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pulley system, calculate acceleration

  1. Jul 13, 2017 #1
    IMG_2742.JPG 1. The problem statement, all variables and given/known data
    this is a pulley system,
    each masses are moving with acceleration with a1,a2,a3..
    question)
    1) How can i calculate the ratio a1:a2:a3 ?
    2) How can i calculate the T(tenstion)?


    2. Relevant equations

    a1,a2,a3: acceleration of each masses.
    g=10m/s2
    weight of all pulleys : 0
    The mass 5kg does not spin.

    3. The attempt at a solution

    i think this is atwood system , but not simple, very complex.
    help me...
     
    Last edited: Jul 13, 2017
  2. jcsd
  3. Jul 13, 2017 #2
    As drawn, the right side is going to jamb the pulley and then act as a single mass. Are you sure its drawn correctly?
     
  4. Jul 13, 2017 #3
    I missed the condition " the mass 5kg does not spin'
    Others, all correctly drawn.im sure....
     
  5. Jul 13, 2017 #4
    Then wouldn't you treat this as 2kg vs 6kg?
     
  6. Jul 13, 2017 #5
    Then a1, a2, a3 would be same...?
    If i treat this as 2kg vs 6kg, all the a=5m/s2,
    I would be happy if The answer is so simple./o\
     
    Last edited: Jul 13, 2017
  7. Jul 13, 2017 #6
    Anyway thank you very much for your replies.
     
  8. Jul 14, 2017 #7

    haruspex

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    I don't think so. Imagine P2 position as fixed. P3 can move up x while a2 moves down x and a3 moves up 2x.
     
  9. Jul 14, 2017 #8
    you are right. if P3 is fixed, M3 moves up 2x, m2 moving down 1x, but P3 is also moving up, by 1x.the M2 is drawing with 2T tension. so net of M3 is 3x.the not fixed P3 makes this problem complicated.
     
  10. Jul 14, 2017 #9

    haruspex

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    So work in terms of relative accelerations. What equation can you write relating the acceleration of the 5kg relative to P2 to the acceleration of the 1kg relative to P2?
     
  11. Jul 14, 2017 #10
  12. Jul 14, 2017 #11

    haruspex

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  13. Jul 14, 2017 #12
    while 1kg, moves up 2x to p3, p3 moves up 1x, so 1kg will move 3x to p2.

    whe
     
  14. Jul 14, 2017 #13

    haruspex

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    Very good.
    So, what equation does that give you for the accelerations?
     
  15. Jul 14, 2017 #14
    IMG_2746.JPG
     
  16. Jul 14, 2017 #15

    haruspex

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    Don't worry about masses and forces yet, just think about the relationships that must apply to the accelerations because of the string lengths remaining constant.
    In terms of a1, a2 and a3:
    - what is the acceleration of P2?
    - what is the acceleration of the 5kg mass relative to P2?
    - what is the acceleration of the 1kg mass relative to P2?
    - according to what you found in post #12, what equation connects those?
     
  17. Jul 16, 2017 #16
    good morning sir,
    i can calculate a1 a2 a3 to pulleys
    but about equation of motion, im very confused because of existance of 5kg.

    5kg is connected to p3 and also tp p2.
    T= 1*a3 + 1*g'---p3 equation
    3T-5*a2=5g'
    then, what?
    i m not sure the motion equation to each pulley, p1,p2,p3.
     
  18. Jul 16, 2017 #17

    haruspex

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    I don't know what you mean by that. Please answer my questions in post #15.
     
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