Center of gravity vs center of buoyancy

In summary: However, the overall summary of this conversation is that the stability of a floating body is determined by the relationship between the weight of the body and the force of buoyancy. When the center of gravity is above the center of buoyancy, the body will remain stable. If the center of gravity is above the center of buoyancy, the body will become unstable and may capsize. The position of the center of buoyancy also plays a role in determining stability, with a further distance between the center of buoyancy and the center of gravity resulting in a greater restoring moment that helps to keep the body upright. The direction of the torque also plays a role, with a torque in the same direction as the tilt causing the body to capsize, while a
  • #1
werson tan
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1

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
 

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  • #2

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 teh 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.>>
 

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  • #3
For a floating body (stable/unstable), what is the relation betweeen the weight of the body and the force of buoyancy?
 
  • #4
werson tan said:
..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?

werson tan said:
... 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.
 
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  • #5
Merlin3189 said:
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
 
  • #6
werson tan said:
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 FB is a restoring torque. If you feel weird with the ship example, try it with a simple box.
 
  • #7
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)
boat.png


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.
 
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What is the difference between center of gravity and center of buoyancy?

The center of gravity is the point where the entire weight of an object can be considered to act. It is the point where the force of gravity is exerted on the object. The center of buoyancy, on the other hand, is the point where the buoyant force, or the upward force exerted by a fluid on an object, is considered to act.

How do the center of gravity and center of buoyancy affect the stability of an object?

The stability of an object is determined by the relative positions of its center of gravity and center of buoyancy. If the center of gravity is below the center of buoyancy, the object will be stable and will not tip over. However, if the center of gravity is above the center of buoyancy, the object will be unstable and may tip over.

Can the center of gravity and center of buoyancy change?

Yes, the center of gravity can change depending on the distribution of weight within an object or the position of the object. The center of buoyancy can also change if the object is submerged or partially submerged in a fluid, as the buoyant force will act on different parts of the object.

What are some real-life examples of the importance of understanding the center of gravity and center of buoyancy?

The understanding of the center of gravity and center of buoyancy is crucial in fields such as naval architecture, where the stability of ships and boats is of utmost importance. It is also essential in the design of aircraft, automobiles, and other vehicles to ensure their stability and safety. Additionally, understanding these concepts is crucial in activities like swimming and diving, where body position and buoyancy play a significant role.

How can the center of gravity and center of buoyancy be calculated?

The center of gravity can be calculated by finding the average position of the weight of an object or by using specific formulas depending on the shape and distribution of weight. The center of buoyancy can be calculated by finding the centroid of the displaced fluid or by using specific formulas depending on the shape and density of the object and the fluid it is submerged in.

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