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Calculate Magnitude of Moment in 3D

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data

    The turnbuckle is tightened until the tension in cable AB is 1.5 kN. Calculate the magnitude of the moment about point O of the force acting on point A.


    2. Relevant equations
    ƩMO = sqrt(Mx2 + My2 + M2)


    3. The attempt at a solution

    First I identified the coordinates of points A and B:

    A = (1.6, 0, 2.4)
    B = (2.3, 1.4, 0)

    OA = r = <1.6, 1.4, 0>
    AB = <0.7, 1.4, -2.4>

    |AB| = 2.865

    λAB = AB/|AB|
    λAB = 0,2443i + 0.4877j - 0.8377k

    Then I took the dot product with the tension in the cable AB and the unit vector of AB

    TABAB = 0.36645i + 0.73305J - 1.25655K

    ƩMO = rXTAB

    (0-1.75932)i -(-2.81796)J + (1.17288)k

    ƩMO = 3.523

    But it says my answer is wrong and I don't know where I'm going wrong.

    Suggestions would be appreciated
     

    Attached Files:

  2. jcsd
  3. Sep 26, 2012 #2
    I've just checked my working and found that I miscalculated the dot product.

    <1.6, 0, 2.4> X <0.36645, 0.73305, -1.25655>

    = -1.75932i + 2.88996J + 1.17288K

    When I take the magnitude of this I get 3.58 which is the correct answer.
     
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