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A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? Young's modulus for steel is 2.0 × 1011 N/m2

Respuesta :

Answer:

10.1 N

Explanation:

Your answer is 10.1 N, I don't actually know how to do it but I hope it helps.

Cricetus

The needed force will be "10.098 N".

Given:

Diameter,

  • d = 0.300 mm

Length,

  • L = 70.0 cm

Stretched by,

  • dL = 0.500 mm

Young's modulus,

  • Y = [tex]2\times 10^{11} \ N/m^2[/tex]

As we know,

→ [tex]A = \pi r^2[/tex]

      [tex]= \pi (\frac{d}{2} )^2[/tex]

      [tex]= \pi\times (0.3\times 10^{-3})^2[/tex]

Now,

→ [tex]F = Y\times A\times \frac{dL}{L}[/tex]

By putting the values, we get

      [tex]= 2\times 10^{11}\times \pi\times (0.3\times 10^{-\frac{3}{2} })^2\times \frac{0.5\times 10^{-3}}{70\times 10^{-2}}[/tex]

      [tex]= 10.098 \ N[/tex]

Thus the above answer is right.  

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