A steel string on an electric guitar has the following properties.

Question 14

A steel string on an electric guitar has the following properties.

diameter = 5.0 × 10^-4 m

Young modulus = 2.0 × 10¹¹ Pa

tension = 20 N

The string snaps, and contracts elastically.

By what percentage does a length l of a piece of the string contract?

A 5.1×10^-4 %             B 5.1×10^-2 %             C 1.3×10^-4 %                         D 1.3×10^-2 %

Reference: Past Exam Paper – November 2009 Paper 11 Q22 & Paper 12 Q21

Solution:

Answer: B.

Percentage of the length that contracts = e/L × 100%

But e/L is the strain of the string.

So, percentage of the length that contracts = strain × 100%

Young modulus, E = stress / strain

Strain = Stress / E

Stress = F / A

Strain = F / EA

Cross-sectional area. A = πd² / 4

Strain = 20 / [(2.0×10¹¹) × (π×(5.0×10^-4)²/4)]

Strain × 100% = {20 / [(2.0×10¹¹) × (π×(5.0×10^-4)²/4)]} × 100%

Strain × 100% = 0.0509 % = 5.1×10^-2 %