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Conservation of energy for a system

  1. Sep 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Figure shows a massless wheel of radius R on which at a point a mass m is fixed and a uniform chain of mass 2m is tied to it which passes over the rim of the wheel and half of its length is hanging on other side as shown in the figure. When a small clockwise jerk is given to the wheel, it starts rotating. Find the speed of the mass m when it reaches a point P directly opposite to its initial point.
    xqhJzwE.png
    2. Relevant equations
    The equations for conservation of energy and momentum (both angular as well as linear)

    3. The attempt at a solution Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations. Conservation of momentum? Well,I don't have the inital velocity.
     
  2. jcsd
  3. Sep 13, 2015 #2

    mfb

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    Then show your attempt please.
    The initial velocity is negligible, but conservation of momentum doesn't help here.
     
  4. Sep 13, 2015 #3
    Hmm. Looks like all I have to do is conserve energy.
     
  5. Sep 13, 2015 #4
    Is the equation 2mgl = mgl + 1/2mv^2 + 1/2Iw^2 (I is the moment of inertia about the center of the pulley wheel,while w is the angular velocity) by any chance?
     
  6. Sep 13, 2015 #5

    mfb

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    Where do 2mgl and mgl come from?
    The moment of inertia of what?
     
  7. Sep 20, 2015 #6
    They are the gravitational potential energy terms. Seeing that the length of the chain is not given,we can say that (pi)R = half times the length (which is given in the question itself).
    The moment of inertia of the mass m about the center of the pulley?

    Am I doing something wrong?
     
  8. Sep 20, 2015 #7

    mfb

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    Sure, but potential of what relative to what? They don't look right in the way you used them.
    Okay.
    Yes, and it is unclear what because you don't explain how you got your formulas.
     
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