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Rotational Energy and Pulley System

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Problem reads:
    The pulley in the figure has radius 0.160 m and a moment of inertia 0.480 kgm^2. The rope does not slip on the pulley rim. Use energy methods to calculate the speed of the 4.00-kg block just before it strikes the floor.

    2. Relevant equations


    [tex]v=\omega r[/tex]

    3. The attempt at a solution
    I said [tex]m_{1}[/tex] was the 4.00 kg block and [tex]m_{2}[/tex] was the 2.00 kg block. Setting the initial and final energies of the system equal, I got:


    Since initial angular momentum is zero and so is the height of block 2, and in the final state, height of block 2 is zero, this simplifies to:


    Plugging in numbers:

    I got [tex]\omega=20.21 rad/s[/tex]. Then using [tex]v=\omega r[/tex] I just plugged in the radius and the angular velocity I just found to get v=3.23 m/s

    This is not the right answer according to the homework website unfortunately... help would be appreciated!
    Last edited: Oct 24, 2007
  2. jcsd
  3. Oct 24, 2007 #2


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    You are forgetting that not all of the kinetic energy is in the pulley. The blocks have some too.
  4. Oct 24, 2007 #3
    Alright, I added the kinetic energy into the equation (kept the left side the same since kinetic energy is 0 for both blocks when they're at rest) and solved for v:


    Using [tex]v=\omega r[/tex] and isolating [tex]\omega[/tex] and substituting that into the equation, I got 5.71 m/s.

    But it still says this is wrong... how do I go about getting the right answer?
  5. Oct 24, 2007 #4


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    You are doing everything right and your presentation of this problem is super clear, good job. But if I put the numbers into your equation I don't get what you get for v. Are you just punching in numbers wrong?
  6. Oct 24, 2007 #5
    Ah alright, I got it (v=2.81 m/s)... it turns out I did punch in a wrong number somewhere, I hate it when I do that, heh.

    Anyway, thank you for the help Dick, I really appreciate it!
  7. Oct 24, 2007 #6


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    That's what I get as well. Like I say, I wish all posters presented stuff this well.
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