Every student knows that if you throw a stone into the water, it will drown. On the other hand, a ship that is made of heavy metal floats on the surface of the water. Why do some bodies drown while others swim? This question will be answered by an article that details the navigation of ships.
Fluid and pressure in it
In class 7 physics, ship navigation is considered after the structural features and properties of liquids have been studied. The latter is an aggregate state of matter intermediate between gases and solids. A fluid is able to maintain volume as a solid, and it is a fluid substance, like gas.
Liquid molecules randomly move throughout the volume. The presence of kinetic energy comparable with potential in them causes the existence of pressure on each elementary volume inside the liquid. Since molecular displacements are equally probable, the total pressure on the elementary volume under consideration turns out to be zero (all pressure components cancel each other out).
Nevertheless, many people know that immersion under water creates pain in the area of โโthe ear membranes. This pressure has nothing to do with the molecular pressure discussed above. It is connected exclusively with the gravitational force of our planet.
Any body with mass presses on the surface on which it stands, or stretches the suspension. It's about body weight. In a liquid, this weight is manifested in the form of pressure of the upper layers on the lower ones. It is called hydrostatic. The mathematical expression for calculating this pressure is as follows:
P = ฯ l * g * h
That is, the hydrostatic pressure linearly depends on the immersion depth h and on the density of the liquid ฯ l . It is this pressure that causes ships to sail.
Ancient Greek philosopher and his law
According to one legend, the king of a certain Greek policy instructed Archimedes to determine whether his crown was made of pure gold, or the master deceived him and instead of gold added silver to the alloy. Archimedes successfully completed this order by immersing the crown in a vessel with liquid and thereby proving the fake product. The physical law that the philosopher used was now given his name.
Archimedes' law states that any body immersed in a fluid substance experiences its pushing force, the module of which is equal to the weight of the displaced substance, and the vector is directed upwards. The corresponding force was called Archimedean.
The reason for the appearance of the Archimedean force is the difference between the hydrostatic pressure acting on the lower surface of a solid body, which is immersed in a fluid substance, and the pressure acting on the upper surface of the body. The difference in the values โโof these parameters is due to the different depths at which the upper and lower parts of the body are located (see the formula in the previous paragraph).
The strength of Archimedes F A is determined by the formula:
F A = ฯ l * g * V l
Where V l - the volume of fluid displaced by the body immersed in it. This formula can be obtained independently if we use the expression for hydrostatic pressure and remember that force is the product of pressure and the area of โโimpact.
Why are ships sailing?
This question can be answered if we consider the physical forces acting on a solid object immersed in a liquid. It is easy to guess that there will be only two of these forces:
- upward force of Archimedes;
- downward gravity of the body.
The correlation of these forces will give an answer to the question of this paragraph. From the point of view of physics, the navigation of ships is due to the presence of buoyant Archimedean force, which exceeds the marked gravity modulo.
Formula for swimming conditions
We will figure out the ratio of what physical quantities determines the condition of navigation of ships. We established above that the body will not sink if the force of Archimedes F A is greater in magnitude than the force of gravity F t . Then we have the inequality:
F A > F t
Substitute here the formulas for F A and F t , we obtain:
ฯ l * g * V l > m s * g =>
m s <ฯ l * V l
A critical situation is one in which the body is completely immersed in liquid. In this case, the volume V l displaced by it will be exactly equal to the volume of the body V s itself . The latter allows us to rewrite the resulting inequality in the following form:
ฯ s * V s <ฯ l * V l =>
ฯ s <ฯ l
This is the main condition for sailing ships. That is, if the average density of the vessel does not exceed the density of the fluid substance in which it is located, then this vessel will never sink.
Note that if the densities are equal, the position of the body in the liquid will be unstable. Any minor external impact will be enough to sink the body or raise it to the surface.
Features of using the Archimedes law for swimming in liquids and gases
In water, navigation and ballooning are subject to the same Archimedes law.
In the case of sailing ships, it should be said that their hull is made of metal material. However, the weight of water displaced by them (displacement) exceeds their own weight, so they stay afloat (the average density of a ship with its cabins and hold is much lower than the density of water).
The idea of โโsailing submarines is to change their average density. For this, the submarine uses special ballast tanks into which water from the sea can either be pumped out or pumped out of them. In the first case, the boat will sink, in the second - to float. In fact, this idea was borrowed from nature as a result of observations of how fish use their swimming bladder.
Speaking about the navigation of ships and aeronautics, let us say a few words about the latter. A striking example of an aircraft is a balloon, or balloon. Its volume is filled with air. If this air is heated, then it will begin to expand, which will lead to a decrease in the density of the ball. The latter fact is a consequence of the fact that the Archimedean force becomes more than the weight of the ball, and it takes off.
Below is an informative video on the topic under discussion.
The task of calculating the capacity of the ship
It is known that the maximum displacement of the ship is 1000 tons. The mass of the ship is 300 tons. What maximum cargo can he sail with?
We write down the condition for the ship to sail through the acting forces. In this case, there will be three:
- ship weight P 1 ;
- cargo weight P 2 ;
- buoyancy force F A.
We have:
P 1 + P 2 <F A
Where do we get the weight of the cargo P 2 :
P 2 <F A - P 1
This inequality can be rewritten for the corresponding masses:
m 2 <m A - m 1
Here m 1 is the mass of the ship, m A is the mass of the displaced fluid, which coincides with the displacement.
We substitute the data from the conditions of the problem into inequality and we obtain that the mass of the cargo should not exceed 700 tons.