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3D Equilibrium with cables (statics)

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data

    Diagram is attached.

    The mast OA is supported by 3 cables. If cable AB is subjected to a tension of 500N, determine the tension in cables AC and AD and the vertical force F which the mast exerts along its axis on the collar at A.

    a = 6m
    b = 3m
    c = 6m
    d = 3m
    e = 2m
    f = 1.5m
    g = 2m

    2. Relevant equations

    For this assignment, I'm pretty sure the prof just wants us to consider sum of Fx, Fy and Fz, and to take no moments.

    3. The attempt at a solution

    I have a complete solution, but apparently it's not the right answer according to the teacher assistant (I don't know what the right answer is).

    so vector AB = 2i + 3j - 6k
    AC = -1.5i + 2j - 6k
    AD = -3i -6j - 6k

    and I get that vector Fab = (142.85i + 214.285j - 428.55k)N

    Fac = (-0.2308(Fac)i + 0.30769(Fac)j - 0.923076(Fac)k)N (where the Fac's on the right side of the equation represent the magnitude of the force *vector* Fac)
    and

    Fad = (-0.333(Fad)i - 0.666(Fad)j - 0.666(Fad)k)N

    and of course, F = (Fk)N

    where i, j and k are all unit vectors in the direction of the x, y and z axis, respectively.

    From that, I have that:

    sum of Fx = 0

    Equation 1: 142.85i - 0.2308(Fac)i - 0.333(Fad)i = 0

    sum of Fy = 0

    Equation 2: 214.285j + 0.30769(Fac)j - 0.666(Fad)j = 0

    sum of Fz = 0

    Equation 3: -428.55k - 0.923076(Fac)k - 0.666(Fad)k + F(k)= 0

    That's 3 equations in 3 unknowns. I then rearranged equation 1 to get Fac in terms of Fad. I plugged this Fac equality into equation 2, to get Fad alone.

    My answer for Fad is 910.2 N. Apparently that's wrong. Plugging that in elsewhere, I get that Fac = -694.2 N and that F = 393.9 N, which are both wrong according to the marker.

    Any suggestions/corrections? Did I not approach the question properly or assume too much?

    Thanks
     

    Attached Files:

  2. jcsd
  3. Oct 14, 2008 #2

    Pyrrhus

    User Avatar
    Homework Helper

    This problem is a simple concurrent forces on point A. The sum of this force will equal a resultant force. You tackled the problem correctly, first find the position vectors, then the normalize (unit vectors). Check for mistakes in your numbers. I checked your position vectors and they are right. I also checked on unit vector and it was right.

    By the way, I recommend using fractions instead of decimals whenever possible, so your answers will tend to be more accurate (your rounding is a bit off sometimes).
     
  4. Oct 15, 2008 #3
    Aha, it appears that it was just a simple arithmetic mistake!

    Thanks for the tip.
     
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