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Pulleys and Inclined Planes

  1. Aug 1, 2016 #1
    1. The problem statement, all variables and given/known data
    feynman1-8.jpg

    2. Relevant equations
    Conservation of Energy / Virtual Work
    $$\sum_i m_i g h_i = 0$$

    3. The attempt at a solution
    Moving the pulley I labeled A down by ##\delta y## moves ##w## down by ##\delta y##, and moves ##W## up by ##\frac{1}{2} sin\theta##.

    So by conservation of energy I have $$-w\delta y + \frac{1}{2}W \delta y sin\theta = 0$$ leading to ##W = \frac{2w}{sin\theta}##.

    I feel uncertain about this answer however, because it seems like the mechanics would be the same if you removed Pulley A and replaced it with ##w##.
     
  2. jcsd
  3. Aug 1, 2016 #2

    haruspex

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    Are you sure about that?
     
  4. Aug 1, 2016 #3
    Not sure why you are using virtual work either. I would attack this problem with mechanical advantage of a system of pulleys.

    Regards,
    KQ6UP
     
  5. Aug 1, 2016 #4
    My reasoning here is that if pulley A is moved down to be even with the anchor point, ##w## will have dropped by the initial length between the anchor and the pully. feynman1-8b.jpg
     
  6. Aug 1, 2016 #5
    I see my mistake now! ##\delta y## moves ##w## by ##2\delta y##. So ##W=\frac{4w}{sin\theta}##, which is what I get from force analysis as well.
     
  7. Aug 1, 2016 #6

    haruspex

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    That looks good.
     
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