stress, F is the applied force, and A is the cross-sectional area.

Calculate the tensile stress when force = 373 N, cross-sectional area = 0.000443 m².

Tensile stress = 373 ÷ 0.000443 = 8.42 × 10⁵ Pa.

Calculate the tensile strain when extension = 0.0075 m, original length = 1.8 m.

Tensile strain = 0.0075 ÷ 1.8 = 0.00417.

How can the Young modulus be obtained from a stress-strain graph?

The Young modulus equals the gradient of the linear (elastic) region of the stress-strain graph.

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Mechanics and Materials

The Young modulus

4 things to know
Papers 1 and 3

Overview

Defining the modulus, reading it from a graph, and the wire-stretching experiment.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

How is the Young modulus defined, and how is it read from a stress-strain graph?

Numbers

What does the linear region of the graph represent, and what is plotted to find the modulus?

Numbers

What are the units of the Young modulus and of stress, and why is strain dimensionless?

Evaluation

How is the diameter of a wire measured, and how is its area found?

Questions from this subtopic

Each one with the model answer underneath.

1
How is the Young modulus defined in terms of stress and strain?
Model answer
The Young modulus is defined as tensile stress divided by tensile strain.
2
State the formula for the Young modulus, defining each symbol used.
Model answer
E = FL/(AΔL), where E is the Young modulus, F is the applied force, L is the original length, A is the cross-sectional area, and ΔL is the extension.
3
Write the equation for tensile stress and identify each quantity in the formula.
Model answer
σ = F/A, where σ is tensile stress, F is the applied force, and A is the cross-sectional area.
4
Calculate the tensile stress when force = 373 N, cross-sectional area = 0.000443 m².
Model answer
Tensile stress = 373 ÷ 0.000443 = 8.42 × 10⁵ Pa.
5
Calculate the tensile strain when extension = 0.0075 m, original length = 1.8 m.
Model answer
Tensile strain = 0.0075 ÷ 1.8 = 0.00417.
6
How can the Young modulus be obtained from a stress-strain graph?
Model answer
The Young modulus equals the gradient of the linear (elastic) region of the stress-strain graph.

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