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The value of atmospheric pressure is 101325 Pascal, which is a large value which implies the force exerted by atmosphere is 101325 N m$^{-2}$. Surely this can not be neglected, so why is atmospheric pressure neglected almost all the time in introductory physics?

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    $\begingroup$ What do you mean by "almost at all time atmospheric pressure is been neglected"? $\endgroup$ – ACuriousMind Oct 26 '15 at 15:59
  • $\begingroup$ In my school while dealing with problems in classical mechanis we never consider the effect of atm. Pressure $\endgroup$ – cool joey Oct 26 '15 at 16:00
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    $\begingroup$ Well, what effects in particular are you worried about? You could always check to see if pressure would impact it. Yes, most basic mechanics problems ignore drag effects (because those are hard, amongst other things). But, I live where the air pressure is ~10% less than sea level, and basic physics all works pretty much the same in spite of that. $\endgroup$ – Jon Custer Oct 26 '15 at 16:03
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    $\begingroup$ Are you really asking about the effect of pressure? or are you asking about the effect of air resistance? Pressure, in and of itself, usually has no significance in most high-school homework problems. Whereas airflow... You've heard of the phrase "rocket science?" Well a huge part of what makes rocket science difficult is modelling how the rocket interacts with the air that it flies through. $\endgroup$ – Solomon Slow Oct 26 '15 at 16:13
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    $\begingroup$ Why are the sun's tidal forces always neglected too? $\endgroup$ – whatsisname Oct 26 '15 at 21:58
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The atmospheric pressure is quite large, but it is also about the same everywhere. For example, if you hang a tire swing from a tree, there is atmospheric pressure on it from below, above, left right, front, and back. However, the atmospheric pressure is pretty much the same from all these directions and so there is little net force on the tire and the rope has to support almost the entire weight.

There is a small buoyant force from the atmospheric pressure; this makes the tension in the rope holding up the swing a bit smaller than it would be without the atmosphere.

Also, if you reduce the pressure inside an airtight container, you'll be able to see dramatic effects of atmospheric pressure. A classic demonstration involves boiling a small amount of water in the bottom of an aluminum soda can, then turning the can upside-down in cold water. The water vapor in the can condenses, reducing the pressure in the can, and the atmospheric pressure outside the can quickly crushes it. The can doesn't crush under ordinary circumstances, though, because the atmospheric pressure on the inside is the same as the pressure on the outside.

So we could take atmospheric pressure into account in every calculation, but usually it does not result in a large net force on objects of interest because it's about the same everywhere. You're right that atmospheric pressure is strong, though, so when it isn't roughly balanced everywhere it can have dramatic effects.

You will also need to account for atmospheric pressure when doing thermodynamics, for example finding the boiling point of water.

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    $\begingroup$ So what i understood is that we neglect air pressure because its effect is nullified since it acts in all direction with almost same magnitude.Am i correct $\endgroup$ – cool joey Oct 26 '15 at 16:10
  • $\begingroup$ If a block of surface area 1m^2 is kept on the table air exert a force of 101325 newton which is far greater than block's weight so why we neglect air pressure $\endgroup$ – cool joey Oct 26 '15 at 16:14
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    $\begingroup$ Because the air underneath the block is exerting approximately equal pressure upwards. If you truly made a seal with the table so that no air could get it, it would be extremely difficult to lift the block. This is how a suction cup works. $\endgroup$ – Mark Eichenlaub Oct 26 '15 at 16:18
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Short Answer

Adding in that effect does not alter the answer that much or is too hard.

Longer Answer

Real-world conditions are ignored for several reasons:

  • The inclusion of that effect does not alter the answer that much, and most students (or instruments) may not be able to calculate the effect of it since it's so small. If the effect is immeasurably small, then why bother?
  • The required effort and math to model those affects are not in reach of the student. This is why introductory physics problems often happen in space, or in a vacuum, or on frictionless surfaces.
  • The effects of real-world conditions is not the point of the class. As in so many things, baby steps come first. For instance, if one does not understand forces, adding in more forces to a problem will not help them. It will only confuse and be a negative experience overall.

Approximations and Why We Can Ignore Them

  • Atmospheric Pressure: much like the acceleration due to gravity, atmospheric pressure doesn't actually change the outcome of most problems because the pressure on the top of an object is really close to the pressure on the bottom. If the pressure difference is significant (like in an inflated tire or balloon), this effect is included. One should also note that pressure difference is when pressure generally matters, not absolute pressure.
  • Acceleration due to Gravity on Earth: technically this value changes with height, so every time a slight variation in height occurs, you should have a new value. On the surface of the earth and concerning most everyday objects, this change in value is REALLY SMALL so it's ignored.
  • Friction: friction is often excluded because it's not the point of the homework or lecture. A professor or teacher is busy explaining a different concept, and they don't want to confuse their students. Sometimes, and in special circumstances, it can be neglected when doing "real" physics/engineering. In some cases, like with air resistance, the students do not have the math/models required to accurately account for it.
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Because physics problems are usually abstracted idealizations that only approximate real world conditions. When real conditions have to be taken into account it is called "engineering". Otherwise it's the apocryphal spherical horse moving in a vacuum...

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    $\begingroup$ Pretty thought, but I disagree. While engineering does have an emphasis on modeling real-world conditions, I find that both engineering and physics have effects or conditions they choose to ignore. When under scrutiny, every model made by science/engineering has a level of "good enough." Spherical cow approximations simply have ludicrous amounts of "good enough" in them. $\endgroup$ – PipperChip Oct 26 '15 at 22:57

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