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Atwood's machine

  1. Oct 31, 2012 #1
    1. The problem statement, all variables and given/known data
    A horizontal cylinder on frictionless bearings has a moment of inertia of 0.8kg*m^2 and a radius of 22cm. A 15 kg mass is attached to a 8kg mass with a massless string wrapped around the cylinder. The string does not slip on the cylinder. If the 15 kg mass is released from rest 3.4m above the floor,
    a) what is the velocity of the 8kg mass when the 15kg mass hits the floor?
    b) what is the angular velocity of the cylinder when the 15kg mass hits the floor?


    2. Relevant equations
    Mg-T=Ma
    T-mg=ma
    V^2=V0^2 + 2a(y-y0)
    mgh=1/2mv^2 + 1/2Iω^2

    3. The attempt at a solution
    a)I solved for T in one of the above equations and plugged into the other equation. Then I plugged in the masses and solved for the acceleration which should be the same for both boxes and I got 2.9826 m/s^2 for a. I then used the third equation given that the original velocity is zero, the height is 3.4m, and the acceleration calculated earlier to be 2.9826, and calculated the final velocity which I got as 4.50m/s.
    b) I used conservation of energy and used the fourth equation. I plugged rω in for v and then plugged in for the variables known and solved for ω which I got to be 25.6 rad/s.
     
  2. jcsd
  3. Oct 31, 2012 #2

    ehild

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    The cylinder has mass and moment of inertia. To accelerate it, torque is needed: The tensions are not the same at both sides.

    Your last equation involves only one mass, but there are two of them, moving in opposite directions.

    You need to use only conservation of energy and the "no slip" condition.

    ehild
     
  4. Oct 31, 2012 #3
    How do I do that?
     
  5. Oct 31, 2012 #4

    ehild

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    You know what conservation of energy means?
    No slip means that the speed of the rope (and that of the masses) is v= rω.

    ehild
     
  6. Oct 31, 2012 #5
    yes but I do not know how to use that to find the answers.
     
  7. Oct 31, 2012 #6

    ehild

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    Let be the potential energy zero at the initial height of the blocks. The heavy one drops 3.4 m; the light one rises 3.4 m. What is the new potential energy?

    I hope you can write up the total kinetic energy of the two blocks and the rotational energy of the cylinder.

    ehild
     
  8. Oct 31, 2012 #7
    I wrote up the equation and got Mgh=1/2mv^2+1/2Mv^2+1/2Iw^2+mgh
    where M=15kg and m=8kg. is this right?
     
  9. Oct 31, 2012 #8

    ehild

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    It is right. Replace w=v/r, and solve for v.

    ehild
     
  10. Oct 31, 2012 #9
    i got a velocity of 3.44m/s
     
  11. Oct 31, 2012 #10
    how do you go about solving part b though?
     
  12. Oct 31, 2012 #11

    ehild

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    w=v/r

    ehild
     
  13. Oct 31, 2012 #12
    I got 3.44 m/s for part a and 15.6 rad/s for part b. is that what you got?
     
  14. Oct 31, 2012 #13

    ehild

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    Yes:smile:

    ehild
     
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