How can I find the angle θ for mechanical equilibrium in this problem?

[caddyguy109]

This problem was part of a post in another thread, but it got really messy over there and no one seems to be responding.

So, here's the problem:
http://www.ihostphotos.com/show.php?id=182816"

And I was told this (but it didn't really help me see what to do, much):
"at least it's a 90 degree angle! and frictionless ...
try taking Moments around the place where the two F_N intersect
did you sum F_x and F_z first?"

But what forces do I sum for Fx and Fz? And where exactly is that total moment taken about?

On the FBD, I drew the W force pointing straight downward from the center, as specified, then Na (Normal Force A) perpendicular to the slope on the left, and did the same, but as Nb, on the right. This part makes sense, theoretically, to me at least.

But what the HECK do I add/calculate/find, etc. to get "the angle θ corresponding to equilibrium as a function of M, W, and I"? Still don't know what exactly to do or where to start, as far as finding that.

 

[caddyguy109]

Anyone??

 

[caddyguy109]

This problem is REALLY driving me nuts...

 

[caddyguy109]

...this problem really must be confusing. Seems to be the one all of us in the class are getting stuck on right now.:grumpy:

 

[Pyrrhus]

The moment is a free vector, unlike the forces that are sliding vectors, you have two normal forces acting on each of the ends of the rod. The advice given to you is a good one, but try checking sum of Fx, you might get suprised.

 

[caddyguy109]

Okay, THINK I got it.