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Pulley and friction problem

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data
    At the instant shown the 100-lb block A is moving down the plane at 5 ft/s while being attached to the 50-lb block B. If the coefficient of friction is µk = 0.2, determine the acceleration of A and the distance A slides before it stops. Neglect the mass of the pulleys and cables.
    http://0pcode.ath.cx/photo.jpg [Broken]
    The picture was taken with my phone, so the triangle under A is kinda hard to see. Its hypoteneuse is 5, the vertical leg is 3, and the horizontal leg is 4.


    2. Relevant equations
    F = ma
    m = W/g (slug)
    F(friction) = µ*N
    V[tex]^{2}[/tex] = V[tex]^{2}_{0}[/tex] + 2ad

    3. The attempt at a solution
    I tried finding the frictional force of block A first, which I calculated to be 16-lb. I then found the tension force in the rope at A, which I calculated to be 12.5-lb. I then took those two values and added them together, and got an acceleration value of 9.12ft/s^2. And I found the distance the block slides to be 1.37 feet.
    The answers are supposed to be 1.29ft/s^2, and 9.70 feet. I don't know where I went wrong, any help would be appreciated :) Thanks.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 11, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi AcecA! :smile:
    Nooo … to find the friction force, you first need to find the normal force, and that will depend on the acceleration.

    In this sort of problem, everything depends on everything else :rolleyes:

    you can't "start at one end and work your way across" (the way we do in most mechanics problems :wink:)

    Hint: call the tensions T1 and T2, and the distance along the slope x, and then use good ol' Newton's second law twice, once for A and once for B. :smile:
     
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