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Rotational Motion / Torque problem (what did i do wrong?)

  1. Aug 12, 2013 #1
    1. The problem statement, all variables and given/known data
    A thin, light wire is wrapped around the rim of a wheel,. The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius R = .280m. An object of mass m=4.2kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. If the suspended object moves downward a distance of 3m in 2s what is the mass of the wheel?


    2. Relevant equations
    Idisk = 1/2mr^2
    τ=Iα
    αr=a
    1/2at^2=x

    3. The attempt at a solution
    First I figured out the acceleration of the block with 1/2at^2=x. With x = 3 and t = 2 you get a=6/4.
    Then i set up τ=Iα=1/2*mw*r^2*(a/r)=mb*g*r
    (mb = mass bock and mw = mass wheel, i also substituted a/r for α.

    This equation reduces to 1/2*mw*a = mb*g
    with a = 6/4 we get
    6/8*mw = mb*g
    mb is given at 4.2 so mw equals 55kg which is wrong. What am I doing wrong? The answer key has them giving the answer using energy equations which is all fine and good, but i'm confused why this isn't working.
     
  2. jcsd
  3. Aug 12, 2013 #2
    I think you are on the right track. Do you know the correct answer?
    You have a correct at 1.5. Alpha = a/r. T = I X alpha. Find the torque. Knowing the acceleration of the 4.2 kg mass you can find the tension in the string. The tension will give you the torque. Plug in and you should be successful.

    From your incorrect answer of 55kg, it seems that you did not calculate the tension in the wire correctly. Draw a FBD of the block show the mg and the T and using the acceleration find the T correctly.
     
    Last edited: Aug 12, 2013
  4. Aug 13, 2013 #3

    haruspex

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    That last part is wrong. Let the tension in the wire be T, and treat the forces on and acceleration of the wheel separately from those on the block .
     
  5. Aug 13, 2013 #4
    The tension in the string, which is the source of torque for this scenario, is not equal to mb*g. Remember that the acceleration that you calculated wasn't g.
     
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