Buoyancy Force question, having hard time starting.

[frozenguy]

Homework Statement

The 3m plank shown in section has a density of 800 kg/m³ and is hinged about a horizontal axis though its upper edge O. Calculate the angle theta assumed by the plank with the horizontal for the level of fresh water shown.

Homework Equations

Whats wrong with the editor? It isn't working properly for me at all.
B=rho*g*V
Sum of M_O=0

The Attempt at a Solution

I bolded in section because I was wondering what that meant exactly. Like I should only consider 1 meter in width? What about its thickness? Am I just supposed to use density of the plank to compare to density of water like in a ratio of some sorts?
I was thinking I need to find that distance from the centroid of buoyancy to the water line so I can find that length and then find theta.. But I'm not to sure on where to go.

 

[frozenguy]

Ok so I've been thinking this over more and I realized I need to take into account the water pressure force acting on the plank. So I have mg and the center of gravity, I have B at the centroid of the section under water, and I have the force of water pressure on the submerged part.

Sum around O=0 should give me my answer ya?

EDIT: I guess the water pressure is NOT a factor in this problem, or its included in the buoyancy.

 

[frozenguy]

Got it! The answer checks with the one provided from the book.

 

[berkeman]

Good job. I clicked into your thread yesterday, but didn't have time to be of help. Glad that you figured it out on your own!