[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 47
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1. The higher the pressure inside, the more likely it is to fall apart and "suck" someone out of it:)
2. The lower the pressure, the lighter the plane, the less fuel it needs.
I'd say the answers are both correct. But, these are second order effects of smallness. There is a bigger reason.
What's that?
Humans have air inside, in the middle ear system. It is under the eardrum. In order for it to vibrate adequately, receiving sound vibrations, the pressure under it and outside must be the same. If it is different, it bends to the corresponding side. Hence the pain. Anyone who has dived knows that at a depth of 4-5m this pain is already very strong. I have to blow air under the eardrum in order to compensate pressure.
In an aeroplane, when you are going up and when you are going down (especially when you are going down because it happens faster than going up), the pressure changes. There is a difference between the pressure in the cabin and under the eardrum. Depending on the condition of the person's nasopharynx, this difference may not be able to compensate naturally. This is the reason for this.
Yurixx, remember how you responded to me when I stated that the pressure of the atmospheric column is not the weight of the column above you? I have a good argument.
Go into a sealed cabin with normal pressure. What is the pressure on you - the column of air in the cabin or just the air pressure after all? According to your argument it turns out that the mass of molecules inside any cabin is the same (at normal pressure inside)...
Alexey, here you are absolutely right, in such a cockpit it is not a pole that pressurizes, but just air.
And on the surface of the Earth pressurizes just air. However, this simple air and its pressure is not taken from the ceiling, but because there is an atmosphere and it (the atmosphere) is in the Earth's gravitational field. As a result, no matter how the molecules fly - chaotically, Brownian or otherwise - they fly in the Earth's field and therefore their trajectories are parabolic. Each span from impact to impact is not a straight line, but a free-fall parabola with g acceleration. This is what causes the atmospheric density to be Boltzmann distributed. (Try explaining Boltzmann's law to me if, for molecules, all directions are equal and trajectories are straight lines with constant velocity.)
Under laboratory conditions, given the magnitude of the average velocity of molecules at n.c. and the volumes of the vessels, this distortion can be neglected. But at distances of hundreds of meters in air (and decimeters in water), this effect is already evident. And it arises, I repeat, as a result of the fact that the atmosphere has weight. If you know the proof of Archimedes' law, you will easily figure out how to prove that the force of air pressure on a horizontal plane is equal to the weight of the air column above it.
In an aircraft, when it gains altitude and when it descends (especially when it descends as it happens faster than it ascends), the pressure changes.
Why does it change, is it leaky?
Why is it changing, is it leaky?
It's certainly not leaky. That would probably be both too complicated and irrational. I'm not an expert, I'd have to ask aviators. Maybe Sveta?
And the conditions for the passengers are provided as follows:
The air pressure in the plane is maintained by the air conditioning system.
On average, it's equivalent to 2,000 to 2,500 meters.
The ears are sore from the unregulated AAC.
P.S. That's the general idea. :)
Mathemat, About the room with the mirrors. I counted two options in dialux. The room is 3x3x3m, with 2x36 watt fluorescent fixtures in the room.
Option 1 - wall reflection coefficient = 50% (normal wall):
Option 2 - wall reflection factor = 95% (i.e. mirrors):
-
As you can see, in the latter case the illuminance is almost twice as high.
If a ton of flies fly continuously in a closed volume, we can approximate replacing it with one equivalent fly. It would hang almost motionless in the centre of the volume and weigh one tonne. The difference in pressure above and below it will depend on the area of its projection on the floor, say for 1000 cm2 this difference is one atmosphere. But we need this difference to be maintained at all times, so our fly should simply hermetically divide the original volume into two equal volumes. If the initial pressure was P0, after our fly takes off it will be P1 under it and P2 above it. Neglecting thermal effects we will have P0 = (P1+P2)/2. The force acting on the fly will be (P1-P2)*S = 1t, the addition in the downward force will be (P1-P0)*S. Note that the areas are the same. Then given the condition P0 = (P1+P2)/2 we obtain for the lifting force the expression 2*(P1-P0)*S = 1t. By comparing it with the formula for the downward force (i.e., weight) we see that this force will be equal to 0.5t.
It remains to be seen what effect the reduction in area of our fly will have on the effect, i.e. the occurrence of leakage. Obviously, in order to maintain pressure difference we have to install fan, and the smaller is its area, the more powerful it should be. The actual calculation, I think, would be quite complicated. But somehow it seems to me that the result will be the same in the first approximation.
P.S. By the way, my answer is also the average of the positions of the parties :)
Интересно, как бы вы ответили на задачу N1: https://www.mql5.com/ru/forum/123519/page44
I'm thinking of jumping up at the same time :) . Then the recoil will first compress the support and then its reaction will propel the vessel (lighter, by the way) upwards.
I'm thinking of jumping up at the same time :) . Then the recoil will first compress the support and then its reaction will propel the vessel (lightened, by the way) upwards.
I meant a prolonged levitation of the vessel - minutes, hours, etc.
Я имел ввиду длительную левитацию сосуда - минуты, часы и т.д.
Flies must cast a spell of levitation :)
By the way, also on the previous post
Candid, if a fly weighs a ton and its projection area is 1000 sq cm, what is its density? My guess is that it would be higher than the density of an osmium, by a factor of one and a half.
That depends on how tall it is :)