Center of gravity vs center of buoyancy

[werson tan]

Homework Statement

why the floating body still stable when G ( center of gravity ) is above the B ( center of buoyancy)?

Homework Equations

The Attempt at a Solution

in my opinion , the statement is worng , because when G is above B , G has the tendency to move downward , causing the object to be unstable

 

[werson tan]

Homework Statement

when the ship is tilted more , the ship will become inclined more ( bigger portion of right hand side part of the ship will be submerged in water ) . this caused the center of buoyancy to be located more to the right , this cause the B is very far from the G . The ship will capsize...

why the author gave when the point B is sufficiently far , the forecs will create the restoring moment , i would say the forces create overturning moment , causing the ship to turn over...Which is correct ?
Me or the author ?

Homework Equations

The Attempt at a Solution

<<Moderator's note: this question was merged with the first one as they are essentially two parts of the same question.>>

 

[Qwertywerty]

For a floating body (stable/unstable), what is the relation betweeen the weight of the body and the force of buoyancy?

 

[Merlin3189]

..when the ship is tilted more , ...( bigger portion of right hand side part of the ship will be submerged in water ) . this caused the center of buoyancy to be located more to the right , this cause the B is very far from the G . The ship will capsize...

I don't understand why you say, the ship will capsize. Which way is the ship tilting (rotating) and which way is the BG torque?

... the author gave when the point B is sufficiently far , the forecs will create the restoring moment , i would say the forces create overturning moment , causing the ship to turn over...Which is correct ?
Me or the author ?

The author!
You seem to be confusing "turning" moment with "overturning" moment.
The further B is from G, the greater turning moment you will get. BUT this moment acts in the opposite sense to which the ship is tilted, so it is a restoring moment, not an overturning moment. To get an overturning moment, you need it to act in the same direction (sense) as the tilt.

 

[werson tan]

I don't understand why you say, the ship will capsize. Which way is the ship tilting (rotating) and which way is the BG torque?

The author!
You seem to be confusing "turning" moment with "overturning" moment.
The further B is from G, the greater turning moment you will get. BUT this moment acts in the opposite sense to which the ship is tilted, so it is a restoring moment, not an overturning moment. To get an overturning moment, you need it to act in the same direction (sense) as the tilt.

can you show me where is the r for the FB to generate restoring moment and overturning moment in the diagram ? so that i can understand better what you said

 

[CrazyNinja]

can you show me where is the r for the FB to generate restoring moment and overturning moment in the diagram ? so that i can understand better what you said

The r will be drawn from the center of gravity. Clearly you will observe that the torque due to F_B is a restoring torque. If you feel weird with the ship example, try it with a simple box.

 

[Merlin3189]

Well I've scribbled on your diagram. I don't know whether it will help. I just don't see any problem. The two forces are equal, the magnitude is unimportant (for now), only the direction of the couple determines whether there is a righting moment or capsizing moment. That is obvious from a glance at your diagram.
If the torque or couple is in the sense (direction) of tilt you sink, if it is opposite to the the tilt then it opposes the tilt and tries to right you.
The real question about boat stability is how the centre of buoyancy moves as the boat tilts (which may be described as the movement of the metacentre)

Edit: I see C.Ninja has posted while I was drawing. Yes r can be the perpendicular distance between Fb and Fg. I took it as the distance from their midpoint, so my r is half of his and I end up with 2r.Fg or 2r.Fb since Fb and Fg are equal in magnitude.