[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 35
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Силой трения в колёсах мы пренебрегаем, она мала. Сейчас реактивные двигатели такие, что способны поднимать самолёт вертикально.
Например, тяга 2х двигателей СУ-27 - 25 тон, а пустой самолёт весит 16,4 тонны (в снаряжении - 23 тонны).
In that case, the plane will take off due to the airflow that the moving runway will push underneath it, it will have to constantly increase its speed :)In that case, the plane will take off due to the airflow that the moving runway will push under it, it will be forced to constantly increase its speed :)
That flow is too weak, especially if the runway is "very flat", but you're right, it also contributes to its take-off.
А Swetten об этом наверняка знала, а вот сейчас спокойно спит...
A challenge:
The bad boys catch a cat and tie a tin can to it on a string.
The cat runs, the can rattles.)
How fast does the cat have to run to avoid hearing the sound of the can?
A challenge:
The bad boys catch a cat and tie a tin can to it on a string.
The cat runs, the can rattles.)
How fast must the cat run to avoid hearing the sound of the can?
It must not run at all. If the sound conduction by the string = 0, which is unlikely, then the cat could also run at supersonic speed, although that is even more unlikely.
There' s an articlehere about an aeroplane task. A couple of quotes:
And Swetten must have known about it, but now she's sleeping peacefully...
I actually like Swetten, who threw her task into a crowd of men, and is now watching this dump with a chuckle. :-)
I was just trying to make a joke! I thought Mathemat knew about it! Well, that's how it turned out! :)
How fast does a cat have to run to not hear the sound of a can?
Case in point:
Two crows flying at subsonic speed. One crow calls out to the other:
-- A wall!
-- I see it!
Splat! Slap!
Two crows are flying at transonic speed. One screams to the other:
-- The wall!
Smack!
-- I see it!
Slap!
Two crows flying at supersonic speed:
Smack! Smack!
-- Wall!
-- I see it!
:)
For simplicity and clarity, you can even EXCEPT IMPULSE for a while (even though you called me bad words. see how kind I am?).
Forget impulse. Work by Blaise Pascal. Flies block the box like a piston. They flap their wings. They're hovering because the average pressure BELOW them is 1000 kG MORE than the pressure BELOW them. This difference in pressure is what compensates for gravity. This pressure difference is called "lifting force". Thus, the air pressure on the BOTTOM WALL OF THE BOX is 1000kG MORE than on the BOTTOM WALL.
And if they are not hanging (the problem does not say what they are hanging and where they are going :)), but some flies at the moment of weighing flew down
a) were falling in free fall
b) were accelerated, faster than the acceleration of free fall (can flies do this? :))
what are they pushing on in this case and how will this affect the weight?
if at the moment of weighing a body falls on the support that was in free fall (the system was closed), the weight will change?
The pool is standing on the scale, the diver was sitting on the bottom of the pool and then started to surface abruptly. Will the weight change?
Or simpler: the person was standing on the scale and jumped up. At the moment of pushing off the scale will their readings change?
In short, the weight may change, because part of the flies may have had an acceleration at the moment of weighing with the total vector directed anywhere. Accordingly, the pressure may not necessarily be completely on the bottom and may create a weight unequal to the weight when all the bodies (flies))) are at rest.
It is necessary to study features of flight and mass psychology of flies)))
С процитированным сверху согласен. Взлетит. А вот если бы не было реактивного двигателя и винта, а самолёт бы разгонялся колёсами - то не взлетел бы.
Mathemat, ещё раз хочу повторить, что давление на дно бочки выше, чем на её стенки сверху. Немного, но выше.
There are no planes that accelerate to take-off (breakaway) speed with their wheels.
Here's another fun challenge.
We have a wooden barrel with champagne in it. The pressure of the champagne is close to the strength of the barrel (a bit more... and bang!). A carbon dioxide bubble bursts from the bottom of the barrel and drifts upwards. Will this fact lead to the death of the champagne barrel?
Think of the liquid as incompressible. The barrel is not deformable. There is only one gas bubble and it does not multiply. The barrel is completely filled (no bubbles other than the one mentioned). All conditions are considered ideal. There are no transients.
Вот ещё одна прикольная задачка.
У нас имеется деревянная бочка с шампанским. Давление шампанского близко к пределу прочности бочки (ещё чуть-чуть... и БАХ!). От дна бочки отрывается пузырёк углекислого газа и утремляется в верх. Приведёт ли сей факт к смерти бочки с шампанским?
Жидкость считать не сжимаемой. Бочку не деформируемой. Пузырёк газа всего один и он не размножается. Бочка заполнена полностью (пузырьков, кроме упомянутого, нет). Все условия считать идеальными. Переходных процессов нет.
No. The pressure inside the barrel will not change. The pressure of the liquid on the bubble will decrease as it rises to the surface, but this will be compensated for by a decrease in the level of liquid in the barrel as the bubble collapses at the surface. The only reason for the increased pressure in the barrel can only be fermentation - the release of new bubbles. No quiet movement of the bubbles (without the formation of new bubbles) leads to a (noticeable) change in pressure. Only when the barrel is shaken (as with any bubbly bottle) does the carbon dioxide dissolved in the liquid "clump" and accumulate on top of the liquid, when it is abruptly opened it is released and the remaining gas dissolved in the liquid is instantly boiled off.
I am writing in such detail so that you colleagues will argue less. If the barrel can withstand the increase in pressure when the bubble forms at the bottom, then it can also withstand its upward movement.
Here's another fun challenge.
We have a wooden barrel with champagne in it. The pressure of the champagne is close to the strength of the barrel (a bit more... and bang!). A carbon dioxide bubble bursts from the bottom of the barrel and drifts upwards. Will this fact lead to the death of the champagne barrel?
Think of the liquid as incompressible. The barrel is not deformable. There is only one gas bubble and it does not multiply. The barrel is completely filled (no bubbles other than the one mentioned). All conditions are considered ideal. There are no transients.
The difficulty in answering such a question is the insignificance of the bubble compared to the barrel. The barrel must burst from an increase in pressure on its walls, even an insignificant one. The appearance of the bubble does not lead to an increase in pressure, because the pressure inside the bubble is the same as the pressure of CO2 dissolved in the liquid. However, the question here is: how does the volume of the liquid change when the bubble appears? If there is a space above the liquid with CO2, then the barrel will definitely not have a problem. But if there isn't, if the barrel is 100% full. Then the emergence of such a bubble can be considered impossible, the volume increases, and the liquid is not compressible according to the condition of the problem. Thus, if a bubble is formed, it means that there is CO2 above the liquid surface and the barrel is not completely filled, which contradicts the conditions of the problem.
My answer is that the formation of a bubble under the conditions of the problem is impossible.