[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 55
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If the light were to increase, you could put a single candle in the centre of the huge room and then light up the whole room with a system of mirrors.
By the way, how do you make the sound of a person's speech louder in a huge room? Make the walls reflect it.
A dome, for example, or a wall in the form of a hyperbola in general can focus it into one point, roughly speaking.
I'm wondering what to offer as compensation for innocently murdered intrigue.
I don't have a problem. But I've got a little twist with some good suspense in it. Just right for fans of statistics.
I'll give you an introduction: Everyone knows... I'm lying. Not everyone. Let's just say quantum physicists and some Wikipedia buffs know that elementary particles
are divided by their statistical properties into two families - Fermions and Bosons...
// Those who are not familiar, please read the links to them, as well as the relevant statistics.
Now laying out what the frozen intrigue is all about.
I somehow noticed that in the macrocosm, many social and biological processes and systems tend to the same kind of regularities, i.e. some are bosonic (herding, for example), while others are the opposite of fermionic (well, for example, the role arrangement in a given flat). Moreover, they are often adjacent and mutually influencing or mutually controlling. However, sometimes the influence is one-sided, for example: Red and Green on adjacent sides of a traffic light are obvious fermions (they cannot be in the same states). But people and especially cars around them "boson" - they run in formation and pull up their speeds to the positive correlation. Now it is probably possible to lay out the fog in the forehead...
Hypothesis: ALL interacting processes tend to be either symmetric (bosonic) or antisymmetric (fermionic). Neutrality (bosonic-fermionic) is only a dream for us.
Required: to prove or disprove.
// As a side-effect, there may be some good ideas about curbing forex... :)
What's in blue is fundamentally different from what you brought up later. The blue highlighting is not for economy, but to create a space effect. But the rest is, yes, to save money.
Yes, true, but it saves energy on lighting too. If you have such a device - a luxmeter, put it near the mirror and measure the light intensity. And then without moving the gauge over the mirror, see the difference.
MetaDriver, we'll get to uranium oxide that way, figuratively speaking. Ready to think about it tomorrow, but not half past three in the morning. See you tomorrow.
А потом не перемещая прибор загородите зеркало, увидите разницу.
There might be a difference. But if you take and sum up all the readings of the luxmeter in each point of the room (integrate) with and without mirrors, will it make a difference?
2 MetaDriver: strong, strong generator. But the problem, I'm afraid, is more of a philosophical problem.
MetaDriver, мы так до окиси урана дойдём, образно говоря. Готов подумать завтра, но не пол третьего ночи. До завтра.
:)
OK.
However, I checked Wiki and got upset - it's completely vague and almost nothing about statistics... :(
I have to recommend google/yandex in its entirety.
OK, I see. The problem is incorrect, because forces not assumed in the problem condition (see below) have to occur. You can see that you are trying hard to get the plane to stand still relative to the air.
OK, we describe the horizontal forces acting on the plane - turbine thrust force and... something else. There is no friction in the wheels, the bearings are perfect.
But then what is the nature of the force in the wheels that would have to compensate for the turbine thrust so that the bastard stays stationary relative to the ground? Maybe some kind of gyroscopic force (due to the giant torque of the wheels) - or a rolling friction force? What kind of force is that, Sergei? If it's not there, the plane will still be moving forward relative to the air - and it doesn't care about the frantically spinning wheels, which don't interfere with the movement in any way.
Господи, да почему же Вы такие умные с Юрием!? Я даже не обижаюсь на ту хрень, которую писали. Но за МАИ - ответите! :о) Поймите правильно - не взлетит. По одной простой причине - читайте условие задачи. Я не знаю, как технически эти условия реализовать, но не взлетит. В условиях это написано. Только, что бы их соблюсти, - нужно удержать самолет на месте, а для этого лента транспортера должна крутиться с охренительно большим ускорением. Уж не помню в точности все вычисления (и даже не буду их повторять), но ускорение ленты транспортера должно прибавляться на пару, тройку км/сек^2. Ну не помню, может меньше, может еще чуть меньше.
В теории этот вариант не летает. Практически - проверить невозможно, по причине отсутствия нужного транспортера.
Если не можете понять - просто запомните, это условие - не летает :о)
Есть несколько вариантов этой задачи, этот вариант - не летает. Если бы скорость транспортера была бы равна скорости самолета - то да, легко, проблем бы не было, вообще никаких. Но читайте условие задачи. Все! Честно, надоело. Удачи, изобретали машин времени. Сюда лучше не заходить - как наркотик. Тайм киллер какой то и зачем это нужно?
PS: Юрий, от тебя я не ожидал такой ху%ни. Честно - не ожидал.
I am duplicating Alexey's answer so that you, Sergei, can finally get the hang of it.
Suppose you are right and the plane is standing still relative to the ground. The turbines work and create a horizontal force F pointing forward on course. According to Newton's third law, the body is at rest (our case) if the action of all forces on it is compensated to zero. Consequently, to meet the condition of rest of the aircraft on the moving conveyor, there must be a force equal to -Fand directed in the opposite direction.
This force, Sergey, has nowhere to come from! That is the reason why the plane will take off in any case, so you are wrong.
I agree with Yury that you, as an MAI graduate, should be aware of such trivial things and try to less rely on your intuition, which sometimes fails. Although, perhaps you have a special understanding of the conditions of the problem. One can assume that you take into account in the solution the unconditional presence of inertial (dynamic) forces. But you have not mentioned it anywhere. In this case the problem becomes more complicated and the solution of the balance of forces must be considered taking into account the acceleration forces arising from the spinning-out of the wheels of the plane with a non-zero mass ( Alexey mentioned it above). Indeed, it is possible to find what should be the wheel rotation acceleration (radians per second squared), that would compensate the force of turbines F. Probably, in such a formulation your 2-5 km/s^2 for conveyor belt acceleration would arise.
In any case, you are wrong - in first case, giving an answer to wrong problem conditions, and in second case, having not justified (or not being able to do so) your answer.
P.S. Regarding the problem about aeroplane pressure and tinnitus when landing an airliner, the correct answer is this:
The cabin pressure at an altitude of 10-11 km is maintained specifically below atmospheric pressure at ground level by 25% and this is monitored by electronics. This pressure is almost 4 times higher than the air pressure outside the cabin. During landing, the tracking system equalizes the pressure to what we are used to and it is this fact that leads to the inevitable pain in the middle ear.
Why all this? It turns out that the air we breathe dissolves in the blood and if for some reason or another to abruptly reduce the pressure by 4 times (depressurization of the cabin at cruising altitude), there will be "boiling" of dissolved gas in the blood, clogging of small vessels in the brain and, consequently, inevitable death. The effect is identical to what we see when opening a two-litre plastic bottle of Pepsicola - open the lid sharply and half of the bottle will burst with foam. Now picture it in your head (literally).
Accidents on modern aeroplanes are rare, but they do happen. Sometimes it is a depressurisation of the aircraft cabin that does not result in loss of control. In these conditions, due to a 25% drop in pressure at 10 km altitude, we remain alive (no boiling) and if we are lucky, we will make an emergency landing. Otherwise, there will be nobody to land - there will be 5 balloons sitting in the cockpit. So, this measure is forced, not defined by bad adjustment of devices and is directed at our own good.
P.P.S. One more interesting task:
Do you think the surface temperature of the Sun would become higher if a barrel of gunpowder were exploded in its centre?
There might be a difference. But if you take all the luxometer readings at each point in the room and integrate them with and without mirrors, will there be a difference?
OK. You propose to integrate illuminance shown by the luxmeter. We integrate by length of the room or more exactly by its area, including the area of the walls. But then you do not get illuminance, but another unit of measurement - luminous flux. You confuse these two notions. Luminous flux is the product of illuminance by the area of the room, figuratively speaking. Theluminous flux emitted by a llama is independent of the wall material.
But, the luminous flux which hits the photoresistor in the luminaire (or figuratively speaking the shirt of the person in the room) does depend on the material of the walls. And here's why. The thing is that it consists of two elements: direct light flux coming from the lamp and light flux reflected from the walls.
It is clear that the direct light flux coming from the lamp does not change due to changes in the wall material. But the component of the reflected luminous flux depends on this radically. If the walls are completely black it will be equal to zero. If the walls are perfectly reflective, it will be significant.
Now take a look at the screenshots of Dialux and feel the difference:
This is with perfect-black walls:
This is with mirrored walls:
Mathemat, By the way, note an interesting detail. In the case of mirrored walls, ceilings and floors, the light distribution in the room is much more uniform (see Emin\emach), and this is one of the most important indicators of light quality, along with illuminance and colour rendering itself.
So it turns out that one small candle can illuminate a large room, figuratively speaking.
However, we should not forget that in addition to mirrors, there are other objects in the room that absorb light.