Center of Buoyancy: Finding the Answer

In summary: The center of buoyancy and center of gravity of the submerged portion are both at (48/3, 55/3). In summary, the buoyancy force is found to be 1945N and the center of gravity of the submerged portion is at (48/3, 55/3). To find the center of buoyancy, one can use the definition of it being the centroid of the immersed part of a ship or other floating body. This means that for a uniformly dense body in a constant gravitational field, the center of mass and center of gravity will coincide. Therefore, the center of buoyancy in this case is also at (48/3, 55/3).
  • #1
foo9008
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Homework Statement


the buoyancy force i found id 0.751(1000)(9.81)(0.5x0.55x0.96) = 1945N , i also found that the center of gravity of submerged portion is (48/3 , 55/ 30 = (16 , 18.3) , how to find the center of buoyancy ? is the cnter of buoyancy acted half of the submerged portion , which is (48, 27.5) ?

Homework Equations

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  • #2
Where is the mass centre of a triangular lamina?

By the way, the question is a bit strange. It gives you the spcific gravity, but not the depth into the page of the block, so you cannot find the volume. The 'force' you end up with is really a force per unit length.
 
  • #3
haruspex said:
Where is the mass centre of a triangular lamina?

By the way, the question is a bit strange. It gives you the spcific gravity, but not the depth into the page of the block, so you cannot find the volume. The 'force' you end up with is really a force per unit length.
mass center = center of gravity of submerged portion is (48/3 , 55/ 30 = (16 , 18.3) ? am i right ? how to find the center of buoyancy ?
 
  • #4
foo9008 said:
mass center = center of gravity of submerged portion is (48/3 , 55/ 30 = (16 , 18.3) ? am i right ? how to find the center of buoyancy ?
Yes, 48/3, 55/3, if your coordinate system is what I guess it to be.
How do you think centre of buoyancy is defined? (So Google it.)
 
  • #5
haruspex said:
Yes, 48/3, 55/3, if your coordinate system is what I guess it to be.
How do you think centre of buoyancy is defined? (So Google it.)
center of buoyancy is the centroid of the immersed part of a ship or other floating body.
 
  • #6
foo9008 said:
center of buoyancy is the centroid of the immersed part of a ship or other floating body.
Right. So do you have your answer?
 
  • #7
haruspex said:
Right. So do you have your answer?
is it 48/ 3 , 55/3 ? so the center of gravity coincide with the center of gravity ?
 
  • #8
foo9008 said:
is it 48/ 3 , 55/3 ? so the center of gravity coincide with the center of gravity ?
The centre of buoyancy is at the centre of gravity of the displaced fluid.
For a uniformly dense body, the centre of mass is the centroid of the volume.
In a constant gravitational field, centre of mass is centre of gravity.
Combining those facts should give you what you need.

(Thought experiment: consider a parcel of water floating in water. If the centre of gravity of the parcel were not at its centre of buoyancy, what would happen?)
 
  • #9
haruspex said:
The centre of buoyancy is at the centre of gravity of the displaced fluid.
For a uniformly dense body, the centre of mass is the centroid of the volume.
In a constant gravitational field, centre of mass is centre of gravity.
Combining those facts should give you what you need.

(Thought experiment: consider a parcel of water floating in water. If the centre of gravity of the parcel were not at its centre of buoyancy, what would happen?)
so , in this case , the center of buoyancy is at 48/ 3 , 55/3 ? and the center of gravity at 48 , 36 ?
 
  • #10
foo9008 said:
the center of gravity at 48 , 36 ?
The centre of gravity of the whole block is at 48, 36.
 
  • #11
haruspex said:
The centre of gravity of the whole block is at 48, 36.
when consider the center of gravity , we will consider the whole object , but not only the submerged portion ?
 
  • #12
foo9008 said:
when consider the center of gravity , we will consider the whole object , but not only the submerged portion ?
For the centre of gravity of the block, yes.
The block as a whole has a centre of gravity; the submerged portion has a centre of gravity which is the same as the centre of buoyancy.
If you just write "centre of gravity" I cannot be sure which you are referring to.
 
  • #13
haruspex said:
For the centre of gravity of the block, yes.
The block as a whole has a centre of gravity; the submerged portion has a centre of gravity which is the same as the centre of buoyancy.
If you just write "centre of gravity" I cannot be sure which you are referring to.
just to double conform , the center of buoyancy and center of gravity of submerged portion is 48/ 3 , 55/ 3 ?
 
  • #14
foo9008 said:
just to double conform , the center of buoyancy and center of gravity of submerged portion is 48/ 3 , 55/ 3 ?
Yes.
 
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FAQ: Center of Buoyancy: Finding the Answer

1. What is the center of buoyancy?

The center of buoyancy is the point at which the upward force of buoyancy, acting on an object immersed in a fluid, is considered to originate.

2. How is the center of buoyancy determined?

The center of buoyancy can be determined by finding the centroid of the fluid displaced by the object. This can be done by using a variety of methods, such as mathematical calculations or physical experiments.

3. Why is the center of buoyancy important?

The center of buoyancy is important because it affects the stability and equilibrium of an object in a fluid. If the center of buoyancy is located above the object's center of gravity, it will be stable. If it is below the center of gravity, the object will be unstable and may capsize.

4. Can the center of buoyancy change?

Yes, the center of buoyancy can change depending on the shape, size, and orientation of the object in the fluid. It can also change if the density or volume of the fluid is altered.

5. How does the center of buoyancy differ from the center of mass?

The center of buoyancy is the point where the buoyant force acts, while the center of mass is the point where the object's mass is evenly distributed. The two points may not necessarily be in the same location, especially for irregularly shaped objects.

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