How Do You Calculate Buoyant Force on Submerged Ice?

[Jbreezy]

Homework Statement

What is the buoyant force on 0.760 kg of ice held completely submerged underwater.

Homework Equations

The Attempt at a Solution

My book gives
Fb = (m_w) x (g) = (density of water / density of ice)x ( mass of ice) x (g)
g is gravity m_w is mass of water.
I really don't understand this. What is really confusing me is is the density of water / density of ice
I don't get it.
Thanks

 

[ravikannaujiya]

Homework Statement

What is the buoyant force on 0.760 kg of ice held completely submerged underwater.

Homework Equations

The Attempt at a Solution

My book gives
Fb = (m_w) x (g) = (density of water / density of ice)x ( mass of ice) x (g)
g is gravity m_w is mass of water.
I really don't understand this. What is really confusing me is is the density of water / density of ice
I don't get it.
Thanks

As I understand,
buyont force=mass of the water removed by ice * g
now mass of water removed by the ice= volume of the water*density of the water
since, volume of the water removed by the ice will be equal to the volume of ice itself.
so mass of the water=volume of ice* density of water
so,
Fb= volume of ice* density of water*g
Fb= (mass of ice/density of ice)*density of water*g
or Fb=(density of water / density of ice)x ( mass of ice) x (g)
I hope it may help.

 

[barryj]

Think about the concept of Archimedes's principal. Forget the formula. The buoyancy force is equal to the weight of the water displaced.

 

[ravikannaujiya]

Think about the concept of Archimedes's principal. Forget the formula. The buoyancy force is equal to the weight of the water displaced.

ohk...remove the removed by displaced...:)

 

[haruspex]

Fb = (m_w) x (g) = (density of water / density of ice)x ( mass of ice) x (g)

What physical quantity would (mass of ice) /(density of ice) represent?
What would multiplying that by (density of water) give you?

 

[Jbreezy]

What physical quantity would (mass of ice) /(density of ice) represent?
This would be the volume or the ice?

What would multiplying that by (density of water) give you?
Then it would give you the total density of the mass and the ice?

But my solution did the density of water/ density of ice
multiplied by the mass of the ice.
I'm sorry I'm having a hard time putting this together.

 

[haruspex]

What physical quantity would (mass of ice) /(density of ice) represent?
This would be the volume of the ice?

Yes.

What would multiplying that by (density of water) give you?
Then it would give you the total density of the mass and the ice?

No, you're multiplying a volume by a density, so it should give you a mass - but the mass of what?
Remember, the volume of the ice is equal to the volume of water it displaces.

 

[Jbreezy]

The mass of water?
I just got really confused because of how it was written and I need to understand the principle that the volume of an object submerged (or partially) is equal to the volume of the water that is displaced. ( Whatever it is in)

I did this

M_i / Di = Vi
Vi x D_w = M_w
Because Vi= V_w

So then we has mass of water so mass of water times gravity is the good old
F = ma
Right or not correct my thinking.
Thanks to the help

 

[barryj]

Think about the problem this way.

You are given the mass of the ice. Look up the density of ice and find the volume.
This is the volume of water displaced.
Look up the density of water, and knowing the volume of water displaced, find the mass of the water displaced.
Multiply the mass of water displaced by g to get the weight.
That is all there is to it.

 

[haruspex]

The mass of water?

The mass of water displaced, yes.

So then we has mass of water so mass of water times gravity is the good old
F = ma

Yes. So do you now see how the formula in the book works?

 

[barryj]

As to formulas, you need force = mass X g and density = mass/volume
(volume of ice) = (mass of ice)/(density of ice)
(volume of water ) = (volume of ice)
(mass of water) = (volume of water)(density of water)
(force) = (mass of water)g

Put it all together and you get the formula