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Rotation with pulleys

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data
    A block has a mass of 500 g, another block has a mass of 460 g. Both are attached to a pulley with a frictionless wire that does not slip. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 seconds. What is the magnitude of the blocks' accleration? What is the magnitude of the pulley's angular acceleration?

    Fig: http://i212.photobucket.com/albums/cc150/deadfishfactory/1.jpg


    2. Relevant equations
    Torque = Moment of Inertia * Angular Acceleration
    Force = Mass * Acceleration
    Acceleration = Angular Acceleration / Radius
    Moment of Inertia = (1/2)MR^2

    3. The attempt at a solution
    T=tension; W=weight; A=accleration; R=radius; I=moment of inertia
    M(1) = left box; M(2) = right box; M(3) = pulley

    A(1) = A(2) = a/R = A

    1. T(1) - W(1) = m(1) * A; T(1) = W(1) + M(1) * A
    2. T(2) - W(2) = -m(2) * A; T(2) = W(2) - M(2) * A
    3. T(1)R - T(2)R = I * A / R
    T(1) - T(2) = M(3) * A
    W(1) + M(1) * A - W(2) + M(2) * A = M(3) * A
    Solved for A.

    Well, I started plugging things in and stuff, but I can't solve the problem because the mass of the pulley is unknown. I'm pretty sure I did it wrong so can someone point out my mistake or show me how to do it if I did it completely wrong? Thanks!

    answer: a) 6.00 cm/s^2 b) 1.20 rad/s^2
     
  2. jcsd
  3. Oct 30, 2007 #2

    rl.bhat

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    Homework Helper

    Using kinematic formula, find the acceleration of the falling body. Using this value find the angular acceleration of the pully. In this problem mass of any object is not needed
     
    Last edited: Oct 30, 2007
  4. Oct 30, 2007 #3
    Still having trouble finding the acceleration of the blocks.

    I found the angular acceleration of the pulleys by using the constant acceleration equation like you said. I got 1.22 rad/s^2, which is close enough. I can't figure out how to find the acceleration of the blocks since I used gravity for the block's acceleration to find the angular acceleration. My physics skills aren't too good, can you explain it to me very precisely since I'm kinda slow.
     
  5. Oct 30, 2007 #4
    Heavier block falls 75.0 cm in 5.00 sec. (The system was released from rest.) Can you find A from the basic equations of Kinematics. (Remember those s-u-v-a-t equations??)
     
  6. Oct 30, 2007 #5
    Ohhhh. Pfft. When you said "heavier block falls 75.0 cm in 5.00 sec," it immediately smacked into me. Haha. I'm such an idiot for not noticing. Anyways, I got the answer. Thank you very much!
     
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