Quick answer: Hooke's law says extension is proportional to force (F = kx) up to the limit of proportionality. This Physics 11-12 lab on Young modulus gives the aim, the equipment, the safety points, a step-by-step method, sample results and 8 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How stiff is a steel wire? Hang increasing loads on a long thin wire, measure each tiny extension and use the gradient of a force–extension graph, together with the wire dimensions, to calculate the Young modulus.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.4.2
Aim
To determine the Young modulus of a metal wire from a graph of load against extension.
Equipment
- Long thin steel wire (about 2.5 m), strong clamp at the top
- Mass hanger and slotted masses, 0.50 kg each
- Fixed scale (a vernier or travelling microscope reading to 0.01 mm) and a small marker on the wire
- Micrometer screw gauge and metre rule
Safety
Wear eye protection because a wire under tension may snap. Place a thick pad or sand tray under the masses, keep your feet clear and do not exceed 3.0 kg.
Method
- Measure the diameter of the wire in at least three places with the micrometer and find the mean.
- Measure the length L from the clamp to the marker with the metre rule.
- Hang the hanger and add a small preload to straighten the wire, then record the scale reading.
- Add 0.50 kg and record the new scale reading; calculate the extension.
- Continue up to 3.00 kg, then remove the masses in steps to check for a permanent extension.
- Plot force (y) against extension (x) and find the gradient.
Results
Wire length L = 2.50 m. Diameter readings: 0.50 mm, 0.51 mm, 0.49 mm (mean 0.50 mm). Extension readings:
| Mass / kg | Force F / N | Extension x / mm |
|---|---|---|
| 0.50 | 4.91 | 0.31 |
| 1.00 | 9.81 | 0.63 |
| 1.50 | 14.71 | 0.93 |
| 2.00 | 19.62 | 1.26 |
| 2.50 | 24.53 | 1.55 |
| 3.00 | 29.43 | 1.88 |
Analysis questions
Question 1 Area of the wire
Calculate the mean diameter and the cross-sectional area.Question 2 Forces
Check the force for 2.00 kg using F = mg with g = 9.81 N/kg, and explain why we plot force rather than mass.Question 3 Stress and strain at the largest load
Calculate the stress and strain at 3.00 kg.Question 4 Gradient
Plot F against x and find the gradient using the first and last points.Question 5 Young modulus
Use E = gradient × L ÷ A to find the Young modulus.Question 6 Uncertainty
The diameter is uncertain by ±0.01 mm. Calculate the percentage uncertainty in A and say what it does to E.Question 7 Stored energy
Calculate the elastic energy stored in the wire at 3.00 kg.Question 8 Improvements
Explain why a long, thin wire is used, and suggest one improvement.
