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J. Perelman
"Entertaining physics". Book 2.
Chapter 3. Circular motion

IN "BEWITCHED" BALL

One entrepreneur in America was organized for the entertainment of the public is very amusing and instructive carousel in the form of a spherical rotating room. The people inside it have such an unusual feeling, what we believe is possible only in a dream or a fairy tale.

Recall first that he is the man standing on the rapidly rotating circular platform.

Rotational movement tends to push the man out; the farther away you stand from the center, the stronger will tend to pull you out. If you close your eyes, you will feel that you are not standing on a horizontal floor, and on an inclined plane, on which hardly keep balance. This will become clear when we consider what forces act here on our body. The effect of rotation drags the body out, gravity pulls down; both movements were formed by the parallelogram rule, give the resulting action, which is inclined downwards. The faster rotating platform, so that the resulting movement and is directed more sloping.


What a man feels on the edge of the rotating platform.

Bring yourself now that the edge of the platform folded up and you stand on this bent inclined part.


People firmly on the inclined end of the rotating platform.

If the platform is stationary, you're in this situation will not resist and will slip or even capsize. Another thing, if the platform rotates: then this inclined plane will be for you, at a known speed, as would be horizontal, because the result of both captivating movements you will go too obliquely, at right angles to the bent part of the platform *.

If a rotating platform to give such a curvature, so that when a certain speed its surface was at every point is perpendicular to the resultant, then placed on the floor, people will feel in all its points, as on a horizontal plane. Mathematical calculation found that such a curve surface is the surface of the special geometry of the paraboloid. You can get it, if you quickly rotate around the vertical axis of the Cup, half filled with water then the water at the edges will rise in Central falls, and its surface will take the form of a paraboloid.

If instead of water, pour in a Cup of melted wax and continue the rotation until such time as the wax cools, the hardened surface will give us the exact shape of the paraboloid. When a certain speed of rotation of this surface is for heavy bodies like horizontal: ball, put in any point, roll down, and remains at this level.


If this glass to be rotated with sufficient speed, the ball will not roll on its bottom.

Now it will be easy to understand the "enchanted" world.

The bottom is a large rotating platform, which given the curvature of the paraboloid. Although the rotation due to hidden under the platform mechanism is done very smoothly, and all the people on the platform would experience dizziness, if the surrounding objects not moved along with them, so as not to give the possibility of the observer to detect movement, the platform is placed inside a large bowl with opaque walls, which rotates with the same speed as the platform itself.


"Bewitched" ball (cut).

This is the device of this merry-go-round called "zakoldovannoy" or "magic" of the sphere. What have you while on the platform inside the sphere? When it rotates, the floor under your feet horizontal at any point of the curve of the platform you were - axis where the floor is really horizontal, or near the edge, where it is tilted at 45°. Eyes see clearly concavity, muscular same sense suggests that you even place.

The testimony of both feelings contradict each other in a most dramatic way. If you go from one edge of the platform to another, you'll feel like the whole huge ball with ease bubble had rolled over to the other side under the weight of your body: after all, any point you feel as if you are on a horizontal plane. And the position of other people standing on the platform inclined, should be submitted to you before extraordinary extremes: you literally would seem that people like flies, walk on walls.


The true situation of the people inside "zakoldovannoy" ball.


The position that is represented by each of the two visitors.

The water poured out on the floor of the enchanted ball, he would spread in an even layer on its curved surface. People it would seem that the water here stands before them sloped wall.

The usual understanding of the laws of gravity as if discarded in this amazing globe and we are transported to a fantastic world of wonders...

Such sensations experienced by the pilot turns. So, if he is flying with a speed of 200 km per hour on a curve with a radius of 500 m, then the earth must seem to him pripozdnivshijsja and tilted at an angle of 16°.

In Germany, in the city of göttingen, was built for scientific research such rotating laboratory. This is a cylindrical room 3 m in diameter, rotating at 50 revolutions per second.


Rotating lab - actual position.

As the floor is flat, when the rotation of the observer, standing at the wall, it appears as though the room leaned back, and he is lounging on the sloping wall.


The apparent position of the same rotating the laboratory.

* This note, incidentally, explains why the curves railway outer rail placed above the interior, and also why cant the inside track to the track for bikes and motorbikes and why by professional drivers can go on steeply sloping circular flooring.

Entertaining physics J. Perelman

 




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