Determination of Young's Modulus (AQA A-Level Physics): Revision Notes

Method

1. Setup:

• Arrange the apparatus as shown in the diagram, with both the test wire and the reference wire attached to the beam.
• Measure the initial length $l$ of the test wire with the metre ruler.

2. Apply Initial Load:

• Attach a 1 kg mass to both wires to make them taut, and record the initial reading on the scale for the test wire.

3. Incremental Loading:

• Add an additional 1 kg mass to the test wire only. Record the new scale reading and calculate the extension $e$ by subtracting the initial reading.
• Repeat this process, adding 1 kg at a time up to around 8 kg, and measure the extension for each mass.

4. Repeat for Accuracy:

• Repeat the experiment twice more for each mass to find the mean extension $e$ for each applied load $m$.

5. Measure Diameter:

• Measure the diameter $d$ of the test wire at several points along its length using the micrometre. Take the mean value to calculate the cross-sectional area $A$.

Safety

• Wire Tension: The wire will be stretched tightly and could snap, which could injure eyes or other parts of the body. Wear safety goggles during the experiment.
• Falling Weights: If the wire breaks, the weights may fall. Place a sand tray beneath the masses to cushion any potential impact.

Key Concepts

• Young Modulus $E$: A measure of stiffness, calculated as the ratio of stress (force per unit area) to strain (extension per unit length).
• Stress and Strain Relationship: Under small deformations, Hooke's Law applies, meaning stress is proportional to strain, and the constant of proportionality is $E$.
• Graphical Analysis: The gradient of the force vs. extension graph provides a proportional relationship, allowing us to calculate $E$ for the material.