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# Why do Body Float?

Why do Body Float? or body floating?
According to the Archimedes’ principle, when a body is partially or fully immersed in water, it displaces water equal to its volume. A body floats in water when its weight is less than that of an equal volume of water. If its weight is same as that of an equal volume of water it will remain afloat.

As you know, some bodies float on the surface of the water. Other bodies sink. There are even bodies that float in the water column, neither rising to the surface nor sinking to the bottom.

The reason for such different behavior of bodies lies in their density. If the density of the body is greater than the density of the liquid, then the body sinks to the bottom. If the density is the same as that of the liquid, then the body will float completely immersed in the liquid. But if the density of the body is less than the density of the liquid, then the body will float on the surface.

This third case is the most difficult, since the body can float on the surface in different ways. It may be that most of it will be under water, or it may be that most of it will be above water. It also depends on the density. The greater the difference between the densities of the liquid and the body, the smaller part of the body will be immersed in the liquid.

Moreover, this dependence is expressed strictly mathematically. If the density of the body is 2 times less than the density of the liquid, then half the volume of the body will be immersed in water. If the density is 5 times less than the liquid, then only 1/5th of the body will sink into the water, 4/5 will float on the surface. If the density of the body is 0.9 of the density of the liquid, then almost the entire body will be in the thickness of the liquid, only 1/10 of it will be on the surface. For example, ice floats in water.

Why does the buoyancy of bodies in liquids depend on densities? Because the density of the body affects the force of gravity acting on the body (F T \u003d m T g \u003d ρ T V T g). The density of the liquid determines the buoyancy force acting on the body (F A = ​​P W = m W g = ρ W V W g). In this case, the volume of the body immersed in the liquid V T is equal to V W . In fact, only the density is different in these formulas.

It is these two forces that act on a body in a fluid – gravity and buoyancy. They are oppositely directed, and it depends on which of them is greater whether the body will float or sink.

If the Archimedes force is equal to the force of gravity (F A \u003d F T ), then the body will be completely immersed in the liquid and float in it at any level, but not sink. If F A T, then the body will sink, since gravity is stronger.

If F A > F T , then the Archimedean force will push the body to the surface of the liquid. The extent to which it pushes the body out of the water depends on which part of the body is immersed, the buoyant force from the side of the liquid becomes equal to the force of gravity acting on the entire body.

The volume of a body part that is immersed in a liquid displaces a volume of liquid equal to this immersed part. The weight of this displaced fluid is equal to the buoyant force. But after all, the Archimedean force balances the weight of the body. This means that the weight of the whole body (P T = ρ T V T g) is equal to the weight of the displaced fluid (P W = ρ W V W g), which is equal to the volume of only a part of the body immersed in the liquid. Here V T is not equal to V W , since V T is the volume of the whole body, and V W is the volume of the part of the body immersed in the liquid or the volume of the liquid displaced by this part. However, the weights of the displaced fluid and the entire body are equal. Therefore, we can write:

ρ Т V Т g = ρ Ж V Ж g

Reducing the gravitational acceleration and transferring the volumes and densities, we get:

ρ T /ρ W = V W / V T

That is, how many times the density of the body will be less than the density of the liquid, the same number of times the volume of the part of the body immersed in the liquid will be less than the volume of the entire body.