Archimedes and floating bodies

in #steemstem6 years ago (edited)


[ One page of Archimedes Palimpsest, On Floating Bodies ](By Matthew Kon - http://www.lix.polytechnique.fr/Labo/Ilan.Vardi/arch_eabig.jpg?36,70, Public Domain, Link)

Everyone knows Archimedes' law of floating bodies. It says that the body, immersed in a liquid or gas, has an EJECTING force. It can also be called the Archimedean force or the hydrostatic buoyancy force.

I do not know when it began to be interpreted by law, but if we turn to the original source, this rule sounds quite different.

[ Domenico-Fetti Archimedes 1620 ](By http://archimedes2.mpiwg-berlin.mpg.de/archimedes_templates/popup.htm, Public Domain, Link)
Archimedes is an ancient Greek mathematician, physicist and engineer from Syracuse. Lived in 287 BC. e. - 212 BC. e. They wrote several works, one of which will be of interest to us - a Treatise on floating bodies (περὶ τῶν ὀχουμένων).
At the very beginning of this work, we can read the following conclusion, made by Archimedes, most likely which formed the basis of Archimedes' law.
"Suppose that a liquid is of such a nature that, from its particles located at the same level and adjacent to each other, the less compressed are pushed out more compressed and that each of its particles is squeezed by the liquid above it in the plumb, unless the liquid is enclosed in any vessel and is not compressed by anything else. "
I am very impressed with the old definitions, which for some reason are forgotten or changed to new concepts. It's like renaming some names. But as a result of this we lose the original meaning, which was laid by the discoverer. What makes the essence of the action difficult for perception and comprehension.

[ Principio di Archimede galleggiamento ](Public Domain, Link)
On the example of Archimedes' law I will try to show this. As you could read above, the rule put forward by Archimedes suggested that the liquid is a substance consisting of elastic particles, otherwise they would deform, and not be pushed out.
Let's start with the fact that on any body, in the conditions of the Earth, the force of gravity of the Earth acts. Even if it is a fluff, it will still be attracted by the Earth and its movement will always be directed towards the Earth, simplistically, it will fall to Earth. All bodies fall to the Earth with the same acceleration, which is called the acceleration of free fall. But in reality, it's not like that at all. Because our imaginary fluff is not in space free from other bodies. I deliberately wrote bodies, although it is difficult for us to imagine that the atmosphere is a body, since it is gaseous. But nevertheless, even gas is a body, and in this case the Earth attracts the body, so the law of universal gravitation implies the interaction of two bodies, and not the body and any substance. As far as I know, the same principle applies to aircraft construction, when the gaseous atmosphere in which the wing of the aircraft is moving is defined as the body.
This means that we have: our fuzz, to which the only Force acts - This is the force of gravity of the Earth and the atmosphere, to which the force of gravity of the Earth also acts. These forces are directly proportional to the amount of matter and size that the body has. Now we will transfer all this into liquid, as Archimedes described.
We have a liquid and a trial wooden spherical body (hereinafter ball), which we immerse in the liquid.

  • the liquid is affected by the force of gravity of the Earth,
  • the force of attraction of the earth acts on the ball.

It is logical to assume that both bodies will move toward the Earth. But this does not happen, and the ball moves in the opposite direction and floats up. We are well aware that the tree does not sink in the water. Why is it happening. The force is one, the direction of the force is one, and the motions are directed in opposite directions.
Once again, the force is directed in one direction, but the bodies move in the opposite direction !!!
And that's why the interpretation of this phenomenon in the definition of Archimedes is correct. We put a body in the water that took a certain amount of water, but by the amount of matter, it is different. The amount of matter is less than if this volume occupied the liquid. It is not difficult to conclude that since the amount of matter is less then the force directed from the Earth side will be less, and the liquid will be greater. As Archimedes asserted, the more compressed particles of water (and in our case, the more the substance, the more pressure it will exert on the support) will be pushed to the side of the less compressed. The reason for this pressure is the same gravitational force of the Earth. As a result of this action, the liquid will be squeezed out to the side where the pressure is less.
The force of attraction acts on the water and the body - the ball. Where did the action of the liquid come from? She began to somehow change? No. Only its position and shape change, as a result of the force of attraction. But the total volume of the liquid is constant. Of course, we can say that through the liquid or through a liquid, the force of attraction acts on the ball. But in this case, the liquid, not the object of the impact, but the method of transmission of the impact. Perhaps you guessed how it is called, if not at the end of the article I will inform you.
In order for the fluid to exert influence, it must somehow change. If we heat water, it will increase in volume or with an unnamed volume, pressure will increase - the effect of the liquid. In this case, we can assert that the liquid is pushed or pushed out. And it does it precisely because of the emergence of internal forces.
In the case of floating bodies, the situation is completely different. For example, imagine that you put someone on your shoulders. And now, squat. When you squat, this is tantamount to the body drowning, in this case the body sits on your shoulders, and you are liquid. When you go up, the body will float, because the amount of liquid under the body has increased. But I would not say that you push the body out. So in my understanding, if you do not change the relationship with the body, then you do not act on it. As a result of the action of force, the position of the body must change relative to the source. If this does not happen, then the force of the action is zero. You do not say that the car in which you are driving acts on you.
On the body, which is in a liquid or in a gas, on the side of a liquid or gas, the force can not act if this body does not change its position relative to the liquid or gas. Not from the bottom not from above, there is no strength. Lateral interaction certainly is, so the body in the liquid in these areas moves. And of course from the opposite direction of the movement, the same effect.
But from the side of the fluid of impact, there is no push.
Once again, Archimedes asserted that the liquid (particles) is squeezed out to the side of less compressed. This is the cause, the movement of the body in a liquid or gas. The fluid changes its shape as a result of the Earth's attraction.

[Submarine control surfaces](By XLerate at the English language Wikipedia, CC BY-SA 3.0, Link)
If the liquid could push out the bodies, there would be no problem raising the body from the bottom, for example, a submarine. If the boat lands on the bottom, then no pressure of the liquid is capable of raising it or pushing it out. Because once again I draw your attention, the body moves along with the liquid (like a sitting man on the shoulders), the fluid relative to the body is not mobile. Since the object lies on the bottom, then there is no liquid under it, and even if it is a fluff, and many times lighter than water, it will never come up. Because to float the input you must be on the water, from above, to be a continuation of the water. In submarines for such a case there are special blowing nozzles that create a pressure capable of raising the boat from the bottom and allowing water to fill the gap between the boat and the bottom. Next, the lifting of the business of engineering and crew calculations.

In conclusion, someone can say that all this is sophistry and in fact nothing changes. The body is pushed out by the liquid if it is lighter than it. So it is, but still it reminds Baron Munchausen with his bike as he pulled himself by the hair from the swamp.
I said before about what the liquid is, if you did not guess, then the liquid in this case is a normal lever that transmits the force created by the force of gravity of the Earth.
The force of attraction, through the lever-liquid, affects the body placed in the liquid.
I wonder your opinion and questions ...

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