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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.

Respuesta :

Answer:

[tex]\Delta L=15\,mm[/tex]

Explanation:

Given:

  • length of a steel-string, [tex]L=1m[/tex]
  • area of the string, [tex]A=0.5\,mm^2[/tex]
  • Young's modulus of the steel, [tex]Y=2\times 10^{11} Pa[/tex]
  • force of tension on the string, [tex]F=1500\,N[/tex]

We have the relation for change in length:

[tex]\Delta L=\frac{F.L}{A.Y}[/tex]

[tex]\Delta L=\frac{1500\times 1000}{0.5\times 10^{-6}\times 2\times 10^{11}}[/tex]

[tex]\Delta L=0.015m[/tex]

[tex]\Delta L=15\,mm[/tex]

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