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STATICS: Chapter 2, net force of lifting a given mass.

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data

    "A derrick boom is guyed by cables AC and AD. A worker is lifting a 20kg block by pulling on a rope that passes through the pulley at A. Knowing that the boom AB exerts a force A that is directed from B to A, determine this force and the force in each of the two cables."

    [​IMG]

    ANSWER: (From back of Textbook)
    F(AB) = 1742N
    T(AC) = 1517N
    T(AD) = 403N


    2. Relevant equations
    F(net) in every direction = 0 (Hence statics)

    F(AB) = (TensionAB)(Unit Vector Lambda)

    Lamda = AB(position vector from A to B)
    ----
    |AB|(Magnitude of AB)
    3. The attempt at a solution




    Coordinates:
    A = 0x + 6y + 0z
    B = -6x + 0y -3z
    C = -10.5x + 0y -8z
    D = -6x + 0y -7z
    E = +6x +1.5y +0z



    All forces of all the ropes and the weight force must be equal to the one supporting object: the boom(Tab).

    I drew a triangle with AE as the hypotenuse.

    Tan(theta) = (opp/adj) = [(6-1.5)/6]
    (theta) = arctan(4.5/6)
    (theta) = 36.87degrees

    [(4.5^2) + (6^2)]^(1/2) = Hyp
    Hyp = 7.5

    W = (m)(g) = 196N = Tae

    .: (196N/7.5m) = (Taex/6m) = (Taey/4.5m)
    Taex = (6m)(196/7.5m) = 156.8N
    Taey = (4.5m)(196/7.5m) = 117.60N


    Sum Fx = 0 = Tab(6/9) - Tac(10.5/14.5) - Tad(6/11) - 156.8N
    Sum Fy = 0 = Tab(6/9) - Tac(6/14.5) - Tad(6/11) -(9.8*20kg) - 117.60N
    Sum Fz = 0 = Tab(3/9) - Tac(8/14.5) - Tad(7/11)

    From here I used simple substitution and elimination to solve for the variable Tab, Tac and Tad; but I keep getting numbers that are off by around 150N for each value. I have tried this problem so many times, can somebody check to see if my equations above are correct? I am assuming my problem lies there and not in my simultaneous equation solving skills.
     
  2. jcsd
  3. Sep 16, 2008 #2

    stewartcs

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    How about a drawing, I can't visualize what you are describing.

    CS
     
  4. Sep 16, 2008 #3
    A drawing of what?
     
  5. Sep 16, 2008 #4
    Anybody have a clue?
     
  6. Sep 17, 2008 #5

    stewartcs

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    A drawing of the problem. If you have inserted one already, I'm not able to see it for some reason (most likely my company is blocking the link behind the scenes).

    CS
     
  7. Sep 18, 2008 #6

    nvn

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    Homework Helper

    SnickerGTI: Nice work. You just made a couple of sign errors. Notice the fourth term in your summation(Fx) equation should be 156.9, not -156.8 N. (Also, generally always carry four or five significant digits for all quantities throughout your calculations, then round the final answer to three, or maybe four, significant digits.) Secondly, the third term in your summation(Fz) equation should be Tad*(7/11), not -Tad*(7/11). Give it one more try.
     
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