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
- Hang both wires from the same overhead support. Attach a small fixed load to the reference wire to keep it taut.
- Measure the unstretched length L of the test wire using a metre rule.
- Measure the diameter d of the test wire at three positions along its length using the micrometer; calculate mean cross-sectional area $A = \pi(d/2)^2$.
- Add masses to the test wire in 100 g increments. After each addition, read the extension x from the vernier scale.
- 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.
Q14 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.
Q23 marks
Explain why a reference wire is used alongside the test wire in this experiment.
Q32 marks
After removing all masses, the student notices the wire is longer than at the start. Explain what this indicates.