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experiment - beer bottle and ping pong ball

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Hello.
I have a question about experiment. You know it. You need beer bottle, water and ping pong ball.
You completely fill the beer bottle with water and you take the ball on the top of the bottle. The ball will not fall, if you take the beer bottle upside down.
OK, the atmospheric force have same value but opposite direction than hydraulic force, it is right? So, the ball will not fall. However, what about buoyancy force? It depents on it?
And the most important question - why does the ball fall if the beer bottle is not full of watter? The hydraulic force is not attract, only gravitional force and atmospheric force attract. The gravitional force is bigger? It is right? Or why?

Thank you very much!
Oomph!

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