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Three Cylinders (rotational kinematics!)

  1. Nov 4, 2008 #1
    [​IMG]

    Three identical, solid, uniform density cylinders, each of mass 16 kg and radius 1 m, are mounted on frictionless axles that are attached to brackets of negligible mass. A string connects the brackets of cylinders #1 and #3 and passes without slipping over cylinder #2, whose bracket is attached to the ledge. Cylinder #1 rolls without slipping across the rough ledge as cylinder #3 falls downward.

    This system is released from rest from the position shown -- with cylinder #3 at a height of 4.4 m above the ground.
    a) How fast is cylinder #3 moving just before it hits the ground?
    v = 5.36

    b) What is the rotational speed of cylinder #2 at the time in (a)?
    w = 5.36

    c) Cylinder #3 is now replaced by a sphere of the same mass. How fast is it moving just before it hits the ground?
    v'= 5.36

    d) Finally, cylinder #1 is replaced by a sphere of the same mass and radius. How fast is cylinder #3 moving just before it hits the ground?
    v'' = ????

    This is where I'm having problems. This should be exactly the same as pt. A except we have a sphere so c=2/5. So I did
    mgh = 2/5mv^2
    (16)(9.81)(4.4) = 2/5(16)v^2
    and I got 10.388 = v'' but apparently that's wrong, anyone know what's going on?


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 4, 2008 #2

    tiny-tim

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    Hi r34racer01! :smile:

    You've left out the energy of cylinder #2.
     
  4. Nov 4, 2008 #3
    Ok now I tried 690.624 = (1/2)*I(sphere)*w^2 + (1/2)*I(cylinder)*w^2
    690.624 = (1/2)((2/5)mr^2)(v^2/r^2) + (1/2)((1/2)mr^2)(v^2/r^2)
    690.624 = (0.2)mv^2 + (0.25)mv^2
    690.624 = 3.2v^2 + 4v^2
    9.79388 = v
    But that's still wrong. What am I doing wrong?
     
  5. Nov 7, 2008 #4

    tiny-tim

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    sorry!

    Hi r34racer01! :smile:

    I'm sorry I've taken so long to reply :redface:

    (have an omega: ω and a squared: ² :smile:)
    You've left out the translational KE of masses 1 and 3. :smile:
     
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