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Help with this pulley question please

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  1. Jun 26, 2017 #1
    1. The problem statement, all variables and given/known data
    Two objects of equal masses A and B are connected to a system of pulleys as shown in the figure uploaded. The pulleys are assumed to be smooth. Calculate the acceleration of A.

    2. Relevant equations
    F=ma


    3. The attempt at a solution
    Mg-T=ma
    I can't figure out the second equation for b becaus I think it is attached to the pulley and will remain stationary. However, in the proposed solution, there's an equation for the movement of b too. How is that possible?
     

    Attached Files:

  2. jcsd
  3. Jun 26, 2017 #2

    phinds

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    Well, yeah, B does not move relative to the pulley but what is the pulley doing?
     
  4. Jun 26, 2017 #3
    Pulley is just moving and b is an additional load on the second pulley.
    Also, B doesn't move relative to the observer too.
     
  5. Jun 26, 2017 #4

    phinds

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    You might want to rethink that
     
  6. Jun 26, 2017 #5
    There can be two scenarios which aren't specified in the question.
    1) B is loosely held at the centre so that B stays ALMOST stationary to the observer.
    2) B is tightly attached to the pulley and it rotates in a circle.
     
  7. Jun 26, 2017 #6

    phinds

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    You and I seem to be working on entirely different problems. I read this as a very simple, straightforward, standard pulley problem. I have no idea what you are talking about.
     
    Last edited: Jun 26, 2017
  8. Jun 26, 2017 #7
    Listing all of the relevant equations helps you to develop a clear understanding of the problem.

    Mass A and B are equal.
    In what direction (up or down) will mass A travel? What about the travel direction of mass B?
    Why?

    Hint: Annotate your drawing with known and unknown variables, directions of travel, etc.
    Use more precise and unambiguous naming, for instance, maA and maB for the accelerations of mass A and B.

    In a larger sense, become acquainted with George Polya's four principles, and as a wise man once said, "Learn it, Know it, Live it".
     
  9. Jun 26, 2017 #8

    haruspex

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    You seem to be misinterpreting the diagram. The pulley above B rests on the string. It is firmly attached to the mass B, but not to anything else. That pulley and its mass are free to move up and down as a unit.
     
  10. Jun 26, 2017 #9
    If mass A moves upward, the part of the string supporting mass A gets shorter. If the total length of string is constant, what happens to the length of the part of the string supporting mass B? (a) its length doesn't change (b) its length gets shorter or (c) its length gets longer.
     
  11. Jun 26, 2017 #10

    ehild

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    upload_2017-6-27_6-52-23.png

    The mass B is attached to the axis(represented by the black dot) of the hanging pulley.It moves together with the axis up or down.
    The pulley rotates about the axis.
    The length of the string is constant. If A moves downward, the left piece of the string gets longer, so the right pieces should get shorter, raising the pulley and mass B.
     
  12. Jun 28, 2017 #11
    Try drawing a free body diagram, taking into account the forces of gravity and tension.
     
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