Moment Balance - Angled Wine Bottle Holder

[riddle_me_phys]

Hey all!

I think I have the problem within my grasp, just would like a second opinion to help me cross the finish line...

Homework Statement

Consider the following diagram of the bottle holder assembly (see attachment). The weight of the bottle is 11N, and the weight of the board is negligible. List all assumptions that are made. Solve for the reaction forces and/or moments.

Homework Equations

T = r x F
∑M_{z} = 0

The Attempt at a Solution

So I see that the counterclockwise moment from the wine bottle (around the pivot) is what creates the static equilibrium and allows the holder to stand.

I was initially confused at thinking about the center of gravity. I wasn't sure if it was the midpoint of the length of the wine bottle regardless of the cocked angle, but after pretending to be an angled wine bottle, I (re)confirmed with myself that the center of gravity will move depending on the orientation of the bottle. =)

However, I'm not sure how I can figure out where the center of gravity moved to with the 22 degree angle...

If I consider the system to be the holder + bottle, then the forces are: weight of wine (vertical component), and vertical reaction force at the...wine/holder interface? Do I count reaction forces at the holder base? I don't think there's internal moment at the pivot, since it's not anchored.

The moment equation about the wine holder pivot would be

∑ M_{z} = 0 = r_{wine} x (11 N) - r_{?} x F

I need some other moment force to counteract the weight of the wine bottle. So does that come from the reaction force at the wine/holder interface?

If so, then the reaction force there is F = 11N, and the r's would have to be the same value...
Which is saying that the wine's center of gravity is where the wine/holder interface is.


?

 

[riddle_me_phys]

Oops, forgot attachment. Now attached.