In an experiment to measure the Young modulus of a metal, a wire of the metal of diameter 0.25 mm is clamped, as shown.

Question 5

In an experiment to measure the Young modulus of a metal, a wire of the metal of diameter 0.25 mm is clamped, as shown.

The wire passes from a clamp, around a frictionless pulley, and then to a second frictionless pulley where loads F are applied to it. A marker is attached to the wire so that the total length of wire between the clamp and the marker is initially 3.70 m. A scale is fixed near to this marker.

The graph shows how the reading on the scale varies with F.

What is the Young modulus of the metal?

A 5.5 × 10¹⁰ Pa           B 9.4 × 10¹⁰ Pa           C 1.6 × 10¹¹ Pa           D 2.2 × 10¹¹ Pa

Reference: Past Exam Paper – November 2018 Paper 13 Q19

Solution:

Answer: D.

Young modulus E = stress / strain

Stress = Force / Area = F / A

Strain = extension / original length = e / L

E = (F/A) / (e/L) = FL / Ae

The original length L (= 3.70 m) is initially at the marker position of 4.5 mm on the scale (refer to the graph on the y-axis when F = 0 N).

When the force F = 10 N, extension e = 8.0 – 4.5 = 3.5 mm = 3.5×10^-3 m

Cross-sectional A = πd² / 4

E = FL / Ae

E = 4FL / πd²e

E = 4 × 10 × 3.70 / (π × (0.25×10^-3)² × (3.5×10^-3))

 
Young modulus E = 2.2×10¹¹ Pa