# Center of buoyancy

1. Mar 10, 2016

### foo9008

1. The problem statement, all variables and given/known data
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) ?

2. Relevant equations

3. The attempt at a solution

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2. Mar 10, 2016

### haruspex

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. Mar 10, 2016

### foo9008

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. Mar 10, 2016

### haruspex

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. Mar 10, 2016

### foo9008

center of buoyancy is the centroid of the immersed part of a ship or other floating body.

6. Mar 10, 2016

### haruspex

7. Mar 10, 2016

### foo9008

is it 48/ 3 , 55/3 ? so the center of gravity coincide with the center of gravity ?

8. Mar 10, 2016

### haruspex

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. Mar 10, 2016

### foo9008

so , in this case , the center of buoyancy is at 48/ 3 , 55/3 ? and the center of gravity at 48 , 36 ?

10. Mar 10, 2016

### haruspex

The centre of gravity of the whole block is at 48, 36.

11. Mar 10, 2016

### foo9008

when consider the center of gravity , we will consider the whole object , but not only the submerged portion ?

12. Mar 10, 2016

### haruspex

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. Mar 10, 2016

### foo9008

just to double conform , the center of buoyancy and center of gravity of submerged portion is 48/ 3 , 55/ 3 ?

14. Mar 10, 2016

Yes.