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J. Perelman
"Entertaining physics". Book 2.
Chapter 2. Power. Work. Friction

GALVANOVSKIS ATHLETE AND EULER'S FORMULA

You remember the Jules Verne athlete-the athlete Matipo? "Great head, proportional giant growth; breast, similar to blacksmith bellows; the legs are as good logs, hands - these lifters ticking, with fists like hammers..." Probably from the exploits of this hero, described in the novel "Mathias Support"you memorable astounding incident with the vessel "Trabaccolo"when our giant force powerful arms delayed the descent of the whole ship.

Here it tells the novelist about this fight:

"The ship is exempted from the props that supported him on each side, was ready to go. It was enough to take sartov to the ship started to slide down. Already half a dozen carpenters were busy under the keel of the vessel. The audience with a lively curiosity watched the operation. At this point, skirting the coast ledge, appeared a pleasure yacht. To enter the port, the boat should pass before a shipyard, where he was preparing descent "Trabaccolo", and as soon as she gave the signal, had, in order to avoid any accidents, delay the descent to again take up the case after the passage of boats in the channel. If the court is one thing, standing across, another, moving with great speed, collided, the yacht would have been killed.

Work stopped pounding hammers. All eyes were on the graceful vessel, white sails which seemed to be gold in the slanting rays of the Sun. Soon the boat came opposite shipyard, where stood a thousand people curious. Suddenly there was a cry of terror: "Trabaccolo" staggered and was in motion at the very moment when the boat turned his starboard! Both vessels were ready to face; there was neither the time nor the ability to prevent this collision. "Trabaccolo" quickly slid down the slope... White smoke caused by friction spun in front of his nose, while the feed has already plunged into the water of the Bay (ship went down astern. - J. P.).

Suddenly a man grasps sartov hanging in front of the "Trabaccolo", and tries to hold him, bent down to the ground. One minute he pulls sartov on hammered into the ground metal pipe and, at the risk of being crushed, keep with superhuman powers in the hands of the rope in the course of 10 seconds. Finally sartov dropped. But these 10 seconds was enough: "Trabaccolo", immersed in water, only slightly touched the boat and swept forward.

The boat was saved. With regard to man, whom no one had time to help, so quickly and suddenly everything happened, it was Matipo".

How would he be amazed the author of the novel, if he said that to carry out such a feat does not need to be a giant and have, as Matipo, "by the power of the tiger". Every smart person could do the same!

Mechanics teaches that when sliding the rope that is wrapped around the Cabinet, the friction force reaches a large size. The greater the number of revolutions of the rope, the more friction, the rule increases the friction is such that, with increasing speed in arithmetic progression, friction grows in geometric progression. Therefore, even a weak child, holding the free end of the rope 3 to 4 times wound on the stationary shaft, can balance a huge force.

On the river steamship wharves teenagers stop this technique suitable for marinas, ships with a hundred passengers. Helps them not phenomenal power of their hands, and the friction of the rope on the pile.

The famous mathematician of the eighteenth century, Euler found the dependence of the friction force on the number of turns of rope around the piles. For those who are not afraid of the compressed language of algebraic expressions, given this instructive Euler's formula:

Here F is the force against which directed our effort f. The letter e is denoted by the number 2,718... (the base of natural logarithms), k is the coefficient of friction between the rope and cupboard. Letter and marked "angle navipane", i.e., the ratio of the arc length covered by the rope, to the radius of the arc.

Apply the formula to that case, which is described by Jules Verne. The result will be amazing. Force F in this case is the thrust force of the vessel, moving on to Doc. The weight of the vessel known from the novel: 50 tons. Let the slope of the slipway 0,1; then, the rope was not acting full weight of the vessel, and 0.1 to him, i.e., 5 tons, or 5,000 kg

Next, the value of k - the coefficient of friction of the rope on iron Cabinet - will be considered equal to 1/3. Size and easily determine if we assume that Matipo wrapped the rope around tables only three times. Then

substituting all these values in the above formula of Euler, we get an equation

Unknown f (i.e., the amount of necessary effort) can be determined from this equation, with the assistance of logarithms: Lg 5000 = lg f + 2n lg 2,72, where f = 9,3 kg So, in order to perform the feat, the giant was enough to pull the rope with a force of only 10 pounds!

Do not think that this figure is 10 kg only theoretical, and that will require much more effort. In contrast, our result is even exaggerated: when hempen rope, and a wooden pile, when the friction coefficient k is greater, the force required is ridiculously tiny. If only the rope was strong and could withstand the tension, then even a weak child could Aviv rope 3-4 times, not only to repeat the feat galvanoscope hero, but to exceed it.

Entertaining physics J. Perelman

 




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