Calculate stress, strain and Young modulus
Use force per cross-sectional area, fractional extension and their ratio to compare a material's stiffness.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 6. The wire investigation is an original study guide and data-analysis practice, not a supervised laboratory activity or proof of practical competence. Full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use force, area, length, extension and graph gradient with consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is tensile strain?
What you will learn
- Define stress as tensile force per cross-sectional area
- Define strain as extension divided by original length
- Calculate Young modulus from stress divided by strain
Stress and strain describe deformation independent of specimen size
Tensile stress is force divided by original cross-sectional area: σ = F/A. It is measured in pascals (Pa). Use the area perpendicular to the tensile force and convert it to square metres.
Tensile strain is extension divided by original length: ε = x/L. Strain is a ratio and has no unit. A longer wire can extend more than a shorter one under the same stress while having the same strain.
Young modulus is stress divided by strain
Young modulus E = stress/strain = (F/A)/(x/L) = FL/(Ax). It describes the stiffness of a material in the linear elastic region. Its unit is Pa because strain is dimensionless.
Use the original dimensions in the formula. For a circular wire, cross-sectional area A = πd²/4. A small diameter measurement error can strongly affect area because diameter is squared, so measure carefully and repeat at several points in an actual experiment.
Pause and explain
Why is strain dimensionless?
Worked example
A wire of original length 2.0 m and area 1.0 × 10⁻⁶ m² extends 1.0 mm under a 100 N tensile force. Find stress, strain and Young modulus.
Show the worked solution
- Stress = 100/(1.0 × 10⁻⁶) = 1.0 × 10⁸ Pa.
- Strain = 0.0010/2.0 = 5.0 × 10⁻⁴.
- E = stress/strain = (1.0 × 10⁸)/(5.0 × 10⁻⁴).
Answer Stress 1.0 × 10⁸ Pa; strain 5.0 × 10⁻⁴; Young modulus 2.0 × 10¹¹ Pa.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A wire of area 2.0 × 10⁻⁶ m² carries a tensile force of 40 N. Calculate its stress.
Give me a hint
Divide force by cross-sectional area.
Compare my reasoning
- σ = F/A.
- σ = 40/(2.0 × 10⁻⁶).
- Give stress in Pa.
2.0 × 10⁷ Pa.
Look for these in your work
- Area used
- Division correct
- Pa unit included
A 1.5 m wire extends by 0.60 mm. Find its strain.
Give me a hint
Convert extension to metres, then divide by original length.
Compare my reasoning
- x = 0.60 mm = 6.0 × 10⁻⁴ m.
- ε = x/L = (6.0 × 10⁻⁴)/1.5.
- Strain is dimensionless.
4.0 × 10⁻⁴, with no unit.
Look for these in your work
- Extension converted
- Correct ratio formed
- No unit attached
A metal wire has stress 1.2 × 10⁸ Pa and strain 6.0 × 10⁻⁴ in the linear elastic region. Find its Young modulus and explain what the value describes.
Give me a hint
Divide stress by strain; since strain is dimensionless, the result has pressure units.
Compare my reasoning
- E = stress/strain.
- E = (1.2 × 10⁸)/(6.0 × 10⁻⁴) = 2.0 × 10¹¹ Pa.
- A higher Young modulus means less strain for the same stress in this region.
Young modulus = 2.0 × 10¹¹ Pa; it describes material stiffness in the linear elastic region.
Look for these in your work
- Ratio correct
- Value and unit calculated
- Material meaning explained
Common mistakes
- Using diameter as area
- Leaving extension or dimensions in mixed units
- Giving strain a unit
What can you explain now?
What is tensile strain?
Compare with the explanation
Extension divided by original length
It is a fractional length change.
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Make it stick
Why are stress and strain more useful than force and extension alone when comparing materials?
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