## Why not crushed by air?

1. The problem statement, all variables and given/known data
It has been estimated that the mass of nitrogen alone in the column of atomsphere above each square metre of the Earth's surface amounts to about 8 tonnes. Why aren't we crushed by this?

2. Relevant equations
none

3. The attempt at a solution
Air in the atomsphere is not just nitrogen and they are dense as the question suggested. Are we are not crushed by them essentially because of Newton's third law?

We are surrounded by dense air in ground level. What kind of molcules are they? They surround us and collide with our bodies and make us not as cold if without them.

The different densities of air all exert forces to the next layer and due to the third law there is an upward force from the succeeding layers. These layers does the same and you get somewhat of a cancellation of forces on each layer. Hence equilibrium is reached for each layer as there is no net force and we are not crushed by the upper level air. So a cushioning effect is passed down through the layers.

The image tries to illustrate this.
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 We can't be crushed by earth's atmosphere because air spreads out equally. The only way you could be crushed by air is if you were in a tank and someone kept pumping in air.
 Recognitions: Gold Member Science Advisor Staff Emeritus The air pressure at the surface of the earth is 14.7 psi. This force does not act in a single direction (downwards) -- it acts in all directions. In other words, the air pushes on your left side with the same force that it pushes on your right side. The force is balanced on both sides, so you don't go sliding sideways. The same is true of the forces in any two directions, including up and down. This is easily understood when you realize that pressure is caused by molecules of air moving in all directions, randomly, imparting forces upon things they strike from any direction. Water is essentially imcompressible, meaning that it does not change volume much with changing pressure. Thus, we stay the same size even when the air pressure changes due to weather or when we walk up hills. - Warren

## Why not crushed by air?

 Quote by chroot The air pressure at the surface of the earth is 14.7 psi. This force does not act in a single direction (downwards) -- it acts in all directions. In other words, the air pushes on your left side with the same force that it pushes on your right side. The force is balanced on both sides, so you don't go sliding sideways. The same is true of the forces in any two directions, including up and down. This is easily understood when you realize that pressure is caused by molecules of air moving in all directions, randomly, imparting forces upon things they strike from any direction. Water is essentially imcompressible, meaning that it does not change volume much with changing pressure. Thus, we stay the same size even when the air pressure changes due to weather or when we walk up hills. - Warren
But the net force of the air in the atomsphere is towards the earth because of gravity. I was trying to illustrate the net effect with the arrows. Is my diagram correct? If so it seems that we are not crushed by air above us because the air the surrounds us cusions the above air. Correct? And the air that surrounds us dosen't crush us because of the reason you suggested.
 Recognitions: Gold Member Science Advisor Staff Emeritus The net force due to the air pressure is zero, because the air pushes on you from every direction. I cannot understand your 'cushioning' concept, but I can tell you immediately that it's not useful. - Warren
 Have you ever tried to suck all the air out of a plastic coke bottle? Yup, it gets crushed. Our bodies would too if we weren't filled with air and liquid.

 Quote by chroot The net force due to the air pressure is zero, because the air pushes on you from every direction. I cannot understand your 'cushioning' concept, but I can tell you immediately that it's not useful. - Warren
Imagine most of the nitrogen is on the top few layers on my diagram. It's dense as specified in the question - although maybe not because it is spread out over a large volume. Gravity acts it towards the earth. So why doesn't it all come down and crush us all at once? The reason is as I suggested in my previous post.
 Recognitions: Gold Member Science Advisor Staff Emeritus No. No offense, but your notion is nonsense. We understand gas very well via a theory known as statistical mechanics, which is derived immediately from Newton's laws of motion. The reason the gas doesn't all come down at once is: Thermal energy The individual gas particles have thermal energy, and move about randomly. They rise and fall in ballistic trajectories, just like baseballs (except there are many, many collisions). - Warren

 Quote by chroot No. No offense, but your notion is nonsense. We understand gas very well via a theory known as statistical mechanics, which is derived immediately from Newton's laws of motion. The reason the gas doesn't all come down at once is: Thermal energy The individual gas particles have thermal energy, and move about randomly. They rise and fall in ballistic trajectories, just like baseballs (except there are many, many collisions). - Warren
So you think the gravitational force on the air molecules are neglible compared to their random forces from thermal energy. Although gravity is still a factor because air dosen't just escape into space. However hydrogen does because it's even lighter. So there is still a net force toward the surface of the earth from the atomsphere. I am talking in a very macroscopic way.

Is that the reason why some bollons rise but some don't. The ones that do are filled mostly with hydrogen.

As for the original question, the answers in the book suggested: "While the atmosphere exerts a pressure on us, we exert an equal pressure back." The pressure on us must be very small because the effect of gravity is tiny. The overriding force are random forces due to thermal motion as you say. That is why they don't crush us because it's also good that they don't escape into space as would be predicted without gravity.

 Quote by pivoxa15 Is that the reason why some bollons rise but some don't. The ones that do are filled mostly with hydrogen.
Helium actually, but that's just bifurcating bunnies...

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 Quote by pivoxa15 So you think the gravitational force on the air molecules are neglible compared to their random forces from thermal energy. Although gravity is still a factor because air dosen't just escape into space. However hydrogen does because it's even lighter. So there is still a net force toward the surface of the earth from the atomsphere. I am talking in a very macroscopic way.
Of course there is a force on the earth's surface due to the weight of the atmosphere. But there's no net force on you due to atmospheric pressure, since the air is pressing on you from all sides. (Actually, there is a small upward buoyant force due to the change in pressure with height--the upward buoyant force on you will equal the weight of the air you displace.)

 Is that the reason why some bollons rise but some don't. The ones that do are filled mostly with hydrogen.
The reason some balloons rise is because they are light enough (they are filled with a gas less dense than air) that the buoyant force from the surrounding air is greater than the weight of the balloon plus its contents.

 As for the original question, the answers in the book suggested: "While the atmosphere exerts a pressure on us, we exert an equal pressure back."
That's not a very good answer, since that statement would be true whether we were crushed or not! (Imagine an elephant stepping on a peanut. The peanut exerts the same force on the elephant that the elephant exerts on the peanut--but the peanut is surely crushed.)
 The pressure on us must be very small because the effect of gravity is tiny. The overriding force are random forces due to thermal motion as you say. That is why they don't crush us because it's also good that they don't escape into space as would be predicted without gravity.
The pressure on you is not small--it's about 14.7 lbs per square inch (at sea level). But we are perfectly capable of handling it. (For one thing, we wisely keep our lungs full of air at the same pressure as the outside air.)

 Quote by Doc Al The pressure on you is not small--it's about 14.7 lbs per square inch (at sea level). But we are perfectly capable of handling it. (For one thing, we wisely keep our lungs full of air at the same pressure as the outside air.)
But the net pressure is virtually 0 as net force is 0.

But imagine a person standing on the ground. He is more exposed to air on top of him than from below him so there is a net force downwards from the atomsphere? And if you factor in gravity than that is another tiny bit more net force directed towards your feet.

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 Quote by pivoxa15 But the net pressure is virtually 0 as net force is 0.
Sorry, but this is incorrect. The fact that the net force might be zero tells you nothing about the pressure. Recall my example of the elephant crushing the peanut. The net force on the peanut is zero, but the pressure is very high. Pressure is a force per unit area.

Further, air pressure is not zero!

 But imagine a person standing on the ground. He is more exposed to air on top of him than from below him so there is a net force downwards from the atomsphere?
That would make some sense if your feet made an airtight seal with some surface, but that's unlikely to be the case. Rather than a person standing, imagine a suction cup stuck on a smooth surface. It sticks to the surface because air pressure pushes it. When you break the seal, air (at atmospheric pressure) gets inside and neutralizes the net force from the air.

Note that the orientation of the suction cup and surface is irrelevant: the surface can be horizontal, vertical, sideways, upside down--it doesn't matter. Air pressure acts in all directions.
 And if you factor in gravity than that is another tiny bit more net force directed towards your feet.
I don't know what you mean by "factor in gravity"; gravity is the source of air pressure.

 Quote by Doc Al Sorry, but this is incorrect. The fact that the net force might be zero tells you nothing about the pressure. Recall my example of the elephant crushing the peanut. The net force on the peanut is zero, but the pressure is very high. Pressure is a force per unit area. Further, air pressure is not zero!
Force is a vector but area is a scalar. So if we assume net force is 0 than how can there be nonzero pressure=force/area?

Or are you saying even though if you add all the forces up, it equals 0, the area these forces act on may not be equal. i.e. There are two forces 8N and -8N. The 8N force act on 2m^2 of the surface only whereas the -8N force act on 3m^2 of the surface only. In this way net pressure is nonzero.

But the mouse could also get completely crushed even if total force and pressure on it is 0. i.e. there could be opposite force and pressure (hence net 0) on top of it and from the bottom. The top exerted by the elephant and the bottom by the ground.

 Quote by Doc Al That would make some sense if your feet made an airtight seal with some surface, but that's unlikely to be the case. Rather than a person standing, imagine a suction cup stuck on a smooth surface. It sticks to the surface because air pressure pushes it. When you break the seal, air (at atmospheric pressure) gets inside and neutralizes the net force from the air. Note that the orientation of the suction cup and surface is irrelevant: the surface can be horizontal, vertical, sideways, upside down--it doesn't matter. Air pressure acts in all directions.
Those things are amazing. There was a time when I didn't know how these thigns worked and thought that new physics was needed to explain them. Then I realised it was only the air around us that was causing it to suck.

 Quote by Doc Al I don't know what you mean by "factor in gravity"; gravity is the source of air pressure.
But a weak source? I was trying to say that on the surface of the earth, the net force of air is towards the earth is not 0 but not much higher either.

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 Quote by pivoxa15 Force is a vector but area is a scalar. So if we assume net force is 0 than how can there be nonzero pressure=force/area?
Area is a vector quantity. Pressure is a scalar.

Note: If the edges of the soles of your shoes make airtight seals with the floor below them, then there will be a net downward force (because there's no air below your feet) of about 1000-2000lbs.

 Quote by Gokul43201 Area is a vector quantity. Pressure is a scalar. Note: If the edges of the soles of your shoes make airtight seals with the floor below them, then there will be a net downward force (because there's no air below your feet) of about 1000-2000lbs.
Force is a vector quantity and if area is a vector quantitiy than Pressure=Force/Area meaning a vector divide another vector. How does that make sense

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$$P = \frac{\vec{F} \cdot \vec{A}}{|A|^2}$$
$$\vec{dF}=P~\vec{dA}$$