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) × (Ï€×(5.0×10-4)2/4)]
Strain × 100% = {20 / [(2.0×1011) × (Ï€×(5.0×10-4)2/4)]} × 100%
Strain × 100% = 0.0509 % = 5.1×10-2 %
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