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A 2.0-m-long string is under 20 N of tension. A pulse travels the length of the string in 50 ms. What is the mass of the string?

Respuesta :

onyebuchinnaji

The mass of the string at the given tension and length is 25 g.

The given parameters;

  • length of the string, l = 2 m
  • tension on the string, T = 20 N
  • time of motion, t = 50 ms

The speed of wave on the string is calculated as follows;

[tex]v = \sqrt{\frac{T}{\mu} } \\\\[/tex]

[tex]v = \frac{L}{t}[/tex]

where;

  • μ is mass per unit length

[tex]\frac{L}{t} = \sqrt{\frac{T}{\mu} } \\\\\frac{L^2}{t^2} = \frac{T}{\mu} \\\\\mu = \frac{Tt^2}{L^2} \\\\m = \mu L = (\frac{Tt^2}{L^2})L\\\\m = \frac{Tt^2}{L}\\\\m = \frac{20 \times (50\times 10^{-3})^2}{2} \\\\m = 0.025 \ kg\\\\m = 25 \ g[/tex]

Thus, the mass of the string at the given tension and length is 25 g.

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