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Accelerating Pulley System

  1. Sep 24, 2016 #1
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    a1 = a2
    a1 = F/(M+m1+m2) | Force/(Mass of entire system) = acceleration of entire system
    *a2 = (m1g)/(m2+m1) | Force = m1g; acceleration of m2 and m1 = m1g/(m1+m2)

    My answer: F = (m1g)(M+m1+m2)/(m2+m1)
    The book's answer: F = (m1g)(M+m1+m2)/(m2)
    *This step is what leads me to a slight variation of the book's provided answer.

    I've looked through the forums, and have done a lot of thinking myself, and I believe what it comes down to is a false assumption. I understand that the force pulling m1 and m2 is m1g, and that the tension that then pulls m2 is equal to m1g, leading to an acceleration of m1g/m2 and subsequently the correct answer, but I do not understand what is incorrect about concluding that the system (looking at m2 and m1) as a whole accelerates at m1g/(m1+m2). Gut feeling tells me that the conclusion I've made is incorrect because the acceleration would be m1g/(m1+m2) in an inertial frame, but not in this case because it is part of an accelerating system.

    Why does a2 = m1g/m2 rather than a2 = m1g/(m1+m2)?
     

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    Last edited: Sep 24, 2016
  2. jcsd
  3. Sep 24, 2016 #2

    Orodruin

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    You have here considered m1 and m2 as a system, but the force you quote is not the force on that system, it is the force on m2 only.
     
  4. Sep 24, 2016 #3
    Is there another force that I would need to account for, such as the applied force on M?
     
  5. Sep 24, 2016 #4

    Orodruin

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    There are forces acting from the wall on m1 and from the pulley on the rope. Computing these forces is not necessary if you chose a better system to consider.
     
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