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Pulley problem: Does the third pulley move up or down?

  1. Nov 12, 2014 #1
    1. The problem statement, all variables and given/known data
    ) The pulley system in Figure 1.b consists of two pulleys of radii a and b rigidly fixed
    together, but free to rotate about a common horizontal axis. The weight W hangs
    from the axle of a freely suspended pulley P, which can rotate about its axle. If
    section A of a rough rope is pulled down with velocity V :
    (i) Explain which way W will move.
    (ii) With what speed will it move?
    THE IMAGE IS IN QUESTION 3 HERE: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Round_1_2013_prt_1.pdf

    2. Relevant equations
    -

    3. The attempt at a solution
    The answer is that the weight will move up because rope B moves down with velocity (b/a)V and D moves up with velocity V, so the centre of the weight rises with speed V(a-b)/2a

    I really can't see why the mass would move up. Surely the same amount of string is fed through to each side of the pulley so it should not move?

    Thank you in advance!
     
  2. jcsd
  3. Nov 12, 2014 #2

    gneill

    User Avatar

    Staff: Mentor

    Imagine that the rope does not slip on the pulleys. If the top pulleys rotate through some small angle θ, how much will a point on segment D rise? How much will a point on segment B drop?
     
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