Boom held by 3 cables (Statics)

[masterflex]

Homework Statement

I've included a picture of the problem so you can see the diagram too. The question is asking for the tension of 1 cable, when 2 are given (problem# 41).

Homework Equations

no equations per se.

The Attempt at a Solution

I resolved cable AC and cable AD, but don't know how to proceed. How do you even analyze it with the given info that "the resultant of the tensions exerted at point A of the boom must be directed along AB"? This is hard. Thanks for helping me.

 

[berkeman]

Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)

 

[AlephZero]

Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)

If the sum of the cable forces is directed along AB, the force in the boom is also directed along AB.

So if you take moments about a point on the line AB, the unknown force in the boom (which you are not asked to find) has zero moment. Point B will do nicely.

Hint: first work out the angle between each cable and the boom AB, then taking the moments is easy.

 

[masterflex]

I understand

Thanks a lot for your help guys. I got this solution from a random professor that I just walked in the door to talk to. I also realized what I was struggling with: there's a force along the line of AB (but not necessarily constrained to that physical distance; just in line with it), but I didn't know what to make of that force even though the problem said it was there. One easy way to know how many forces are in play at any given point is to look at the number of things (booms, cables, hanging things, whatever).

The moment solution should work -- I mean it sounds good :D, and I'll give it a try. Thanks for that.

By the way, the prof approached this like an equilibrium problem just using plane forces. I've attached my work.