[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 409

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ernst: It already flies if g=9.81 m/s^2


There is no catch in the raw data. The whole puzzle is in the behaviour of the particles (flies) inside the vessel. I want to say right away that this problem is directly related not only to gravitation, but also to forex. If you solve it, you will be able to develop a grail by analogy. Although, you will not need the Forex market then.

 
Pretty quickly the flies gobble up the oxygen and die. But even assuming that there is enough time left in their lives to make the flask take off, the flies should line up clearly. Let us suppose that it is not a flask but a test tube - long-long-long and each fly has an opportunity to rest its head against the "ceiling" and flap its wings without disturbing anyone. What will happen in this case? The wings will press on the air which will press on the bottom of the tube. You don't believe me? Put your left hand on the table and raise your right hand and bring it down sharply with a "horizontal palm" and stop abruptly a few centimetres away from your left hand. The left hand will feel a pang of air. This means that if the flies just take off, the total weight of the tube is unlikely to change much. On Discovery they showed the trajectory of the fly's wing. There would indeed be an air impact on the bottom. It doesn't look like the vial will ever take off.
 

Stop! The flies, when they fly up, create a high-pressure area beneath them that presses down on the floor. This means that they all have to fly up to the ceiling and rush down in sync. As a result, the upward air pressure will reduce the weight of the flask and maybe that force will be enough to make it fly off. Although... It's a closed system of forces. In short, the flies should net to the ceiling and synchronously make a wing strike in the air, taking off sharply from the ceiling to the floor.

Theoretically, the pressure on the floor exerted by the fly in flight would be equal to the fly's mass. Since the flies weigh 1 kg and the flask weighs 1 kg, the air pressure on the ceiling should be equal to 1.5 kg, which is half a kilogram more than the weight of the flask.

Is the solution correct?

 

Vladimir, forget the flies, forget the test tube, forget the flask .... That's not the point of the problem. Of course the flask won't fly if they hit the cork, you're right about that. But that is not the point of the problem. Let us replace the flies with particles (molecules, atoms, etc.).

How do the particles have to behave for the body to lose weight without "losing mass"?

 
If the solution is correct, then we have just discovered the secret of alien flying saucers. :)
 
Richie:

Vladimir, forget the flies, forget the test tube, forget the flask .... That's not the point of the problem. Of course the flask won't fly if they hit the cork, you're right about that. But that is not the point of the problem. Let us replace the flies with particles (molecules, atoms, etc.).

How do the particles have to behave for the body to lose weight without "losing mass"?


They have to hit the air in sync so that the upward pressure of the air exceeds the pressure exerted by the body on the plane on which it is standing.
 
At the moment the flask "jumps", its total centre of mass will be outside the flask at the top. That is why it will fly up - it tends to its outlined centre of mass. What to do further to the particles to maintain levitation of the flask, something does not come to mind. Alas, I have not studied physics of liquids and gases :(
 

Perhaps there's one more thing. Let there be only one fly. Suppose it starts from the ceiling and hits a column of air directed not vertically upwards, but at an angle of 45 degrees. In this case the flask will not jump vertically upwards, but upwards at an angle of 45 degrees. Ignoring the fact that the shock wave will return, at this point in time the fly should change the direction of impact by 90 degrees - that is, the impact should now also be at a 45 degree angle, but in the opposite direction. The flask will fly in the opposite direction. But sooner or later the fly will reach the bottom. That's where its attempts to keep the flask in the air will end.

The idea of changing directions of impact back and forth leads to the idea of the fly flying from top to bottom in a spiral. In an ordinary cylindrical spiral and in an Archimedean spiral. In case of the Archimedean spiral and assuming that the bulb has the shape of a perfect ball, it may very well happen that the reflected shock wave at some point in time simply takes the fly again "to the ceiling" and allows it to do it all over again. If that works, a long levitation of the flask would be possible.

Richie, am I right?

 

no one will ever fly anywhere

physics, 8th grade, second quarter, even though it was written by ninth grade Hans Christian Andersen, it's still physics...

inside a sealed vessel, please, the vessel itself, no way.

 
drknn: Richie Am I right?

I've already gone to bed :) A flask is an enclosed space, so no matter how the flies fly there, it won't fly. Theoretically, flies can fully compensate for their weight by their tremendous movement speed, but that's practically not realistic.

Forget the fly flask. Think about how the molecules (or atoms) of a body have to move for the body to lose weight. The movement of molecules is something like the movement of a price: "there is a lot of movement" and "the result is little".

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