Determination of the Young modulus (CP2)
Determine the Young modulus of a metal by measuring the extension of a wire under increasing tensile load.
Apparatus
- Long metal wire (~2 m, e.g. steel or copper) clamped at the top
- Micrometer screw gauge
- Metre rule and vernier scale (or travelling microscope)
- Slotted masses and hanger
- G-clamp and pulley
Safety
- Wear safety goggles in case the wire snaps under overload.
- Place a cushion or tray below hanging masses.
Method
- Clamp the wire vertically. Attach a small initial load to straighten it and record the zero extension reading.
- Measure the unstretched length L of the wire with a metre rule.
- Measure the wire diameter d at three positions; calculate mean $A = \pi(d/2)^2$.
- Add masses in 100 g steps. After each addition, record the extension x from the vernier scale.
- Unload and confirm the wire returns to its original length (elastic behaviour). Plot stress vs strain; gradient $= E$.
Key Variables
Independent
Applied force F (stress $= F/A$)
Dependent
Extension x (strain $= x/L$)
Controlled
Temperature; Original wire length L; Wire cross-section A
Analysis and Results
- $E = \frac{\text{stress}}{\text{strain}} = \frac{FL}{Ax}$.
- Plot F vs x: gradient $= EA/L$, so $E = \text{gradient} \times L/A$.
- Plot stress vs strain for a cleaner determination of E directly from the gradient.
Common Errors
- Measuring diameter at only one position along the wire.
- Overloading past the elastic limit so the wire deforms plastically.
- Not accounting for the initial extension present before the first mass is added.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q14 marks
A copper wire of length 1.8 m and diameter 0.60 mm extends by 0.90 mm when a load of 15 N is applied. Calculate the Young modulus of copper.
Q22 marks
Explain why the wire should be unloaded after the experiment and the extension checked.