# B Why don't we take air pressure into account in calculations?

#### Dishsoap

Summary
When calculating normal forces of, e.g., a block sliding down an incline (with friction), we disregard the weight of the air on top of the block. Why?
I once was explained the answer to this question - something about both the air and the object being incompressible. However, for the life of me I cannot seem to reproduce the answer of why we ignore air pressure when doing basic calculations.

If it matters, the particular system I'm interested in is that of a submerged particle in a fluid. Does the frictional coefficient of the particle to the surface depend on the amount of water above it? My intuition tells me two things:

a) that a particle that is even slightly more positively buoyant (with respect to the fluid) will float to the top regardless of how much fluid is on top of it, and
b) the frictional coefficient is not dependent on the amount of fluid above it (pushing a penny at the bottom of a pool and at the bottom of a beaker requires an identical amount of work).

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#### anorlunda

Mentor
Gold Member
I don't understand your question. A penny at the bottom of the pool is not a penny at the surface. You are using "water on top of it" and "at the surface" in the same sentence.

Are you thinking of something like a floating log? A very light log will have less wetted surface than a log just slightly less dense than water.

#### russ_watters

Mentor
Summary: When calculating normal forces of, e.g., a block sliding down an incline (with friction), we disregard the weight of the air on top of the block. Why?
Because air pressure acts on all sides of the block.
a) that a particle that is even slightly more positively buoyant (with respect to the fluid) will float to the top regardless of how much fluid is on top of it,
That doesn't appear to be the same issue. But yes, an object with a positive net force in a fluid (buoyancy minus weight) will float.
b) the frictional coefficient is not dependent on the amount of fluid above it (pushing a penny at the bottom of a pool and at the bottom of a beaker requires an identical amount of work).
Friction between what and what?

#### Chestermiller

Mentor
For a block sitting on a table or incline, it is true that there is air pressure pushing down on the top of the block toward the contact surface. But there is also air in the interstices of the interface region between the block and the table pushing back in the opposite direction. The table and the block are not perfectly flat. They only make actual contact at the tips of the surface asperities. So the air in the interstices balances the pressure on the top of the block, and the actual contact force between the block and the table is just the weight of the block. This is the same force as if the system of block and table were sitting in vacuum.

#### 256bits

Gold Member
....we disregard the weight of the air on top of the block....

You regard the weight of the air on top of the block - for something like a suction cup.

#### Dishsoap

I don't understand your question. A penny at the bottom of the pool is not a penny at the surface. You are using "water on top of it" and "at the surface" in the same sentence.

Are you thinking of something like a floating log? A very light log will have less wetted surface than a log just slightly less dense than water.
To be clear, I'm not talking about the air-water interface, I'm talking about the solid surface on which the object sits (the bottom of the pool, in this case).

Friction between what and what?
In the thought experiment, the friction between the "block" and whatever it's moving on. In my experiment, I have an SiO2 device submerged in water on top of an SiO2 substrate. I'm curious about the friction between the device and the substrate.

For a block sitting on a table or incline, it is true that there is air pressure pushing down on the top of the block toward the contact surface. But there is also air in the interstices of the interface region between the block and the table pushing back in the opposite direction. The table and the block are not perfectly flat. They only make actual contact at the tips of the surface asperities. So the air in the interstices balances the pressure on the top of the block, and the actual contact force between the block and the table is just the weight of the block. This is the same force as if the system of block and table were sitting in vacuum.
If our block is atomically flat, does this change things?

#### Chestermiller

Mentor
If our block is atomically flat, does this change things?
If you can expel that air, or in your case the water, from the interface between the block and the surface it is resting on, say by using a suction cup or perfectly flat surfaces, that does change things.

#### Dishsoap

If you can expel that air, or in your case the water, from the interface between the block and the surface it is resting on, say by using a suction cup or perfectly flat surfaces, that does change things.

In this case, is the normal force (or frictional force) dependent on the amount of water in the dish?

#### DaveC426913

Gold Member
In this case, is the normal force (or frictional force) dependent on the amount of water in the dish?
No. Similarly, divers standing on the bottom of a lake do not feel a "downward push" of the water above them. This is the case whether the lake is 30 feet deep or 100 feet deep.

What they feel is a uniform pressure from all sides.

#### Chestermiller

Mentor
In this case, is the normal force (or frictional force) dependent on the amount of water in the dish?
If you expel the air from under the block then, as in the case of a suction cup, the normal force and frictional force depends on the pressure at depth.

#### DaveC426913

Gold Member

Homework Helper
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2018 Award
Except for the suction cup effect described above, in general the effect of the atmosphere, by Archimedes' principle, is to add a slight amount of buoyancy to the object in these problems, like a block on an incline. In general, the buoyancy can usually be neglected, but it is this buoyancy that makes a helium balloon or hot air balloon rise in the air. $\\$ Edit: And to see some calculations where this buoyancy is taken into account, see https://www.physicsforums.com/threads/lifting-a-man-with-100m-3-of-helium.943829/#post-5972396 and the "links" in post 3 of this "link".

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#### FactChecker

Gold Member
2018 Award
Suppose there is a complete lack of water/air between the object and the ground and none can enter. Then there would be no additional force from above, but there would be a lack of force from below and the net force would increase downward.

#### JT Smith

As ChesterMiller points out:

If you did this same experiment in a vacuum jar, the block would weigh exactly the same.(Would you expect otherwise?)
The buoyant force due to air on a block is actually pretty easy to measure. It does make a small difference.

#### DaveC426913

Gold Member
The buoyant force due to air on a block is actually pretty easy to measure. It does make a small difference.
Yeah. I rethought that.
Deleted as apocryphal.

"Why don't we take air pressure into account in calculations?"

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