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

`\Delta L=15\,mm`

Step-by-step 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* 10^(11) Pa`

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

We have the relation for change in length:

`\Delta L=(F.L)/(A.Y)`

`\Delta L=(1500* 1000)/(0.5* 10^(-6)* 2* 10^(11))`

`\Delta L=0.015m`

`\Delta L=15\,mm`