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The lever, the block and the inclined plane

The lever, the block and the inclined plane
Already in ancient times for lifting people began to use simple mechanisms: lever, winch and inclined plane. Later they were joined by another unit and the screw. These simple devices allow you to multiply the muscular efforts of man to cope with such weights, which in other circumstances would be completely unaffordable. The principle of operation of simple machines is well known. For example, if you drag the load to a certain height, it is always easier to use the gentle sloping than steep. Moreover, the provisions of the slope, the easier it is to do this work. This relationship has a clear mathematical expression. If the inclined plane has an angle d, then haul the load it will be 1/sin d times easier than to lift it vertically. If the angle is 45 degrees, our effort will be in 1, 5 times less, if 30 degrees — 2 times less, at an angle of 5 degrees we spend 11 times less effort, and at an angle of 1 degree in 57 times! However, all that is won in force is lost in distance, because how many times does our effort, at the same time increases the distance that has to carry the load. However, in cases where time and distance are not important, and very important goal is to lift the load with the least force, inclined plane is indispensable. Another simple mechanism — a lever — our ancestors were constantly used to lift and move heavy rocks and logs. The lever allows you to achieve multiple gains in strength the most simple and available means. Putting a long and strong pole on the stump of a log (support) and fixed the other end of it under a stone, man made the pole in a simple lever. In this situation, the stone began to act in two torque, one of the weight of the stone, and the other from the hand of man. In order for the stone moved that "pushes" point, human muscle power should be more "pressing" the weight of the stone. Time, as we know, equal to the product of the applied force to the length of the lever arm (in this case the leverage is the distance from the end of the pole (point of force application) to log (fulcrum)). It is easy to calculate that if the shoulder on which the man presses in 15-20 times longer, which slipped under a rock, the force of the person respectively, also increases 15-20 times. That is the person, not really straining, can lift a stone weighing a ton! The stationary unit — the third mechanism, widely spread in ancient times — is a wheel with a groove, the axis of which is rigidly attached to the wall or ceiling beam. Slung across the wheel the rope and attaching it to the opposite end to the load can be lifted to the height of the mounting block. Stationary unit no gain in power, but provides an opportunity to change direction that often when lifting weights is very important.

for all its primitive simple mechanisms repeatedly extended the capabilities of ancient man. To see this, it suffices to recall the giant buildings of the ancient Egyptians. For example, the great pyramid had a height of 146 meters, it is Estimated that its construction took 23300000 stone blocks, each weighing an average of about 2, 5 tons. But this was not the limit — in the construction of the temples the Egyptians transported, lifted and installed a colossal obelisks and statues, the weight of which amounted to hundreds of tons! What are the mechanisms used by these ancient builders in order to raise to great heights of gigantic boulders and statues? It turns out that all this can be done using the same simple devices — block, levers and the inclined plane. Colossal statues and blocks of stone were dragged on a massive sled, who pulled a large number of people. Every person involved had a rope thrown over the shoulder. Under the sled was placed rollers, which, after pulling the cargo was selected and again placed under the skids. To overcome obstacles slide lifted with a lever. As they used the cut logs. Stops served specially made wedges of different sizes. The work was accompanied by music. The main lifting device of the Egyptians were inclined plane — ramp. The skeleton of the ramp, i.e., its sides and partitions, at a small distance from each other crossing the ramp was built of brick

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