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Statics, friction of a rope around a post

  1. Jul 22, 2015 #1
    1. The problem statement, all variables and given/known data
    A dockworker adjusts a spring line (rope) which keeps a ship from drifting alongside a wharf. If he exerts a pull of 190 N on the rope, which has 1.25 turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.35.
    20150722_171921_zpszgrymvcs.jpg
    2. Relevant equations
    T2=T1eμβ
    where T2 is in the direction of impending motion.

    3. The attempt at a solution
    20150722_171849_zpsf7gup5ud.jpg
    Not sure what i am missing here, it looks right to me.
     
  2. jcsd
  3. Jul 22, 2015 #2

    Nathanael

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    In this equation, which is the 190N, T1 or T2? Which did you try to solve for?

    You should also run through the algebra again.
     
  4. Jul 22, 2015 #3
    T2 is in the direction of impending motion, so i assumed it was 190N. Re reading the problem statement the ship is pulling on the rope with a much greater force, so then T2 would be T, the unknown.
    Thank you Nathanael.
     
    Last edited: Jul 22, 2015
  5. Jul 22, 2015 #4

    Nathanael

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    If the unknown force of tension were too large, it would cause the rope to slip towards it. We are asked for the maximum force of this unknown tension, so that means the unknown tension is the 'direction of impending motion.'

    If you took T2 to be the 190N tension and solved it for T1 then what you would be calculating is the minimum force of tension the other side needs in order for the rope to not slip towards the dockworker.
     
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