Equilibrium problem with 5 unknowns

[SubZer0]

Homework Statement

This is an equilibrium problem with 3 unknown forces, and 2 unknown angles. I have resolved the horizontal and vertical forces.

Homework Equations

Horizontal components of forces:

-W₁cos Θ + W₃cos ∅ = 0

Vertical components:

W₁sin Θ + W₃sin ∅ - W₂ = 0

Where W₁, W₂, W₃ are weight components, and Θ, ∅ are angles between suspending cables.

The Attempt at a Solution

The goal is to find equations to resolve the angle components. This seems simple enough, but apparently isn't. I have attempted to substitute +/- sqrt(1 - sin² Θ) and +/- sqrt(1 - sin² ∅) for the cos Θ and cos ∅ components respectively, but this just ends up a huge mess. There has got to be an easier way of resolving the angular components in these two equations.

 

[kuruman]

This is an equilibrium problem with 3 unknown forces, and 2 unknown angles.

What is an equilibrium problem? Please provide the statement of the problem as was given to you including diagrams, if any. How can we help you if we don't know what this is about?

 

[SubZer0]

Hi, kuruman, thanks for the reply. The problem that I'm having at the moment is just solving the two equations above for the angle component. Instead of putting all of the force diagrams, etc, I just reduced it down to a problem of solving those equations. The goal is to get two equations from those above, in order to resolve to theta and phi.

 

[kuruman]

I understand what you think your problem is. Simply put, if you have two equations and five unknowns, you cannot solve for the unknowns and that's that. Now maybe, just maybe, one or more of the following is the case (a) one might be able to get additional equations relating the variables; (b) some of the variables that you think are unknown are actually known; (c) there is a special relation between variables, e.g. the angles, that reduces the number of the unknowns; (d) you misunderstood what the problem is asking; (e) there is something else that has escaped you; (f) it's a poorly phrased problem that has no solution. I have seen all of the above in posts by other people and that is why I asked you to show the complete statement of the problem. Clearly, your method led you to a dead end. We cannot help you out of this if we don't have the whole picture.

 

[haruspex]

One unknown can be eliminated straight away. Only the ratios between the forces will matter for the angles.