What did Archimedes mean when he said: “Give me a foothold and I will turn the Earth”

(ORDO NEWS) — Archimedes (287 BC – 212 BC) – the great mathematician, physicist and engineer of Ancient Greece, who made many discoveries in the field of geometry and is the author of important inventions that determined his era.

It is believed that Archimedes is the author of the expression:

“Give me a foothold and I will turn the Earth.”

However, this is an abbreviated version that our contemporaries worked on. The original sounded a little different:

“Give me a lever long enough and a fulcrum that I can place it on and I’ll turn the world around.”

It was this expression that gave rise to the term “Archimedes lever”, which is used today to describe the motor force in general.

What did Archimedes mean when he spoke of the possibility of turning the world upside down?

Naturally, it was a figurative expression, but not absurd. In fact, Archimedes anticipated the foundations of mechanics, ahead of the legendary Newton by nearly 1,800 years.

In order to make it easy to understand the principle of operation of the Archimedean lever and the “overturning world”, together with you we will analyze a simple problem:

Suppose that you decide to tidy up your garden, getting rid of large stones, which, as it might seem at first glance, cannot be budged on their own. However, this is doable with the use of an Archimedean lever.

Let’s say the weight of the stone is 100 kilograms, the height is 30 centimeters, and the radius of the base is 25 centimeters. We need to calculate how much force will be required to move it.

To implement the plan, you need to create a lever, which is shown in the figure below:

What did Archimedes mean when he said Give me a foothold and I will turn the Earth 2

A small stone (point A) will serve as a fulcrum, and a long, strong stick will become a lever, which will be placed under the larger stone, resting on point A.

When lifting, the large stone will rotate about point B, and three forces will act on it:

  • Gravity mg;
  • Support reaction force N;
  • Lever force F3.

At the beginning of the movement of a large stone, the sum of the moments of the forces acting on it will be equal to zero (the second equilibrium condition). Therefore:

What did Archimedes mean when he said Give me a foothold and I will turn the Earth 3

If the shoulder l1 = 120 centimeters and the shoulder l2 = 20 centimeters, then the shoulder ratio is six. This means that to move a 100-kilogram stone, you need to apply a force of about 100N, which is equivalent to moving a 10-kilogram stone.

So, when Archimedes came to this, having proved his case in practice, he realized that the use of a lever allows you to “exchange force for distance.” In other words, if Archimedes had a giant lever and a fulcrum (for example, the Moon ), he could turn the Earth over on his own .

Sounds crazy, but theoretically it’s real.


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