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Whirling Rope

  1. Apr 29, 2010 #1
    Hi,

    In one of the examples of "An Introduction to Mechanics" he argues that the tension at the end of a whirling rope must be zero as the end is free.

    I just don't understand how this can be.
    Below is the example
    Kleppner1.jpg
    Thanks
     
    Last edited: Apr 29, 2010
  2. jcsd
  3. Apr 29, 2010 #2
    is he talking about a length or rope being rotated as a straight line or where the rope is in a sine wave?
     
  4. Apr 29, 2010 #3
    never mind, I see it now.
    the end of the rope has no further mass beyond it or no more rope to provide the tension from the rotational acceleration, at any point r between the ends the tension will be based on the delta from r to the free end and the fixed end.
     
  5. Apr 29, 2010 #4
    I'm sorry but could you please explain better?
     
  6. Apr 29, 2010 #5
    Sounds like you've reached the end of your rope...

    Well if there's nothing beyond the end then how can there be any tension on it?
     
  7. Apr 29, 2010 #6
    The tension at a distance [itex]x[/itex] from the end of the rope acts on the segment of the rope between the end and distance x.

    If the mass of this segment of the rope is [itex]m_x[/itex] and the tension is [itex]T_x[/itex], then [itex]T_x=m_xa_x[/itex], where [itex]a_x[/itex] is the acceleration of this segment of the rope.

    Since [itex]m_x\rightarrow 0[/itex] as [itex]x\rightarrow 0[/itex], then unless the end of the rope is subject to infinite acceleration we must also have [itex]T_x\rightarrow 0[/itex] as [itex]x\rightarrow 0[/itex].
     
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