[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 44
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Не сразу дошло ...
Это Вы опять на сферического коня намекаете? )) (сферического пассажира)
Yeah ))))лучше дымом конопли :)
And by the way, you don't have to take off thenAnd by the way, you don't have to take off then.
whatever :)
TASK #1:
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There is a vessel - a flask made of glass. The flask is sealed tightly with a cork. Inside the vessel there is air and 1.5 kg of flies.
Question: What do the flies have to do to make the vessel lose weight and fly off.
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PS:
1. The vessel is sealed tightly with a cork. The cork must not be removed from the vessel;
2. The pressure in the vessel is normal, 760 mmHg, and the temperature is 20o C;
3. The conditions outside the vessel are normal - 760 mmHg, temperature - 20gC, acceleration of free fall - 9.81 m\s^2;
4. The vessel has only one opening - with a cork, there are no other openings;
5. The mass of the vessel with a cork and air, but without flies is 1 kg.
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 though? According to your argument it turns out that the mass of molecules inside any cabin is the same (at normal pressure inside)...
flies (they're small, very small, they're not helicopters)
This is something new in physics. For flies some laws are small, for helicopters other laws are big. :-)
And there are a lot of them, tens of millions, so statistics will correct all heterogeneities. So they do not create any weight .
When they land, they will now push on the scales. The plane will be a ton heavier.
Yes, the sum of the lifting forces of all the flies is roughly equal to a ton, and this force is directed strictly downwards, But it is distributed over all the walls>> it's not a platform, it's a gas.
Again about the statistics: https://www.mql5.com/ru/forum/123519/page25#264333
The downward pressure of the flies does dissipate as a result of the air molecules colliding with each other. But momentum is transferred unchanged ! There is a law of conservation of momentum for this. Therefore, the pressure dissipation is not to the sides, but across the floor. You can't have a statistic so crudely. She might get offended.
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And the problem (about the flies in the plane) is subverted!
I think you are both right and wrong at the same time.
The fact is that not all of the momentum from the flies hits the airframe. But not all of it is lost! There is also the thermal dissipation of the energy of the flies' wingbeats. Air has viscosity, not just mass, and flies wingbeats warm it. And the smaller the flies are, the more they will warm the air and the less pressure they will put on the floor of the plane. If there were one big fly - then yes... So the weight of the plane would be less, but not by 1 ton!
Modification: a string is tied to the floor from each fly, and the flies are pulled upwards with a force of 1ts. Now what?
TASK #2 (very simple):
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In an insulated vessel, 1 kg of table salt was poured, then 1 kg of menthol was poured, then 1 kg of snow was poured. The contents of the vessel have been mixed well. Question: How will the temperature of the contents of the vessel change after a few minutes?
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PS:
1. Consider the vessel absolutely insulated from the outside environment;
2. Consider the initial temperatures of sugar, menthol, snow and the inside of the vessel to be equal;
There is a law of conservation of momentum for this.
OK, let's start to get a grip on something. Let's divide the class into two sets - {Petya} and {Others} (there are 25 of them). A person with N friends will be called "N" for convenience.
Suppose Petya has 0 friends. Then {Other} can have from 0 to 24 without repetition (person "25" can't exist, because he has to be friends with everyone, and we already have Petya, who is "0").
But there can't be person "24" either, because we have two "0's" who are not friends with anyone, and therefore he's not friends with both of them either.
Consequently, for 25 {Others}, only options from 0 to 23 remain. Contradiction.
Similarly, it is proved that Petya cannot have 25 friends (if it were, then {Other} is from "1" to "25". But two people "25" and the existing "1" is a contradiction, since "1" would have to be friends with both "25").
More subtle reasoning shows that Petey cannot have and only 1 friend. And then I'm stuck.
It looks like the ancient problem that a runner will NEVER outrun a turtle by the same calculation... (the runner has ONE step slightly shorter than the turtle's length) are you kidding?!