Solving Tension Problem with 3 Cables | Philip

[philipc]

I'm a bit stuck on a tension problem, I have a weight supported by three cables.
I will have to admit, up to this point, I have been cheating on these tension problems. What I have been doing is writing various equations and using my TI-89 to solve the system of equations. This method has been working for me when having only two cables or the three cables being some what symmetric. This problem puts the three cables all on the X, Z plane (judging by the picture) but they have no symmetry beyond that. Using my method I have nine unknowns, so I created to what I believed to be 9 valid equations, but my TI-89 didn't really like that.
I once remember my professor talking about some sort of triangle, so my question, is there a better way to solve this sort of problem. I'm not asking for the problem to be solved, I just need a different approach.
Thanks guys and gals
Philip

 

[Doc Al]

To get the needed equations, consider the conditions for equilibrium: The sum of the forces in any direction must be zero; the net torque about any point must be zero.

If you really have 9 equations and 9 unknowns, what's the problem? Solve it, step by step. (To get more targeted advice, show the exact problem and your attempted solution.)

 

[philipc]

Doc,
I was just wondering if there was a different approach that using 9 equations, some general laws I'm missing out on.
To show the exact problem would be much harder than describing it, it's pretty simple, just imagine a mass hanging from three cables, and there three cables can be attached any where on the x,z plane. Where the mass is attached to the three cables on the negative y axis.
Far as my 9 equations, I'm guessing that I went down a wrong path, giving me incomplete data for the TI-89 to work with.
Setting the three separate x,y,z tensions equal only gives me three equations. What would be the next approach to obtain the next 6 equations?
Thanks
Philip

 

[Doc Al]

If you have the angles that the cables make, then all you probably need are three equations. (The tensions are the three unknowns.) If you don't have the angles, then you don't have enough information to solve for the tensions.

 

[philipc]

I just solved it, thanks
I do have the locations of the points where the cables are attached, so I can make the angles. What I was doing was breaking each tension into 3 parts giving me 9 unknowns. I found a similar problems solved where they only used the three tensions as unknowns and used the sum of each i,j,k vector to make 3 equations. This method was much easier and giving only three unknowns, so it all worked out in the end.
Thanks again
Philip