3D Equilibrium with cables (statics)

  • Thread starter kirab
  • Start date
  • #1
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Homework Statement



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

Homework 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.

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
 

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Answers and Replies

  • #2
Pyrrhus
Homework Helper
2,178
1
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).
 
  • #3
27
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Aha, it appears that it was just a simple arithmetic mistake!

Thanks for the tip.
 

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