How does buoyant force relate to weight and pressure?

[ritwik06]

Please look to the thread "9th Homework Doubts" first.

1.A rectangular vessel of volume 100 cm * 60 cm * 200 cm is completelyfilled with a water. Neglecting atmospheric pressure:
find the net force experienced by a metal foil placed at depth of 5 cm from the free surface.
Why ist it 0?

2.If a cuboid is placed at some depth in water. My book says that the upper face experiences pressure due to the weight of the liquid column above it. But why does the lower face experience pressure. The water under it exerts force downwards due to gravity. Isnt it?

My book says:

The resultant pressure on the cuboid will be upward, so it is responsible for the upthrust on the cuboid due to water.

Why upward. Pressure is scalar!

3. If the tube of a faulty barometer is pushed down into the mercury trough, the barometric height will further decrease. Why does this happen?

4.

If a magnet is cut into exactly 2 equal parts , the magnetic strength of this part is half the magnetic strength of the original magnet.

Why does it get halved. What is the formula for magnetic strength>?
What is meant by uniform magnetic field?

5. If I am provided with two similar bars, one is a magnet and the other is soft iron. How can I distinguish between them with out using any other thing?

 

[PhanthomJay]

1.A rectangular vessel of volume 100 cm * 60 cm * 200 cm is completelyfilled with a water. Neglecting atmospheric pressure:
find the net force experienced by a metal foil placed at depth of 5 cm from the free surface.
Why ist it 0?

2.If a cuboid is placed at some depth in water. My book says that the upper face experiences pressure due to the weight of the liquid column above it. But why does the lower face experience pressure. The water under it exerts force downwards due to gravity. Isnt it?

My book says:

Why upward. Pressure is scalar!

3. If the tube of a faulty barometer is pushed down into the mercury trough, the barometric height will further decrease. Why does this happen?

4.
Why does it get halved. What is the formula for magnetic strength>?
What is meant by uniform magnetic field?

5. If I am provided with two similar bars, one is a magnet and the other is soft iron. How can I distinguish between them with out using any other thing?

For question 1, hydrostatic pressure acts in all directions, upwards and downward and sideways and every way. Its pressure at a given distance below the free surface is just p = (water density)(depth). This is a thin foil, mind you. But in question 2, there is greater pressure on the bottom of the cuboid, since it has a greater depth below the surface than its top. Pressure is a scalar, but force (pressure times area) is a vector. The force on the cuboid up is greater than the force on the cuboid down. Whether or not the cuboid moves up depends on its weight. And although gravity exerts a force on the water down, this is unrelated to the force on the cube.

 

[ritwik06]

And although gravity exerts a force on the water down, this is unrelated to the force on the cube.

I understand everything except the above quoted line!

 

[PhanthomJay]

I understand everything except the above quoted line!

I was responding to your question, "The water under it exerts force downwards due to gravity. Isnt it?" The water under it exerts a force upward due to hydrostatic pressure. There is a downward force on the water below the block due to gravity, but this has nothing to do with the upward force on the block, that is, the upward force would be the same regardless of how much water was below the block. But maybe I misinterpreted your question.

 

[ritwik06]

I was responding to your question, "The water under it exerts force downwards due to gravity. Isnt it?" The water under it exerts a force upward due to hydrostatic pressure. There is a downward force on the water below the block due to gravity, but this has nothing to do with the upward force on the block, that is, the upward force would be the same regardless of how much water was below the block. But maybe I misinterpreted your question.

Thanks! But I knew that. I was just thinking that how come the water will exert pressure upwards when the weight is acting downwards. I think there is no answer to that 'cause its a characteristic property of fluids, :zzz: isn't it?

 

[PhanthomJay]

Thanks! But I knew that. I was just thinking that how come the water will exert pressure upwards when the weight is acting downwards. I think there is no answer to that 'cause its a characteristic property of fluids, :zzz: isn't it?

Yes, good point, it does get confusing. . Oddly enough, it is the gravity force on the column of water above the block, that is, the weight of that water column, that is responsible for the downward force on the top of the block, perpendicular to its surface. At the bottom of the block, there is no column of water above it, just the pressure of the water depth at that point that acts in all directions, but it is the vertically upward force (presure times area) that acts on the block. There's the weight of the block itself that also acts down on the block. Bottom line is that the difference between the water force on the bottom and the water force on the top is called the 'buoyant force', and is identically equal to the weight of the water displaced by the block , that is, its volume times the water density. Now if that doesn't confuse you, nothing else will.