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A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity ω. You can ignore the force of gravity on the rope. (a) At a point on the rope a distance r from the end that is held, what is the tension F? (b) What is the speed of transverse waves at this point? (c) Find the time required for a transverse wave to travel from one end of the rope to the other.

Respuesta :

Answer:

Explanation:

a) Tension acting on the rope will be equal to centripetal force

T = Centripetal force

[tex]T=\dfrac{mv^2}{r}[/tex]

we know that

  v = r ω

 [tex]T=\dfrac{m(r\omega)^2}{r}[/tex]

T = m r ω²

B) speed of the transverse wave is

  [tex]V = \sqrt{\dfrac{T}{\mu}}[/tex]

μ is the linear density = m/L

  [tex]V = \sqrt{\dfrac{m\ r\omega^2}{\dfrac{m}{l}}}[/tex]

  [tex]V = \sqrt{l\ r\omega^2}[/tex]

C) time taken

    [tex]t = \dfrac{distance}{speed}[/tex]

    [tex]t = \dfrac{L}{\sqrt{l\ r\omega^2}}[/tex]

   

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