# Buoyancy Force question, having hard time starting.

## 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 MO=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.

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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.

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

berkeman
Mentor
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!