Fluid mechanics of floating wood

[utkarshakash]

Homework Statement

A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. Neglect the compressibility of water. When more air is pushed into the bottle from the pump, the piece of wood will float with

a)larger part in the water
b)lesser part in the water
c)same part in the water
d)it will sink

Homework Equations

The Attempt at a Solution

When more air is pushed the air pressure inside the bottle increases. But what will be its effect on floatation?

 

[haruspex]

I'm not sure it's possible to answer this exactly without more knowledge of how wood responds to changes in air pressure. But I think they're trying to get you to consider what determines the volume of the block that's submerged. Can you state Archimedes' principle?

 

[utkarshakash]

I'm not sure it's possible to answer this exactly without more knowledge of how wood responds to changes in air pressure. But I think they're trying to get you to consider what determines the volume of the block that's submerged. Can you state Archimedes' principle?

The liquid exerts a pressure on the solid immersed which is equal to the weight of the displaced fluid.

 

[haruspex]

The liquid exerts a pressure on the solid immersed which is equal to the weight of the displaced fluid.

Shouldn't say pressure there. It exerts that force (upwards). Pressure is force per unit area.
When an object is floating, at rest, what force would that be equal to?

 

[utkarshakash]

Shouldn't say pressure there. It exerts that force (upwards). Pressure is force per unit area.
When an object is floating, at rest, what force would that be equal to?

Weight of the displaced fluid which is equal to (Density of liq.*vol of solid immersed*g)

 

[haruspex]

Weight of the displaced fluid which is equal to (Density of liq.*vol of solid immersed*g)

True, but what I meant was, what other force is it equal to?

 

[utkarshakash]

True, but what I meant was, what other force is it equal to?

Its own weight.(Mass*g)

 

[haruspex]

Right. Now, what will the increased air pressure do to the mass and volume of the wood?

 

[utkarshakash]

Right. Now, what will the increased air pressure do to the mass and volume of the wood?

Nothing

 

[haruspex]

Nothing

Well, it won't change the mass, but it might squeeze it a bit.