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Three Pulleys 3 masses, find tension

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Three objects mI. m2 and m3 are suspended
    from three massless and frictionless pulleys as
    shown in the diagram. ml is 6 kg, m2 is 2 kg
    and m3 is 3 kg. Find the tension of the string
    when the system is set in motion (i.e. all
    masses are moving). Answer in N

    Options are:
    (a) 11.3 (b) 12.1 (c) 13.5 (d) 14.2

    ..O....O...... Top 2 pulleys attached to ceiling, m1 hangs from 1st pulley, m2 is attached
    .| |..| |..... to the middle pulley, m3 hangs from third pulley.
    .|..O...|
    .|..[]..|
    [] m2 []
    m1....m3



    2. Relevant equations
    Fg=mg
    F=ma

    3. The attempt at a solution

    I made 3 equations, tried to relate them but I am getting 15.68N instead of any of the options (this was an old exam question). It's too far from 14.2 to be right. Here were the four equations I made:

    a1=(m1g-T)/m1
    a2=(2T-m2g)/m2
    a3=(m3g-T)/m3

    2a2=a1+a3

    I keep getting none of the possible answers but I think I'm doing it right. Where did I go wrong?
     
  2. jcsd
  3. Dec 9, 2012 #2

    haruspex

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    Your equations are right but your answer is wrong. Please post your working.
     
  4. Dec 9, 2012 #3
    a1=(m1g-T)/m1=g-T/m1=g-T/3
    a2=(2T-m2g)/m2=2T/m2-g=T-g
    a3=(m3g-T)/m3=g-T/m3=g-T/6


    From 4th eqn:

    2T-2g=g-T/3+g-T/6

    2T+T/2=4g

    5T/2=4(9.8)

    T=15.68
     
  5. Dec 9, 2012 #4

    haruspex

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    Oh, sorry, I misread the end of your first post. I thought you were getting 14.2. So, I agree with you, it's something around 16.
     
  6. Dec 9, 2012 #5
    k thanks
     
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