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The school experiment of hanging two balloons, one filled with air, other empty, on a ruler, show that air has weight.

A person has weight. It's shown on a weighing machine. A pencil has weight. It's shown on a sensitive weighing machine.

None of these machines show the weight of air even under an open sky. Why?

I researched online. Found the following:

  1. Air column under an open sky when standing on the surface of the Earth is heavy enough to be shown even on the large weighing machine.

So, both of my weighing machines should show the weight of of the atmosphere.

  1. Air pressure inside the weighing machines balance the air pressure / weight outside.

That do not seems right. Air inside machine do not change by taking it out under open sky. Its pressure obviously cannot change thus. How do it balance both the air weight in room and under open sky?

Also, if it do where the extra energy came from?

Also, air molecules in the weighing machines have to vibrate more to have more pressure, right? How else would the increase in pressure manifest / happen? More vibration means more temperature because thats what temperature is. We observe no such thing.

I am aware of action reaction phenomena. If I push wall, wall push me back with equal and opposite force. However, this cannot solve this because then the weighing machines would not show weight of me and pencil.

  1. An answer to this question here says pressure is equalized on all sides.

I do not see how this can help even if true my weighing problem. Even if I am squeezing my weighing machines at all sides the upside (where scale is) would show the weight. The body of the weighing machine made of steel and thick enough can handle that pressure at sides.

The pressure is not equal at all sides. (i) There is no pressure from ground direction (upwards). (ii) Sides of my yard where I stand under open sky are much shorter than air length above me (100 km vs 20 ft).

I am careful in changing only one variable. The location of the machines. My friend did the opposite experiment with me at the same time and about 2 feet from me. He got himself weighted under open sky and in the room. His weight comes equal at both places. Why?

I can see that it is something with confining. Air in a balloon is exerting less pressure upwards to counter its weight. May be due to equal sideways and upwards dimensions. The air-filled balloon is somewhat like a ball in my experiment, more air pressure is going sideways than upwards. I filled an oval-shaped balloon with air, hang it with my hand long side up. It quickly fall to side. So, less long dimension get more pressure. Length of atmosphere upwards is just 100 km, breadth is 40,000 km at least at one side wherever you are on earth and on both sides if you are at equator. So, this do seems like the reason why air show no weight on my weighing machine. The pressure of air upwards is more than its weight downwards. Is that it?

This does not explain why sun has fusion though. Where do the pressure comes from if gravity does not work that way? You see if air on earth given column of just 100 km can cancel its own weight plasma in sun which is much more vibrant and have much larger dimension to move into would easily cancel its own weight. Then there would not be enough pressure due to gravity (weight) to reach temperature of millions of degrees of centigrade to start fusion.

Why do observation show air is weightless?

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    $\begingroup$ Agreed that balances and scales are designed and calibrated to measure weight of added bodies. However, how is air if it has weight not an added body in that sense? Do it has anything to do with density? Pencils have less density than me. Their weight is shown on the weighing machines. If I blow high pressure air on the weighing machines their weight is measured. I did that experiment. You can repeat it if you like. Density dont solve this. $\endgroup$
    – Atif
    Jan 11 at 11:57
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    $\begingroup$ My scales are fine. I know this because of various other things I have weigh on many other machines. How can pressure of air inside machine vary to match with whatever the outside pressure is? How do it physically manifest? Mass of air inside machine dont change so it must be velocity of molecules of air inside, right? Where do the energy come from to increase their velocity? Also, why temperature do not increase? $\endgroup$
    – Atif
    Jan 11 at 12:12
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    $\begingroup$ @Solomon Your teacher cheated, didnt do her job. Mine did. Also, you can do that experiment now. I did. You dont have to worry about buoyancy in this. I strongly suggest all answerers and commenters to do the experiments. Its science after all, not philosophy. Thanks. $\endgroup$
    – Atif
    Jan 11 at 13:04
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    $\begingroup$ @Solomon Thats cheating. The experiment is set up to fail. Its ignored that the experiment is taking place in atmosphere. We live in a sea of air. Ofcourse everything thats lighter than air will go upwards. This is why its important to do the experiment with air-filled balloons. $\endgroup$
    – Atif
    Jan 11 at 13:50
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    $\begingroup$ You can do the air filled balloon experiment in normal room. Try it. Its dead easy. Air filled balloon will tilt downwards. $\endgroup$
    – Atif
    Jan 11 at 14:04

3 Answers 3

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All your examples (humans, pencils, etc) are solid bodies. Air is a fluid. It acts differently on surfaces. Basically, unlike solids, it does not preserve the direction of the applied force. A solid, when pushed down on, transmits this force to lower objects as a force pointed downwards. Fluids act differently. For instance, if you take a U-shaped tube, fill it with water and push on the water down in one arm (e.g. through a movable piston), the water will produce/transmit an upward force in the other arm.

Similarly, as @gsomani said, when you try to weigh an air column, you have to make sure that that column has no access to the other side of the weighing plate, as in that case, in addition to the downward force it exerts on the plate from above, it will also push on the plate from beneath (cf. with the U-tube example). Provided the plate is not too thick these two forces will cancel each other almost perfectly.

If you really want to weight an air column, you have to make sure it has access only to one side of the probing surface. One possible way is to use for this purpose the surface of the water in the U-tube discussed above. Make sure the air doesn't push on the other side of the U-tube by sealing it, and voila, you a weighing scales for air. If you do this, you will find out that the entire atmospheric column from the surface of the Earth up to stratosphere and above weighs roughly as much as 10 meter-high column of water with the same footprint area. 10 meters-high U-tube is not an easily thing to maintain, so you can make it shorter by using more dense fluid, like mercury. This is exactly what Toricelli (a student of Galileo's) did to literally "weigh atmosphere". He found that the atmospheric column weighs roughly as mercury column of $\approx 780$mm high (with the same footprint area).

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    $\begingroup$ #John "Air is a fluid. It acts differently on surfaces. Basically, unlike solids, it does not preserve the direction of the applied force." Is it in anyway different than saying air has no weight? Weight is nothing but effect of gravity therefore downward force. If air has no downward force as you said then air has no weight. You qualified it with "surface" so you are saying that air has no weight on surface of earth. $\endgroup$
    – Atif
    Jan 11 at 18:10
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    $\begingroup$ 1. You said "[Air] does not preserve the direction of the applied force" so the direction is lost. If direction is lost what you have cannot be force because force is a vector. If there is no downward force there will be no effect on weighing machine. Without force there cannot be any movement. Force is defined as what cause movement. 2. "And I did not say air does not exert force in the downward direction". You said that. Your previous quote said that direction is not preserve. 3. If there is a downward force why its effect is not shown on weighing machine? $\endgroup$
    – Atif
    Jan 12 at 5:22
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    $\begingroup$ "if you take a U-shaped tube, fill it with water and push on the water down in one arm (e.g. through a movable piston), the water will produce/transmit an upward force in the other arm." I can take rocks in the U-shaped tube, push it down, the rocks will push upward force on the other arm. How is that different from water? I can take any solid, even one that don't have gaps in between, fill the tube with powder for example. It will become a little bit denser when pushed, it will not keep getting denser all the way to black hole. After a little pushing it will start rising at the other hand. $\endgroup$
    – Atif
    Jan 12 at 6:02
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    $\begingroup$ You are implying that weight, which is a force, is for fluids not acting downwards as it do for solids. You are saying that its somehow acting side ways. How its weight then? Weight is defined as downward force. How can we say that air even have a property called weight if its not showing the defining behavior of acting downwards? $\endgroup$
    – Atif
    Jan 12 at 9:38
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    $\begingroup$ 1. Fluids put pressure wherever its molecules hit. On the upper surface of weighing machine it then should put an additional force. The weighing machine should show more weight therefore, not zero. 2. There cannot be any gradient in pressure on the upper surface of weighing machine because air column above is of same height, of same material (air), same temperature etc. Every square inch of the upper surface of the weighing machine would get some pressure. $\endgroup$
    – Atif
    Jan 12 at 10:05
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It is because air is not a single column just above the weighing machine. There is air all around it including below the weighing machine which leads to net upward buoyancy force.

The buoyancy force is very small compared to its weight due to air being much less dense(about a factor of 1000) than weighing machine. It would be equal to 10g for a 10kg weighing machine.

So, atmospheric pressure, in fact, causes net upward force (and not downward).

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    $\begingroup$ To have net upward buoyancy force air under the machine must have more pressure upwards than air above the machine, right? $\endgroup$
    – Atif
    Jan 11 at 17:00
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    $\begingroup$ Thats downward pressure. I asked about upward pressure by air under machine. Do that pressure equal or increase downward pressure by air above the machine? How do you have upward buoyancy? $\endgroup$
    – Atif
    Jan 11 at 17:08
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    $\begingroup$ Isnt pressure force per unit area anymore? Or force sieze to be a vector? $\endgroup$
    – Atif
    Jan 11 at 17:37
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    $\begingroup$ Are you saying that the miniscule amount of air under weighing machine outperform the gigantic amount of air above the weighing machine? How do that manifest? Remember no increase in temperature. No independent observation whatsoever. Also, where do the energy come from for that? Why it only work under open sky? Where do it go when weighing machine is taken in room? $\endgroup$
    – Atif
    Jan 11 at 17:45
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    $\begingroup$ Air Pressure has no direction. So, there is no force of air on weighing machine. How do it cancel weight of air? $\endgroup$
    – Atif
    Jan 11 at 17:48
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They ideally do measure the weight of the atmosphere. But this measurement is set to 0 so that it is convenient for us to use.

If you took a scale to a vacuum, where there is no air to measure its weight, and set that measurement to 0 - Then when you get it back to normal conditions, under the air, it would measure the weight of air.

But this is useless in our life, so we set the initial reading to zero.

However for mechanical scales with plates, as someone already explained, air can get under the plate, and it exerts the same force pushing the plate upwards as the air above it exerts pushing it downwards, so atmospheric pressure would not matter all that much.

As to how this works, lets take a look at this - Heres a block of air, stationary. There is force exerted on it from all directions. The force from up is the weight of the air above it. But this does not push the block of air down? Therefore there must be some some force acting upwards to balance that weight. And this is a properties of fluids and pressure, where in the deeper you get in a fluid , the more pressure is exerted to balance the fluids weight. enter image description here Now imagine that we replace this block of air with a block of steel. The force the air exerted on it is the same as what was exerted on the block of air, so everything pretty much balances out in this case. (For a more dense fluid, bouyant force would be considerable, but in the case of air it is negligible when replaced with steel)

And then if we consider this block of steel to be the plate, the plate does not move even if you change the atmospheric pressure. (apart from the effect gravity would have on it regardless of air)

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