Mechanical Engineering 3D force system

1. Sep 14, 2010

sami23

1. The problem statement, all variables and given/known data
A system of cables suspends a crate weighing W = 420 lb. The dimensions in the figure are as follows: h = 20.9 ft, l = 5.70 ft, x = 7.05 ft, $$\theta$$ = 36.0$$\circ$$, and $$\phi$$ = 20.0$$\circ$$. Determine TA, TD, and TE, the tensions in cable segments CA, CD, and CE, respectively.

2. Relevant equations
vector F = (magnitude F)(unit vector)
$$\sum$$F = 0
FCA + FCB + FCD + FCE + FCF + W = 0

3. The attempt at a solution
How do I start by finding the coordinates:
C(0,0,0), D(x,0,h), A(?) E(?)

I can't see how to find the correct coordinates A,B,C,D,E,F

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2. Sep 14, 2010

pongo38

Do you agree that A B C and D all lie in the xz plane?

3. Sep 14, 2010

sami23

yes they do. coordinates for D:(7.05,0,20.9)
C is at origin (0,0,0)
E and F are at some weird y plane (here's my attempt)
E: (x,l,-h)
F: (-x,-2l,-h)
A is all over the place with a weight

4. Sep 14, 2010

pongo38

It looks to me like E is at 0, l, -h and F is at 0, -l, -h
For the vagueness of A, you might realize that it's the angles that matter. The forces are independent of the actual distances. more dependant on distance ratios, that is angles. So to solve it you could say: Without loss of generality x of A=1 etc

5. Sep 14, 2010

sami23

I see how E(0,l,-h) and F(0,-l,-h). They're at the same y-plane just at opposite ends.
Now A makes those angles at the x-plane. AB forms phi and AC forms theta. All I really know about B is that it's in the -h z-plane. Can I treat A as a 2D problem in the xz-plane?

6. Sep 14, 2010

pongo38

Sloppy language when saying "They're at the same y-plane just at opposite ends", when you mean y-z plane. When you say "All I really know about B is that it's in the -h z-plane" I think you should say ....in the x-z plane.
When I said that WLOG, x of A can be set at unity, I implied that x of B can similarly be attributed a distance as long as it is bigger that x of A.
If you suppress the y-axis and look only at the x-z plane with E on top of F, you will get a meaningful result for DC CA and AB, but the result for C to EF will need to be partitioned in the y-z plane. That's the simple way to look at it. Or you could invoke vector algebra with i j k terms. If you start with the joint at A, you can solve the forces there. Then you have enough information to go to C, where you will need three equations for the three unknowns. That's where 3 reference axes are helpful to bring the question to a successful conclusion. Can you do it now?

7. Sep 14, 2010

thanks