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Dynamics question about boy pulling himself up via pulley

  1. Oct 18, 2012 #1
    1. The problem statement, all variables and given/known data
    A 45 kg boy stands on 30 kg platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the boy. The masses of the rope and pulley are negligible. Ignore the friction in the pulley.

    a) If the rope and the boy are at rest, what is the tension in the rope?

    The boy now pulls on the rope so that the acceleration of the boy and the platform is 1.5 m/s^2 upward.

    b) What is the tension force in the rope under these new conditions?
    c) Under these conditions, what is the force exerted by the platform on the boy?

    After a short time, the boy and the platform reach and sustain an upward velocity of 0.3 m/s.

    d) Determine the power output of the boy required to sustain this velocity.

    2. Relevant equations

    For a-c, we need Newton 2 ƩF = ma.
    For d, Power = Fv

    3. The attempt at a solution

    The problem here is really only part c. The book's answer and my answer agree on the other parts. Unfortunately, the book is wrong often enough that I don't always trust their answer. So, I want confirmation.

    Here's what I did. Free Body Diagram on boy yields:
    1. Fn upwards (Platform on boy)
    2. Ft upwards (boy pulls down on rope, and by Newton 3, his force is Ft upwards). From part b, Ft = 431.25 N
    3. mg downwards
    ma = 45 * 1.5
    In equation form,
    Fn + Ft - mg = ma
    Fn = ma + mg - Ft = 45*1.5 + 45*10 - 431.25 = 86.25 N
    Unfortunately, the book says 131.25 N. I'm guessing that they added the weight of the platform to the ma side of the equation. Who's right? If the book is, why add the weight of the platform to the ma side.
     
  2. jcsd
  3. Oct 19, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Your solution is correct.

    ehild
     
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