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Mechanical Waves problem

  1. Oct 1, 2009 #1
    1. The problem statement, all variables and given/known data

    a uniform rope with length L and mass M is held at one end and whirled in a horizontal circle with angular velocity [tex]\omega[/tex]. you can ignore the force of gravity on the rope. find the time required for a transverse wave to travel from one end of the rope to the other.


    2. Relevant equations

    v=(T/[tex]\mu[/tex])^(1/2) where [tex]\mu[/tex]=density
    [tex]\Sigma[/tex]F=ma

    3. The attempt at a solution
    This is the solution that the professor gave, but i don't understand why:

    [tex]\Sigma[/tex]F=F[tex]_{T}[/tex]=[tex]\Delta[/tex]a[tex]_{c}[/tex]
    dF[tex]_{T}[/tex]=(dm)r[tex]\omega[/tex][tex]^{2}[/tex]
    dF[tex]_{T}[/tex]=[tex]\mu[/tex]r[tex]\omega[/tex][tex]^{2}[/tex]dr
    integrate with respect to r, from r to t.

    I
     
    Last edited: Oct 1, 2009
  2. jcsd
  3. Oct 2, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi pjkily! Welcome to PF! :smile:

    (have a square-root: √ and a mu: µ and an omega: ω and a sigma: ∑ and a delta: ∆ :wink:)
    The tension, T (no need to call it FT :wink:) increases towards the end of the string.

    And the speed depends on the tension.

    So you need to integrate along the string. :smile:
     
  4. Oct 2, 2009 #3
    OH! that's the part I didn't understand.
    THANK YOU SOOOO MUCH, Tim!!!
     
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