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Chapter 14: Q. 33 (page 385)

An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2000 N by turning the tuning screws. By how much is the string stretched?

Short Answer

Expert verified

The string is stretched by0.010m.

Step by step solution

01

Given information

The length of the string is L=80cm=0.80m.

The radius of the string is role="math" localid="1650298194619" r=1mm2=0.5mm=0.0005m

The tension in the string is T=2000N

Young's modulus isY=20×1010N/m2

02

Elongation of the string

Young's modulus is given by Y=TA∆LL.

The elongation of the string is

role="math" localid="1650298181390" ∆L=TALY=2000π0.000520.8020×1010=0.010m

Therefore, the string is stretched by0.010m.

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