1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Whirling Rope

  1. Apr 29, 2010 #1

    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
    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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook