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I have a question about a problem related to waves in a rope

  1. Mar 3, 2016 #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 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?
    2. Relevant equations
    (Wave´s speed)=(lambda)*(Frenquency)
    (Wave´s speed)=((Tension)/(Mass per unit lenght))^(1/2)

    3. The attempt at a solution
    I don´t know how to start, how does the tension vary along the rope? can somebody give me a hint of how the tension vary along the rope?
     
  2. jcsd
  3. Mar 3, 2016 #2
    Well, I'm by no means an expert, but doesn't centripetal force exerts an influence? When you whirl the rope in a horizontal circle, centripetal force on a portion of the rope will change in function of the distance r from the end that is held - the radius of the circle changes.

    EDIT: Do your question is related somehow to slide 6 in this link?
    http://www.iitg.ac.in/asil/Lecture-4.pdf
     
    Last edited: Mar 3, 2016
  4. Mar 3, 2016 #3

    billy_joule

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    What made you think this question involved waves?

    Imagine a simpler case; a stationary hanging rope. At the top the rope supports the entire weight of the rest of the rope so tension is at it's maximum, at the bottom tip it's supporting no weight at all so the tension is zero.
    The same applies to your rotating rope. Draw a free body diagram,You must make the simplifying assumption that the rope is straight and radial*.
    Apply Newtons laws, solve for T as a function of r.

    *For bonus points:can you predict/experiment what an actual rope would do? What shape would it assume? Do you have enough information to solve for that much more complicated case?
     
  5. Mar 3, 2016 #4
    Actually, looks like this question is in a chapter about mechanical waves in some physics textbook:
    http://web.uvic.ca/~jalexndr/295Ch15YFproblems.pdf
    Anyway, is the case you mentioned related to the link I posted?
    http://www.iitg.ac.in/asil/Lecture-4.pdf
     
    Last edited: Mar 3, 2016
  6. Mar 4, 2016 #5
  7. Mar 4, 2016 #6

    billy_joule

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    Yes. But the the OP hasn't made it to b) or c) so waves aren't relevant yet.

    It isn't somewhat related to the link, the link shows the exact solution to your problem!
    The only difference is they use 'M' to represent the mass where as you will use 'm'.

    Forget about waves for now, you are looking for tension as a function of r.
    Have you made any attempt? A free body diagram? Applied newtons laws?
     
  8. Mar 4, 2016 #7
    Tension as a function of r is: F=(m/L)*(L-r)*g; right?
    if so, how the presence of waves can affect the tension in the rope?
     
  9. Mar 4, 2016 #8

    haruspex

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    No, you were told to ignore gravity. Where did you get that equation from?
    As billy_joule says, the question you posted has nothing to do with waves.
     
  10. Mar 4, 2016 #9
    Sorry, I hugely misunderstood the problem, I was imagining the rope with waves, confusion solved, thanks.
     
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