Undergrad Proportion in 2D and 3D static equilibrium?

[Eric Wintjen]

If you were to look at a simple 2D or 3D static equilibrium diagram, where a mass is suspended by multiple ropes at different angles, my gut feeling is that there is a fairly simple proportion between the distance between the center of mass and the rope (the distance created opposite of the angle) and the percentage of the total mass that rope is supporting. I have been unable to derive this proportion mathematically if it exists. If my instincts are correct, what is this proportion and how is it derived?

 

[A.T.]

Its not clear what distance you mean. Can you post a diagram?

 

[CWatters]

The traditional way of solving this type of problem is to realize that in order for the object to be stationary (not accelerating in any plane) then the net force in that plane must be zero.

So you write several simultaneous equations each summing the component forces in that plane to zero. Then solve them.

In a 2D problem you usually only need 2 equations. In. 3D problem you need 3.

I suggest you post a 2D example and your attempt to solve it so we can see where you are getting stuck.

It's not a simple proportion. Trigonometry is involved.