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

THE LACK OF WEIGHT

Some Joker announced one day that he knew the way without cheating hang round buyers. The secret is to buy goods in the countries of Equatorial and sell - closer to the poles. It is well known that near the equator things have less weight than near the poles; 1 kg moved from the equator to the pole, will increase in weight by 5, it is Necessary to use, however, is not ordinary weights and spring, though made (graded) at the equator, otherwise no benefit will not work: the goods will be heavier and much harder will become weights. If you buy a ton of gold somewhere in Peru, and to sell it, say, in Iceland, it is possible, perhaps, this is something earn - free allowance, of course.

I don't think this trade could somebody enrich, but essentially good sense of humor is right: the force of gravity actually increases with distance from the equator. This happens because the body at the equator describe when the rotation of the Earth the large circles, and also because the globe as if swollen near the equator.

The main share of the deficiency of the weight caused by the rotation of the Earth; it reduces the weight of the body near the equator on 1/290 share compared with the weight of the same body at the poles.

The difference in weight when moving the body from one latitude to another for light bodies is negligible. But for heavy objects it can reach values pretty solid. You had no idea, for example, that the steam locomotive, weighing in Moscow 60 tons, upon arrival in Arkhangelsk is 60 pounds heavier, and upon arrival in Odessa at the same easier. In his time with the island of Spitsbergen annually exported in more southern ports up to 300 000 tons of coal. If this number were delivered in some Equatorial port, found there would be a shortage of 1,200 tons, be outweighed by the burden upon acceptance on spring scales, taken from Svalbard. Battleship weighing in Arkhangelsk 20 000 tons, upon arrival in the Equatorial water becomes lighter than 80 tons; but it remains imperceptible, as respectively become easier and all other body, not excluding, of course, and the water in the ocean *.

If the earth rotated on its axis faster than now, for example, if the day did not last for 24 hours, and, say, 4 hours, the difference in the weight of bodies at the equator and the poles would be noticeable sharper. A four-hour day, for example, weight, weighing on the pole 1 kg would weigh on the equator just 875, these are approximate conditions of gravity on Saturn: near the poles of this planet all the bodies 1/6 heavier than at the equator.

Since the centripetal acceleration increases in proportion to the square of the velocity, it is easy to calculate at what speed it is on the earth's equator should be 290 times more, i.e., equal to the force of gravity. It will come with speed, 17 times larger than at present (17*17 - almost 290). In this state, the body will cease to exert pressure on their feet. In other words, if the Earth revolved 17 times faster things at the equator did not have weight! On Saturn it would come at speed, just 2, 5 times more than the present.

* So, among other things, the vessel sits in the Equatorial waters as deep as in the Arctic; it is though easier, but much easier and displaced them water.

Entertaining physics J. Perelman

 




System Orphus

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