Question

Consider a steel guitar string of initial length L=1.00 meter and cross-sectional area A=0.500 square millimeters. The Young's modulus of the steel is Y=2.0×10¹¹ pascals. How far ( ΔL) would such a string stretch under a tension of 1500 newtons? Use two significant figures in your answer. Express your answer in millimeters.

Answer 1

Answer:

$\Delta L=15\,mm$

Explanation:

Given:

• length of a steel-string, $L=1m$

• area of the string, $A=0.5\,mm^2$

• Young's modulus of the steel, $Y=2\times 10^{11} Pa$

• force of tension on the string, $F=1500\,N$

We have the relation for change in length:

$\Delta L=\frac{F.L}{A.Y}$

$\Delta L=\frac{1500\times 1000}{0.5\times 10^{-6}\times 2\times 10^{11}}$

$\Delta L=0.015m$

$\Delta L=15\,mm$