The principle that Archimedes discovered while taking a bath: buoyancy is equal to the weight of the displaced water. How do you understand it?

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The buoyancy is equal to the weight of the water displaced, which can be accurately stated as follows: the buoyancy of an object immersed in a stationary fluid is equal to the weight of the fluid displaced by the object. Therefore, the so-called buoyancy is equal to the weight of the water displaced, which means that this weight is exactly equal to the force that floats an object, not that the weight of the water displaced is exactly equal to the weight of the object, so don't get it wrong.

The buoyancy formula is: Fbuoy = ρliquid gVdisplaced, where Fbuoy represents buoyancy, ρliquid represents the density of the displaced liquid, g represents the acceleration of gravity, and V is the volume of the displaced liquid.

The water displaced by an object when it sinks into the water is the volume of the object, not the weight of the object. This is because the density of objects is different, and the volume of water displaced by objects of the same mass is also different.

Of course, if you know what substance is put into the water to displace water, you can also find out the weight or volume of the substance by calculating the volume of water displaced and then back-calculating based on the density of the substance.

density

To understand buoyancy, we must first understand the density of a substance. Density refers to the mass of a certain volume of a substance. The greater the density, the greater the mass of the same volume. The symbol for density is ρ, and the unit of density is generally kg (kilograms)/m^3 (cubic meters), and sometimes g (grams)/cm^3 (cubic centimeters).

The formula for calculating density is: ρ=m/V. Here ρ represents density, m is the mass of the object, and V is the volume. According to the formula, we can use the known to find the unknown, thus obtaining the modified formula: m=ρV or V=m/ρ. The first formula can be used to find the density of a substance when the mass and volume are known; the second formula can be used to find the mass of a substance when the density and volume are known; the third formula can be used to find the volume of a substance when the mass and density are known.

Any common substance on earth is composed of elements, so the density of a substance is generally the density of the elements or molecules that make up the substance. For example, the density of water is 1000kg/m^3, or 1g/cm^3. For the sake of convenience, we will use g/cm^3 as the unit and omit the unit.

Density of common substances: Gases include air 0.00129, hydrogen 0.00009, oxone 0.00018, neon 0.0009, oxygen 0.00143, nitrogen 0.00126, fluorine 0.001696, argon 0.00178, carbon dioxide 0.00198, radon 0.00973, etc.; Liquids include gasoline 0.7, alcohol 0.79, kerosene 0.8, vegetable oil 0.9, water 1.0, milk 1.03, hydrochloric acid 1.2, sulfuric acid 1.8, honey 1.4, etc.

Gases and liquids are fluids and have buoyancy, while solids have a very low density and have no buoyancy.

Common solids include: cork 0.25, dry wood about 0.5~0.8, ice 0.92, glass 2.6, aluminum 2.7, granite about 3.0, cast iron about 7.4, carbon steel about 7.85, copper 8.9, silver 10.5, lead 11.3, mercury 13.6, gold 19.32, platinum 21.4, iridium 22.56, osmium 22.59, etc.

The above densities are all in g/cm^3, and are only approximate numbers. From the densities of these substances, we can see that in general, the gas state is less dense than the liquid state, and the liquid state is less dense than the solid state, so only liquid and gaseous substances produce buoyancy. But there are exceptions. There are also solid substances that are less dense than liquid substances, such as cork and dry wood, so these solid substances can float on the water.

Although the density of solid matter is lower than that of liquid matter, it does not have buoyancy. Therefore, the so-called buoyancy is only a "patent" of liquid and gas states.

The density of an object is affected by air pressure and temperature. Under a certain pressure, the density of a substance will increase, and thermal expansion and contraction will also cause the density to change. Therefore, for the density of a pure substance, it refers to the density at 0°C and a standard sea level atmospheric pressure, that is, 101325 N/^2, or 101325 Pa.

Moreover, the density of a substance can generally only be accurately measured for pure substances. However, many substances in reality are compounds, not composed of pure elements, such as granite. Therefore, the density is only an approximation.

buoyancy

Buoyancy is of course related to the density of the material, but it does not depend entirely on the density of the material. For example, a ship made of steel can also float on the water, and a submarine can both dive into the water and float on the surface. In fact, the same is true for people, who can swim underwater or on their backs.

The textbook explanation of buoyancy is that the vertical upward force exerted on an object immersed in a fluid is called buoyancy. Therefore, buoyancy refers to the difference in fluid pressure on all surfaces in the fluid, that is, the resultant force. In layman's terms, the magnitude of buoyancy is equal to the weight of the fluid displaced by the object.

The buoyancy principle was created by Archimedes in 245 AD and is defined as: Fbuoyancy = Gdisplacement, that is, the buoyancy F is equal to the gravity G of the liquid displaced by the object after it sinks and comes to rest. The calculation formula is F=ρgV, where ρ represents density; g is the gravity constant, which is about 9.8N/kg; and V represents the volume of the displaced liquid, in m^3.

Some friends may find it difficult to understand these theories. In layman's terms, the source of buoyancy is still the density of matter. Although the density of steel is much greater than that of water, if the volume of a ship is increased, the average density will be much lower than the density of water, so of course it can float on the water.

For example, the density of carbon steel is about 7.85g/cm^3, while the density of water is only 1g/cm^3. So if you drop a piece of carbon steel into water, it will sink to the bottom with a "plop". But if you make a sealed box of 1 cubic meter with 1kg of carbon steel, its density will become 0.001g/cm^3, which is 1000 times lighter than water. How can it not float on the water?

Submarines also rely on this principle, by increasing their volume, their density decreases, and they can float on the water. However, in order to dive into the ocean, submarines are equipped with ballast tanks. As long as seawater is filled into the ballast tanks, the average density of the submarine volume increases, and it will sink. The depth of the submarine can be adjusted by the amount of water in the ballast tanks, and water must be discharged to rise.

There is a swim bladder in the belly of a fish, which is the white bubble you see in the belly when you kill the fish. It can hold gas. The density of gas is much smaller than that of water. Fish float up and down in the water by adjusting the amount of gas in the swim bladder and changing the density of its overall volume. Long-term evolution has enabled them to flexibly complete this adjustment.

The reason why people can float up and down in water is that the density of the human body is about the same as that of water, about 1.02g/cm^3, so as long as the hands and feet move slightly, they can float up and down. In theory, as long as a person stays calm and motionless in the water, he can float his mouth and nose on the surface of the water to breathe, but it is difficult to do this without good training.

Why can buoyancy test the purity of a substance?

Legend has it that Archimedes discovered the buoyancy theorem during a forced experiment. Archimedes was the greatest philosopher, mathematician, and physicist in ancient Greece, and was even known as an encyclopedic scientist, meaning he knew almost everything and was not stumped by anything.

Once, the king asked a craftsman to make him a pure gold crown. After it was made, the king suspected that the craftsman had embezzled the gold, so the crown was not pure gold. However, when the weight was weighed, it was the same as the gold the craftsman had taken away. Therefore, how to determine whether the craftsman had adulterated the gold was difficult for all the ministers and the king.

So the king summoned Archimedes, who was known as omnipotent, and asked him to solve the problem, otherwise he would be punished. Archimedes had no idea for a while, and he thought about it day and night. One day when he was taking a bath, he entered the bathtub and saw that the water in the bathtub was overflowing. He was so excited that he ran out shouting "Found it! Found it!" without even putting on his clothes.

After doing the experiment in the laboratory, he came to the palace and placed two basins full of water in front of the king. Then he put the crown and a piece of pure gold of the same weight into the two basins respectively. The water in the basins overflowed. He carefully collected the overflowing water from the two basins and weighed them. He found that the basin containing the crown overflowed more water than the basin containing pure gold. He concluded that the crown was adulterated.

Why is this so? This is because the density of gold is 19.32, and other cheaper silver, copper, and lead have lower densities than gold. Therefore, objects of the same weight will have a larger volume, and of course more water will overflow. Metals such as platinum and iridium, which have higher densities than gold, are rarer and more expensive than gold. Of course, craftsmen are not stupid enough to pay for them, so if they want to forge something, they can only use metals with lower density.

The king punished the craftsman and reduced the loss of the treasury. But these are not comparable to the significance of Archimedes' experiment, because it was Archimedes who discovered the law of buoyancy, which states that the buoyancy of an object in a liquid is equal to the weight of the liquid it displaces. The guiding role of this law in human civilization is incomparable to a crown.

Archimedes' brain is different from that of ordinary people. This master who lived more than 2,200 years ago could come up with eternal laws just by taking a bath, while ordinary people can only wash out a bunch of soap bubbles and dirt after taking a bath all their lives.

Since all substances have a certain density, which is the ratio of mass to volume, we can use the principle of buoyancy to measure the purity of a substance. The premise is that the measuring tool and the observation scale are precise enough. Put an object into a measuring cup filled with water, and you can get the density or purity of a substance by the amount of water displaced. The density table tells you what kind of substance it is and how pure it is.

For example, 1 gram of gold displaces only 0.0518 ml; 1 gram of silver displaces 0.0952 ml; 1 gram of copper displaces 0.1124 ml; 1 gram of lead displaces 0.0885 ml, and so on.

By measuring whether the displacement is consistent with the density of these substances, we can get the purity of these substances. However, there are many ways to measure the purity of these substances and the volume of objects. This old and clumsy method is rarely used.

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