Everyone knows that some bodies thrown into the water drown, while other objects remain on the surface of the liquid and float in it. What is the physical reason for this behavior? This article will answer this question, in which the conditions for swimming bodies are considered.
Fluid and hydrostatic pressure
Before setting forth the conditions for swimming bodies, one should study the properties of the medium in which they are located. A liquid is a disordered state of matter in which molecules and atoms have a binding energy approximately equal to their kinetic energy. The latter fact allows them to move freely throughout the fluid volume. At the same time, there is no certain direction for the indicated movement. That is, each molecule is displaced equally likely by any vector in three-dimensional space.
If we consider the microscopic volume of liquid inside it, then molecules will exert pressure on it from all sides. All pressures are equal in magnitude and opposite in direction, so they are balanced, and the volume under consideration is at rest.
The action of gravity leads to the appearance of the so-called hydrostatic pressure (for gases it is called aerostatic). This pressure arises due to the fact that the upper layers of the liquid press with their weight on the lower ones. The hydrostatic pressure P g is calculated by the formula:
P g = Ο * g * h.
Here Ο is the fluid density, h is the depth, g = 9.81 m / s 2 . Thus, the greater the depth, the higher the value of P g .
Archimedes Law
The conditions for swimming bodies are closely related to the law discovered by the ancient Greek philosopher Archimedes. This law can be formulated as follows: any solid body immersed partially or completely in a fluid substance (gas or liquid) experiences a buoyancy force, the value of which is equal to the weight of the displaced substance. Note that the law is valid for both liquids and gases. The indicated buoyancy force was called Archimedean.
The reason for the appearance of the Archimedes force can be understood if we mentally conduct the following experiment: suppose that we have some solid body that we immerse completely in a liquid, for example, in water. We assume that the body is limited by three surfaces: lateral, upper and lower. Hydrostatic pressure acts on all these surfaces, but its resulting value on the lateral surface will be zero.
Hydrostatic pressure directed upwards acts on the bottom of the body. It also acts on the upper body, but is directed downward. The difference in these pressures leads to the formation of a buoyancy force F A. For the experiment in question, we can write the following expression:
F A = (P 2 - P 1 ) * S = Ο * g * S * (h 2 -h 1 ) = Ο * g * V.
Here S is the area of ββthe upper and lower surfaces, h 2 and h 1 are the depths at which the lower and upper surfaces of the body are located, respectively. The value of V is the volume of the body (here, for simplicity, we assumed that it has the shape of a rectangular prism).
Thus, we have obtained a formula for determining the Archimedean force. Note that the product of density and the volume of the displaced fluid (in the experiment it is equal to the volume of the body) is the mass of the fluid.
Forces acting on a body immersed in a liquid
As already noted, the Archimedean force and the swimming conditions of bodies are interconnected. Consider this relationship from the point of view of mathematics.
Newton's first law states that the body will maintain a state of rest if external forces do not act on it. As applied to the case of a body immersed in a liquid, it can be said that it will float when all the forces that have an effect on it balance each other. There are only two such forces:
- body weight;
- buoyancy force.
If the first is larger than the second, then the body will never be able to swim and will sink. If the second is larger than the first, then the body can never drown. To immerse it completely in the liquid, you will have to apply some external force.
The physics of the swimming conditions of bodies is in the numerical ratio of the considered forces.
When will the bodies swim?
The basic condition for swimming bodies has already been mentioned above. Here we consider it from a mathematical point of view and get some important conclusions.
A body will be in equilibrium in a liquid if its weight and Archimedean force are equal:
P = F A =>
m * g = Ο l * g * V l .
Here m is the body mass, Ο l , V l is the density of the fluid and its displaced volume. Since the body is completely immersed in substance, the following equality holds:
V s = V l .
Here V s is the volume of the body. Writing the mass m through the density and volume of the body, we obtain:
Ο s * V s * g = Ο l * g * V l =>
Ο s = Ο l .
We got a simple formula that reflects the condition of floating bodies in a liquid. It turns out that the buoyancy of bodies does not depend on their mass, shape, volume. And it does not even depend on the material from which they are made. Buoyancy is determined only by the ratio between the average density of the body and fluid. If the density Ο s is greater than Ο l , then the force of gravity will exceed the ejection value. And the body will begin to sink. Conversely, if Ο s is less than Ο l , then the body will remain on the surface of the liquid.
Where is this phenomenon used?
Archimedes' Law finds application in a number of natural phenomena and technological solutions. We list only a few of them:
- Sailing ships in water and balloons in the air would not have been possible without the presence of buoyancy force. Although the ship is made of materials whose density is much higher than this value for water, it has many voids (cabins, holds) inside it filled with air. The latter fact leads to the fact that the average density of the ship is less than water.
- The change in the depth of immersion of the fish is due to a change in their average density due to the contraction or inflation of the swimming bladder.
- The measuring device used to determine the alcohol content or check the purity of milk uses the principle of Archimedes for its functioning.
Problem solving example
We apply the stated theoretical material to solve a practical problem. It is known that a cube with a side of 20 cm has a mass of 7.2 kg. Will this cube swim in water?
To answer the question of the problem, you should use the condition of swimming bodies. To do this, it is necessary to calculate the density of the cube and compare it with this value for fresh water (density 1 g / cm 3 ). We have:
Ο s = m / V = ββm / a 3 = 7200/20 3 = 0.9 g / cm 3 .
The cube density Ο s is 10% less than this value for water, so the cube will float in the liquid.