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Drawing Free Body Diagrams

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A man of mass 64.2 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 23.2 kg and is 3.2 m long. Suppose the man stands to the right from the middle of the scaffold that is a distance one sixth of the length of the scaffold. What is the tension in the right rope? What is the tension in the left rope?

    3. The attempt at a solution
    im always confused on how exactly to draw out the scenarios and start the question. For this particular problem i got this far:
    1. straight bar for scaffold with an arrow pointing down, half way (the center of gravity)
    2. a man closer to the right rope, with an arrow pointing down, (his weight F=mg)
    3. the two ropes on either side are tension (arrows pointing up)

    Now im not sure if there would be torque, because one rope has more force than the other, if so where would the pivot point be?? or if i should some how solve it be equating the tensions since the system is static??
    Help would be greatly appreciated
     
  2. jcsd
  3. Feb 17, 2009 #2

    LowlyPion

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    Homework Helper

    If it is in equilibrium (it is), then the ∑ F and the ∑ T are both 0.

    So choose an end and balance out the torque.
     
  4. Feb 17, 2009 #3
    so the torque applied (right rope) = torque(scaffold) + torque(man)
    Fr = Fr + Fr
    Fr = (23.2)(9.81)(3.2/2) + (64.2)(9.81)(3.2*2/3)
    F = 1707.7/3.2
    F = 533.66 N
    so the tension in the right rope is 534 N??
     
  5. Feb 17, 2009 #4

    LowlyPion

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    I suppose you mean that

    ∑ F = 0 = Tl + TR - ∑ m*g

    You should have the equation for the torque about end the man is farthest from.

    And that should solve for the T of the rope he is closest to - the right Tension. And your answer looks OK.

    Then you can figure the other tension directly from the first ∑ F.
     
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