All subjects · Physics · WPH11 (Unit 1)

Core practical 3: determining the Young modulus

Core practical 3 measures the Young modulus of a material, usually a long thin metal wire. You need the method, the graph and the sources of uncertainty.

Method

Clamp a long wire (about 2 m or more) and pass it over a pulley, or hang it from a beam (Searle's apparatus uses a second, reference wire).
Fix a marker (or vernier) to the wire next to a metre rule.
Measure the original length x from the clamp to the marker with a metre rule or tape.
Measure the diameter with a micrometer at several places and in different directions; average and calculate A = πd²/4.
Add masses in equal steps, recording the extension each time; then remove them to check the wire returns (elastic behaviour).

Analysis

Plot force F (y-axis) against extension Δx (x-axis). In the straight section, gradient = F / Δx, and

E = (F / A) / (Δx / x) = gradient x x / A.

Alternatively plot stress against strain: the gradient is E directly.

Good practice and safety

A long, thin wire gives a larger extension, so the percentage uncertainty in Δx is smaller.
The reference wire in Searle's apparatus cancels effects of temperature change and support sagging.
Wear eye protection in case the wire snaps, and put a sand tray or soft surface under the masses.

Worked example

A wire has original length 2.50 m and diameter 0.40 mm. The gradient of its force-extension graph is 1.0 x 10⁴ N/m. Find E.

A = π(0.20 x 10^-3)² = 1.26 x 10^-7 m²
E = gradient x x / A = 1.0 x 10⁴ x 2.50 / 1.26 x 10^-7

Answer: E = 2.0 x 10¹¹ Pa

Key idea: Long thin wire; micrometer for diameter; F against Δx; E = gradient x original length / area.

Check yourself

Why is the diameter measured at several points and in different directions?
- Because the micrometer has a zero error
- To find the length of the wire
- To make the wire stretch evenly
- To allow for the wire not being perfectly uniform and to reduce random error
Show answer
To allow for the wire not being perfectly uniform and to reduce random error. Averaging several readings gives a better value for a wire that may vary along its length or not be perfectly round.
Why is a long, thin wire used?
- It has a larger Young modulus
- It gives a larger extension, reducing the percentage uncertainty
- It is less likely to break
- It makes the force larger
Show answer
It gives a larger extension, reducing the percentage uncertainty. Extensions are tiny; a longer, thinner wire stretches more for the same force.
A wire has a diameter of 0.38 mm. Find its cross-sectional area in mm², to 3 s.f.
Show answer
0.113 mm². A = π(0.19)² = 0.113 mm².
The gradient of a force-extension graph for a wire is 1.6 x 10⁴ N/m. The wire's original length is 2.00 m and its area is 1.6 x 10^-7 m². Find E in GPa.
Show answer
200 GPa. E = gradient x x / A = 1.6 x 10⁴ x 2.00 / 1.6 x 10^-7 = 2.0 x 10¹¹ Pa = 200 GPa.
In Searle's apparatus, what is the purpose of the second (reference) wire?
- To double the extension
- To measure the diameter
- To cancel out effects of temperature change and sagging of the support
- To carry half of the load
Show answer
To cancel out effects of temperature change and sagging of the support. Both wires expand and sag together, so only the extension due to the load is measured.
Why are readings also taken as the masses are removed?
- To check the wire has not gone past its elastic limit
- To measure the breaking stress
- To find the diameter
- To reduce the force on the clamp
Show answer
To check the wire has not gone past its elastic limit. If the wire returns to its original length, the deformation was elastic.
Which safety precaution is most important?
- Wear gloves to keep the wire clean
- Work in a darkened room
- Wear eye protection in case the wire snaps
- Keep the wire warm
Show answer
Wear eye protection in case the wire snaps. A snapping wire under tension can whip back towards the face.

Practise with instant feedback

Sources

Last updated 7 November 2026. Spotted a mistake? Tell us.