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J. Perelman
"Entertaining physics". Book 2.
Chapter 4. World attraction

IN A BOTTOMLESS PIT

What was happening in the depths of our planet, we know still very little. Some believe that under the solid crust hundred kilometers thickness begins fiery liquid mass; others believe the entire globe hardened to the center. To solve the issue is difficult because the deepest borehole extends no deeper than 7.5 km, the deepest mine, which has penetrated people located at a depth of 3300 m*, and the radius of the earth is equal to 6400 km. If you could drill through the planet through the well, cutting through the globe in diameter, then these issues would be resolved. Modern technology is far from possible implementation of such companies, although all dug in the earth's crust boreholes, taken together, would constitute a length exceeding the diameter of our planet. About digging through a tunnel across the globe dreamed of in the eighteenth century mathematician Maupertuis and philosopher Voltaire. For this project, though in a different, more modest scale back the French astronomer Flammarion; we reproduce here the title figure of his articles on this topic.


If you drill the globe in diameter...

Nothing like that, of course, has not yet been made; but let's use an imaginary bottomless well to do the same kinda problem. What do you think would happen to you if you fell into this bottomless pit (on the air resistance at the time will forget)? To shatter on the bottom you can't, the bottom is not there, but where do you stop? In the center of the Earth? No.

When you're dolerite to the centre, your body will have such a tremendous speed (about 8 km/sec), what about stopping at this point can not be and speeches. You will go forth and will burn, gradually slowing until at head with the edges of the opposite end of the well. Here you will have stronger grasp the edges, otherwise you will make a walk through the well to the other end. If not here you will be able to grasp something, you will fly into the well will swing so on without end. Mechanics teaches that under such conditions (if only, I repeat, ignore air resistance in the well) the body should swing back and forth forever **.

What would be the duration of one such swing? It turns out that the whole way there and back would take 84 minutes, 24 seconds, i.e. round score of one and a half hours.


Falling into the well, dug through the center of the globe, the body will swing continuously from one end of the pit to the other,
making every full swing within 1 hour 24 minutes.

"So it would, " continues Flammarion, if a well was dug along the axis from pole to pole. But it is enough to move the point of departure for any other latitude on the continent of Europe, Asia or Africa, and will have to take into account the influence of the Earth's rotation. It is known that each point of the earth surface runs on the equator 465 meters per second, and at the latitude of Paris is 300 meters as the circumferential speed increases with distance from the axis of rotation, a lead ball, for example, thrown into the well, but falls vertically, and deviates slightly to the East. If you dig a bottomless pit at the equator, its width must be very large, or else it must be strongly oblique, because the body falling from the surface of the Earth, 'd be far to the East of its center.

If the inlet of the well was located on one of the plateaus of South America, at a height of, say, two miles, and the opposite end of the tunnel would have on the level of the ocean, the man who inadvertently fell least in American hole, would have reached the opposite end with such speed that would be left from it to a height of two kilometers.

And if both ends are well accounted for at the level of the ocean, could submit a flying man's hand at the moment of its appearance at the opening, when the airspeed is zero. In the previous case, ought, on the contrary, cautiously aside from too rapid of a traveler".

* Gold mine in Boksburg (Transvaal, South Africa), and the shaft is located at an altitude of 1600 m above sea level, i.e. the depth of the mine from sea level to 1700 m (Approx. as amended).
** If the air resistance swing will gradually fade, and it will end because people will stop in the center of the Earth.

Entertaining physics J. Perelman

 




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