Required Practicals / AQA / Practical 4
4 AS 3.4.2.1

Determination of the Young modulus

Determine the Young modulus of a metal wire by measuring extension under increasing load.

Apparatus

  • Two long wires (~2 m) of the same material clamped from the same support (reference wire and test wire)
  • Micrometer screw gauge
  • Vernier scale or metre rule with millimetre resolution
  • Slotted masses and hanger
  • G-clamp, pulley and stand

Safety

  • Wear safety goggles: the wire can snap under overload and cause injury.
  • Place a tray beneath the hanging masses in case they fall.

Method

  1. Hang both wires from the same overhead support. Attach a small fixed load to the reference wire to keep it taut.
  2. Measure the unstretched length L of the test wire using a metre rule.
  3. Measure the diameter d of the test wire at three positions along its length using the micrometer; calculate mean cross-sectional area $A = \pi(d/2)^2$.
  4. Add masses to the test wire in 100 g increments. After each addition, read the extension x from the vernier scale.
  5. Record load F and extension x for at least eight values; check for elastic behaviour by unloading and confirming the wire returns to its original length.

Key Variables

Independent Applied load F (hence stress $\sigma = F/A$)
Dependent Extension x (hence strain $\varepsilon = x/L$)
Controlled Original wire length L; Cross-sectional area A; Temperature (same throughout)

Analysis and Results

  • Young modulus $E = \sigma/\varepsilon = (F/A)/(x/L) = FL/(Ax)$.
  • Plot stress against strain: straight line through origin in the elastic region; gradient $= E$.
  • Alternatively, plot F against x; gradient $= EA/L$ so $E = \text{gradient} \times L/A$.
  • The use of a reference wire eliminates errors due to thermal expansion and support sag, both of which affect both wires equally.

Common Errors

  • Measuring diameter at only one point; the wire may not be uniform so several measurements should be averaged.
  • Overloading the wire past its elastic limit, so stress-strain is no longer linear.
  • Not accounting for the initial extension already present from the hanger's weight before measurements begin.
  • Bending in the clamp support: the reference wire method corrects for this.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 4 marks

A steel wire of length 2.0 m and diameter 0.50 mm extends by 1.4 mm under a load of 20 N. Calculate the Young modulus of steel.

Q2 3 marks

Explain why a reference wire is used alongside the test wire in this experiment.

Q3 2 marks

After removing all masses, the student notices the wire is longer than at the start. Explain what this indicates.