Could Archimedes have lifted the Earth?

Archimedes was a native of Syracuse, Sicily. It is reported by some that he visited Egypt and there invented a device now known as Archimedes screw. This is a pump, still used in many parts of the world. It is presumed that, when Archimedes was a young man, he studied with the successors of Euclid in Alexandria. Certainly he was completely familiar with the mathematics developed there, but what makes this conjecture much more certain, is that he knew personally the mathematicians working there.

“Give me a place to stand and I will move the earth!”

This is a legend ascribed to the famous Archimedes, genius of antiquity who discovered the laws of the lever. “Archimedes,” Plutarch says, “Once wrote to King Hiero of Syracuse, whose kinsman and friend he was, that this force could be used to move any weight. Carried away by the power of argument, he added that, were there another earth, he would go there and lift our own planet from it.”

King Hiero, who was absolutely astonished by the statement, asked him to prove it. In the harbor was a ship that had proved impossible to launch even by the combined efforts of all the men of Syracuse. Archimedes, who had been examining the properties of levers and pulleys, built a machine that allowed him to single-handedly move the ship from a distance away.

Archimedes knew that by applying a lever, one could lift the heaviest of weights by applying even the weakest of forces. One had only to apply this force to the levers longer arm and cause the shorter one to act on the load. He therefore thought that by pressing with his hand on the extremely long arm of a lever he would be able to lift a weight, the mass of which would be equivalent to that of the earth (For the sake of conceptual clarity, we shall take the “moving” or lifting of the earth to mean the lifting on the earth’s surface of a weight whose mass would be equivalent to that of the earth).

But, if this great scholar of antiquity would have known what an enormous mass the earth possesses, he would have most likely “eaten his words”. Let us imagine for a moment that he had at his disposal “another earth” and also the point of support he sought. Further imagine that he was even able to manufacture a lever of the required length. I wonder if you can guess the amount of time he would need to lift a load equivalent in mass to that of the earth, by at least a centimeter? Thirty million million years- and no less!!

Astronomers know the earth’s mass. On earth a body possessing such a mass would weigh in round numbers.
6,000,000,000,000,000,000,000 tons

Supposing a man could lift only 60 kg directly, to “lift the earth” he would need a lever with a long arm that would be longer than the shorter arm by
1,000,000,000,000,000,000,000 times!!

You can easily figure it out that to have the end of the short arm rise by one centimeter; the other end must describe through space the huge arc of 1,000,000,000,000,000,000 km.

That is the colossal distance Archimedes would have had to push the lever to lift the earth by just one centimeter. So how much time would he need? Presuming Archimedes could have lifted 60 Kg one meter in one second- the work of almost one horsepower! – to lift the earth by just one centimeter, even then he would need 1,000,000,000,000,000,000,000 seconds
or 30 million million years. Though he lived to a ripe old age, Archimedes and his lever wouldn’t have lifted the earth by so much as even the thinnest of hair.

No artifices would have helped him to cut the time noticeably – despite all his brilliance. For according to the “golden rule” of mechanics, the mechanical advantage derived will always be accompanied by a loss in displacement, or, in other words, in time. Even if Archimedes had been able to push the lever with a speed of 0.34 km/sec the speed of sound, he would have lifted the earth by one centimeter only after 93,264,094,069,895.84265 years.

If he had pushed the lever with the speed of light, 300,000 km/sec, nature’s fastest possible – he would have lifted the earth by one centimeter only after ten million years of pushing.

References:-
– Lewis, Albert C. “Archimedes.” Encyclopedia of World Biography. New York: McGraw- Hill, Inc., 1973. vol. 1, pp.219-223.
– Various history books

Take Your Pick – Vacuum or Nothing!

The history of vacuum and its applications. What is vacuum? Can you achieve perfect vacuum? Why isn’t the Earth’s atmosphere being sucked out into outer space? What applications & industries use the principle of vacuum? And more…

What is vacuum? Vacuum is the absence of anything and everything in a given space, therefore a perfect vacuum would be completely devoid of matter.

Till date it has not been possible to achieve pure vacuum, the nearest we have got is molecules one mm apart, not much one may say, but when you consider that at sea level, molecules are millionth of a millimeter apart, it is considerable, or rather considerably less. Also perfect vacuum is by definition obtained only at a temperature of zero degree Kelvin, and reaching zero degree Kelvin is practically impossible.

Of course nature as usual does a better job, there are vast sections of space where matter is ten centimeters apart and it is theoretically possible that billions of light years away, there are parts where matter is spread out more than one meter apart.

But then if one is to go by the saying that ‘nature abhors a vacuum’, why isn’t the Earth’s atmosphere being sucked out into outer space? What the saying essentially means is that air will move in swiftly (if it can) to fill up any vacuum created inside the atmosphere (this is because air is a constant state of flux and will move from a higher atmospheric pressure point to a lower atmospheric pressure point). As one goes up into the atmosphere, air pressure keeps reducing, and at the edge of the atmosphere there is no air pressure and individual air molecules move around freely. The reason they do not move away from Earth is that the Earth’s gravity attracts them and unlike on Earth, there is no air pressure in space to force the molecules to occupy the vacuum.

The first recorded instance of artificially created vacuum was by Evangelista Torricelli, an Italian, he was a physicist, mathematician and is perhaps best known for inventing the barometer, which is used to measure atmospheric pressure.

Around 1643, following a suggestion by Galileo, he filled an approximately four-foot-long glass tube with mercury and closing the open end with a finger, inverted the tube into a dish filled with mercury. When he removed the finger, some of the mercury did not flow out of the tube. When Torricelli measured the height of the mercury in the tube, it was approximately 70 mm. And he presumed, correctly, that the space above the mercury inside the tube was a vacuum.

In 1657, the German physicist Otto von Guerricke physically demonstrated the power of vacuum. He fitted together two copper bowls to make a hollow sphere and then removed most of the air to form a vacuum. Although the bowls were held together only by atmospheric pressure, two teams of horses, pulling in separate directions could not pull them apart.

Otto von Guerricke also invented the first vacuum pump. Of course many different kinds of vacuum pumps have now been devised for creating vacuum by removing molecules of gas from a closed space. But all of them belong to two basic types: air-powered or electric. An interesting fact is that pumps of the same capacity will create the same amount of vacuum, irrespective of the type of pump.

Applications of Vacuum

Since the beginning of time, humans have harnessed the power of inventions and discoveries for practical uses. It was no different with the vacuum.

In 1698, Thomas Savery, an English military engineer, patented the first steam engine. He was working on the problem of pumping out water from coalmines. Using a closed vessel filled with water, he introduced steam under pressure into it, this forced the water upwards, the steam was then cooled, creating a vacuum that sucked more water out of the mine.

In 1712, Englishman Thomas Newcomen used the principle of vacuum to run an atmospheric steam engine (he was helped in this by Savery).
Steam was first pumped into a cylinder and was then condensed to create a vacuum. This resulted in atmospheric pressure operating a piston to create downward strokes, which pumped the water up.

In 1765, James Watt, while working on a Newcomen engine, began to make several improvements. And soon his patented engines became the dominant designs for all steam engines.

The steam engine was one of the main reasons for the start of the industrial revolution; in fact the steam engine was the first major source of power after wind and water. Since then the power of vacuum is being utilized in many industries and has spawned many inventions including the vacuum cleaner and the vacuum flask.

Other practical applications include vacuum distillation, incandescent light bulbs (the vacuum ensures that air does not react with the hot filaments), television picture tubes, vacuum tubes, vacuum clamps (the main advantage is that the clamping force is on one side only) etc.

Some of the industries that use vacuum technology include
– Metallurgical
– Metal working
– Tool manufacturing
– Electrical, electronics & microelectronics
– Solar technology
– Medical technology
– Chemical
– Pharmaceutical &
– Food