Bouyancy Mystifies Me

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Heavier part is going to roll toward the bottom, right?
 
Heavier part is going to roll toward the bottom, right?
If the cube is made of the same material, there is no ‘heavier/denser’ part.

I think it is more about which position is more stable. In theory I think there are many positions which would be in equilibrium but in practice I think face up is more likely and less prone to be disturbed.
 
Is the wooden cube of uniform density through its entire volume, or is there a knot or nail in it?
Uniform
 
The center of gravity of the uniform cube is in the center of the cube. The center of gravity of the volume of displaced water (in the shape of a truncated cube, or square box shorter than the wooden cube) is in the center of that box. That point is directly under the center of gravity of the cube. So the face of the cube is the most stable position for the cube to float in.
 
The center of gravity of the uniform cube is in the center of the cube. The center of gravity of the volume of displaced water (in the shape of a truncated cube, or square box shorter than the wooden cube) is in the center of that box. That point is directly under the center of gravity of the cube. So the face of the cube is the most stable position for the cube to float in.

ZZZZZZZZZZ
 
Definitely a matter of stability. I suspect a log could be made to float vertically, on a perfectly calm day, etc. Just like you could carefully balance the log on end on flat ground. But it would be very unstable with respect to any slight horizontal force and would flip over to horizontal (a position of lower potential energy).
 
The center of gravity of the uniform cube is in the center of the cube. The center of gravity of the volume of displaced water (in the shape of a truncated cube, or square box shorter than the wooden cube) is in the center of that box. That point is directly under the center of gravity of the cube. So the face of the cube is the most stable position for the cube to float in.
The center of gravity of the displaced water is ALWAYS directly under the center of gravity of the cube, so this argument is mute. But you are thinking in the right direction, keep going!
 
It’s late and I want you to get a good nights rest.

Flotation, centre of buoyancy

Stability in Flotation
I read the 1st reference, they are mostly wrong. First, their statement that "The centre of buoyancy is the centre point of the mass below the water and is the point through which the buoyant force acts" is wrong. The centre of buoyancy is the centre point of the volume below the water, because it is the centre point of the displaced water. This makes no difference for uniform objects but for non-uniform objects, like boats and buoys, the difference is significant. Second, for any uniform object, the centre of buoyancy can not be located above the object's mass centre, so their figures are wrong and most of their arguments are wrong.
 
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