Interesting question... - page 11
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There is an even more unusual task in its solution!
We take a flat polished granite slab. We put it strictly horizontally and carefully put the ball from the bearing to one of the edges of the slab.
What will happen?
It turns out that the ball will make oscillatory movements from the edge to the edge of the slab with a period of 48 minutes! This period does not depend on the size of the plate and the mass of the ball!
The trifle is that the Earth is round, and the plate is flat and the ball, being on the edge of the plate, is a little elevated from the centre of the Earth in comparison with the position in the centre, and therefore aspires to roll down to the centre. And so in a cycle. And 48 minutes, this is the characteristic period of oscillation of a 6300 km long pendulum (the Earth's radius) and, at the same time, the period of orbital circulation of the Earth's NEO.
There is an even more unusual task in its solution!
We take a flat polished granite slab. We put it strictly horizontally and carefully put the ball from the bearing to one of the edges of the slab.
What will happen?
It turns out that the ball will make oscillatory movements from the edge to the edge of the slab with a period of 48 minutes! This period does not depend on the size of the plate and the mass of the ball!
The trifle is that the Earth is round, and the plate is flat and the ball, being on the edge of the plate, is a little elevated from the centre of the Earth in comparison with the position in the centre, and therefore aspires to roll down to the centre. And so in a cycle. And 48 min. is a characteristic period of oscillation of 6300 km long pendulum (radius of the Earth) and simultaneously the period of orbit of the Earth's NEO.
cool
You have it all more fresh in your head, of course, but in my opinion it is impossible
First of all, the Archimedean force doesn't apply here (I'm talking about the horizontal part of the problem).
I think there are only two forces.
One, as you say, F=ma
and the second is the impact of air in the direction of movement
and the second one depends only on the shape and area of the ball and has nothing to do with its contents.
but the first one has mass.
Accordingly a 10 g ball and a 100 kg ball (having the same size) move in the opposite direction but with different velocity.
In any physical phenomenon it is possible to distinguish a stationary state, where one type of solution is applicable, and transition regions where stationary solutions are not applicable. In the discussed problem with a balloon, there is a transition region associated with the movement of the entire volume of air in the carriage as a whole at the beginning of the movement of the train. This movement of the air mass under the action of the acceleration force is directed against the motion of the wagon and takes the ball backwards for an instant. This is a transient process. Then, the solution I gave above will be correct and the balloon will roll forward while the train is accelerating. It is not difficult to estimate the characteristic transition time. It is approximately equal to the time of passing of car length moving with acceleration a: S=a/2*t^2=> t=SQRT(2S/a) . During this time the balloon will move with the air against the motion of the train.