Center of Buoyancy: Finding the Answer

[foo9008]

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

The Attempt at a Solution

 

[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.

 

[foo9008]

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 ?

 

[haruspex]

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.)

 

[foo9008]

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.

 

[haruspex]

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

Right. So do you have your answer?

 

[foo9008]

Right. So do you have your answer?

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

 

[haruspex]

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?)

 

[foo9008]

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 ?

 

[haruspex]

the center of gravity at 48 , 36 ?

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

 

[foo9008]

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 ?

 

[haruspex]

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.

 

[foo9008]

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 ?

 

[haruspex]

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

Yes.