Conceptual Issue Dealing With Atmospheric Pressure

In summary, the steel cube floats on mercury due to the atmospheric pressure which pushes down on the steel cube and also pushes down on the mercury which pushes the steel cube back up.
  • #1
ScareCrow271828
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Homework Statement


A 1m^3 steel cube is to be floated on mercury (specific gravity=13.6). On each side of the cube there is a 5mm clearance. Assume that the container is open to atmospheric pressure at 100kPA. Find the mass of the mercury.

Homework Equations


P=F/A

The Attempt at a Solution



I sum-mated the forces in the vertical direction and combined that with an equation for buoyancy. Then I solved for the height of the mercury around the cube, found the volume of the mercury and multiplied it by its density.

My question is: is it right to assume that atmospheric pressure has cancelling effects because it pushes down the steel cube but also pushes down the mercury which would push the steel cube back up? This makes sense conceptually to me, but I am having trouble understanding that since P∝1/A. It seems like by that equation atmospheric pressure would have different effects on the block and on the mercury.
 
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  • #2
ScareCrow271828 said:
atmospheric pressure has cancelling effects because it pushes down the steel cube but also pushes down the mercury
Yes, it cancels. Can you go into more detail on why you think it would not cancel?
 
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  • #3
haruspex said:
Yes, it cancels. Can you go into more detail on why you think it would not cancel?

Thank you! That was my intuition I am trouble understanding how atmospheric pressure acts as a pressure -or at least has units of pressure (Pa)- but in this case seems to act independent of area. By P=F/A shouldn't pressure be dependent on area. Or more specifically Inversely proportional to area?

Ive always thought of pressure as kind of a deform-able blanket that covers and weighs everything evenly so it makes sense to me conceptually. I am just having trouble understanding it mathematically. Wouldn't there be a greater force due to the atmosphere if the pressure was over a greater area since F∝PA?

Another question if you could:
Mass flow rate is equal to the product of density, velocity,and area or ⋅m=ρA∨. Therefore if area is decreased velocity has to increase. The increase in velocity makes sense to me but it seems like that would also increase the pressure since pressure is dependent on the force that molecules exert on surfaces. How would shooting molecules at a higher speed not increase that force? But by Bernoullis equation ∨∝1/P? How does increasing the velocity and therefore decreasing the pressure make any sense conceptually?

Sorry for the simple questions
 
  • #4
ScareCrow271828 said:
Wouldn't there be a greater force due to the atmosphere if the pressure was over a greater area since F∝PA?
Yes, there is a greater force over the upper surface of the cube than there is on the surrounding margin of mercury. But the force on the mercury is transmitted straight down to the bottom end of that margin, i.e. to the level of the base of the cube. At that point, the pressure infinitesimally above the level must equal that immediately below, and that pressure must also be the same all across the underside of the cube. So the force on the underside of the cube due to the atmosphere is the same as that on the top surface.
ScareCrow271828 said:
How would shooting molecules at a higher speed not increase that force?
The movement of the molecules does not create the pressure difference. Rather, the pressure difference accelerates the molecules. If there is a reduction in area in a pipe, the molecules must accelerate as they transit to the narrower section, so the pressure must be greater before the narrowing than after. If it widens again later, the pressure difference goes the other way to slow them down again.
 
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  • #5
haruspex said:
Yes, there is a greater force over the upper surface of the cube than there is on the surrounding margin of mercury. But the force on the mercury is transmitted straight down to the bottom end of that margin, i.e. to the level of the base of the cube. At that point, the pressure infinitesimally above the level must equal that immediately below, and that pressure must also be the same all across the underside of the cube. So the force on the underside of the cube due to the atmosphere is the same as that on the top surface.

The movement of the molecules does not create the pressure difference. Rather, the pressure difference accelerates the molecules. If there is a reduction in area in a pipe, the molecules must accelerate as they transit to the narrower section, so the pressure must be greater before the narrowing than after. If it widens again later, the pressure difference goes the other way to slow them down again.
Great! Thank you very much!
 

Related to Conceptual Issue Dealing With Atmospheric Pressure

1. What is atmospheric pressure?

Atmospheric pressure is the weight of the air pressing down on the Earth's surface. It is caused by the force of gravity pulling the air molecules towards the Earth's center.

2. How is atmospheric pressure measured?

Atmospheric pressure is measured using a device called a barometer. It can be either a mercury barometer or an aneroid barometer. The measurement is typically given in units of pressure such as millibars or inches of mercury.

3. What factors affect atmospheric pressure?

Several factors can affect atmospheric pressure, including altitude, temperature, and humidity. As altitude increases, atmospheric pressure decreases. Higher temperatures lead to lower pressure, while higher humidity can increase pressure.

4. What is the relationship between atmospheric pressure and weather?

Changes in atmospheric pressure can indicate changes in weather patterns. A decrease in pressure is often a sign of incoming bad weather, while an increase in pressure can indicate clear skies and good weather. However, other factors such as temperature and wind patterns also play a role in determining weather conditions.

5. How does atmospheric pressure impact living organisms?

Living organisms, especially those that live at high altitudes, are adapted to specific atmospheric pressures. Changes in pressure can affect the availability of oxygen and other gases, leading to difficulties in breathing and other health issues. Extreme changes in atmospheric pressure can also cause damage to organisms and their environments.

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