Plan a wire experiment for Young modulus
Describe how to measure a metal wire's dimensions and force-extension response, then obtain Young modulus from the data.
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
Why measure wire diameter at several positions?
What you will learn
- Describe an experiment to determine Young modulus of a metal wire
- Measure original length, diameter, force and extension with suitable controls
- Calculate Young modulus or obtain it from a force-extension graph
Measure geometry and stretch the wire in a controlled way
Clamp a long, straight metal wire vertically and measure its original length between fixed reference marks. Measure the diameter at several positions with a micrometer and use a mean to estimate cross-sectional area A = πd²/4.
Add known loads gradually and record the force and extension relative to the unloaded wire. Use a pointer and scale or a suitable extension instrument, avoid parallax, keep the wire straight, and do not exceed its elastic range. Repeat readings and record units.
Use measurements to determine Young modulus
For each load, calculate stress F/A and strain x/L, then E = stress/strain. Alternatively, plot force F against extension x in the straight-line region; the gradient is k, and E = kL/A.
Keep temperature and reference points consistent, add loads gently and safely, and consider wire heating or permanent deformation if loads are too large. A written method supports understanding but is not supervised practical performance.
Pause and explain
For a force-against-extension graph in its linear region, what does the gradient represent?
Worked example
A wire has L = 1.50 m, diameter 0.50 mm, and its force-extension graph has gradient 2.6 × 10⁴ N m⁻¹. Estimate Young modulus.
Show the worked solution
- Radius = 0.25 mm = 2.5 × 10⁻⁴ m; A = πr² ≈ 1.96 × 10⁻⁷ m².
- E = (gradient)L/A = (2.6 × 10⁴)(1.50)/(1.96 × 10⁻⁷).
- Report an estimate with a suitable significant figure count.
Answer E ≈ 2.0 × 10¹¹ Pa. The result is limited by measurement uncertainty, especially diameter.
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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.
List the main measurements and steps needed to estimate Young modulus for a metal wire.
Give me a hint
Include original length, cross-sectional area, applied force and resulting extension.
Compare my reasoning
- Measure the original length between fixed marks and the diameter at several points; calculate mean area A = πd²/4.
- Apply known loads gradually and measure extension from the same reference, repeating readings and staying in the elastic range.
- Calculate E = FL/(Ax), or use E = (gradient of F against x)L/A.
Measure L and several diameter readings, calculate A, record force and extension for gradual loads, then find E from FL/(Ax) or the linear F–x graph gradient multiplied by L/A.
Look for these in your work
- Geometry measured
- Controlled loading and extension described
- Young-modulus calculation specified
A wire is 2.0 m long with area 1.0 × 10⁻⁶ m². A 50 N load causes 0.50 mm extension. Calculate Young modulus.
Give me a hint
Convert extension to metres and use E = FL/(Ax).
Compare my reasoning
- x = 0.50 mm = 5.0 × 10⁻⁴ m.
- E = (50 × 2.0)/(1.0 × 10⁻⁶ × 5.0 × 10⁻⁴).
- Simplify the numerator and denominator.
E = 2.0 × 10¹¹ Pa.
Look for these in your work
- Extension converted
- Equation used correctly
- Pa unit given
A force-extension graph for a 1.0 m wire has a linear-region gradient of 2.0 × 10⁵ N m⁻¹ and cross-sectional area 1.0 × 10⁻⁶ m². Find Young modulus and name one major source of uncertainty.
Give me a hint
Use E = gradient × L/A and consider the squared-diameter area calculation.
Compare my reasoning
- E = (2.0 × 10⁵) × 1.0/(1.0 × 10⁻⁶).
- E = 2.0 × 10¹¹ Pa.
- A diameter uncertainty affects area because A is proportional to d².
E = 2.0 × 10¹¹ Pa. A major uncertainty can be the wire diameter: a small percentage error in d produces about twice that percentage error in calculated area.
Look for these in your work
- Graph gradient linked to k
- E calculated with units
- A realistic uncertainty source explained
Common mistakes
- Measuring only one diameter reading
- Using diameter instead of cross-sectional area
- Including non-linear graph data in a gradient estimate
What can you explain now?
Why measure wire diameter at several positions?
Compare with the explanation
To estimate a representative cross-sectional area and reduce measurement effects
The wire may vary slightly and diameter affects calculated area.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why does uncertainty in wire diameter have a larger effect on calculated area?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.