Mass is one of the important properties of matter. This concept is used in solving problems of various nature, ranging from problems in mechanics to chemical calculations. We consider in the article, with the help of which formulas the mass in physics can be calculated.
What it is?
Before we give mass formulas in physics, we give it a definition. This term refers to a physical quantity that is proportional to the amount of matter contained in a given body. It should not be confused with the amount of a substance that is expressed in moles. Mass in SI is calculated in kilograms. Its other units are tons and grams.
There are two important types of mass:
The first type of the physical quantity under consideration characterizes the inertial properties of the body, that is, the ability of some force to change the speed of the body, as well as the kinetic energy that it possesses.
Gravitational mass is associated with the intensity of attraction between any bodies. It plays an important role in space, because thanks to the attraction between stars and planets, our galaxy and our solar system exist. However, the gravitational mass manifests itself in everyday life in the form of the presence of all bodies of some weight.
Inertia formulas
In physics, the formula for finding the inertial mass is as follows:
m = F / a
Here F is the force that acts on the body and causes the appearance of acceleration a. The formula shows that the greater the acting force and the less it will report the acceleration to the body, the greater the inertial mass m.
In addition to the written expression, one more formula for finding mass in physics, which is associated with the phenomenon of inertia, should be given. This formula has the form:
m = p / v
Here p is the momentum (momentum), v is the speed of the body. The more movement the body has and the less its speed, the greater the inertial mass it has.
Formula for gravity
A mathematical description of the phenomenon of gravity was made possible thanks to numerous observations of the motion of cosmic bodies. The results of all these observations in the XVII century were summarized by Isaac Newton in the framework of the law of universal gravitation. According to this law, two bodies that have masses m 1 and m 2 are attracted to each other with such force F:
F = G * m 1 * m 2 / r 2
Where r is the distance between the bodies, G is some constant.
If we substitute the value of the mass of our planet and its radius into this expression, then we get the following mass formula in physics:
m = F / g
Here F is gravity, g is the acceleration with which bodies fall to the ground near its surface.
As you know, the presence of gravity determines that all bodies have weight. Many people confuse weight and mass, believing that it is the same value. Both quantities are indeed related through the coefficient g, but weight is a variable quantity (it depends on the acceleration with which the system moves). In addition, weight is measured in Newtons and mass in kilograms.
Scales, which a person uses in everyday life (mechanical, electronic), show body weight, but measure its weight. The translation between these values ββis only a matter of calibrating the instrument.
Density and volume
As noted, mass is an integral property of matter, so it can be calculated using other physical characteristics of bodies. These characteristics are volume and density.
Volume is a portion of space that is bounded by the surface of the body. It is measured in cubic units of length, for example, in m 3 .
Density is a property of a substance that reflects the amount of matter placed in a unit volume.
The formula for the mass of a substance through volume and density is written as follows:
m = Ο * V
The larger the body volume and the higher its density, the greater the mass it possesses. In connection with this fact, it is useful to recall the famous riddle about what has a large mass: 1 ton of fluff or 1 ton of iron. In the absence of buoyant Archimedean force, the masses of both substances are equal. Fluff has a much lower density than iron, but the difference in density is compensated by a similar difference in volume.
Relative
The concept of relative mass is used in atomic physics and in chemistry. Since the masses of atoms and molecules have very small values ββ(β10 -27 kg), it turns out to be extremely inconvenient to operate them in practice when solving problems. Therefore, the community of scientists decided to use the so-called relative mass, that is, the considered value is expressed in units of mass in relation to the mass of a known standard. This standard was 1/12 of the mass of the carbon atom, which is 1.66057 * 10 -27 kg. The corresponding relative value is called the atomic unit (a.m.).
The formula for the relative mass M can be written as follows:
M = m a / (1/12 * m C )
Where m a is the mass of an atom in kilograms, m C is the mass of a carbon atom in kilograms. For example, if we substitute the mass of the oxygen atom in this expression, then its a. E. m will be equal to:
M = 26.5606 * 10 -27 / (1.66057 * 10 -27 ) = 15.9949.
Since a. E. m. is a relative quantity, then it has no dimension.
The convenience of applying this term in practice is not only in the small and whole values ββof this unit of measurement. The fact is that the value of a. e. m. coincides in magnitude with the molar mass expressed in grams. The latter is the mass of one mole of substance.
Energy
Different formulas were given above, how to find mass in physics. Concluding the article, I would like to note the relationship of mass and energy. This connection is fundamental in nature, which reflects the spatio-temporal properties of our universe. The corresponding mass formula in physics, obtained by Albert Einstein, has the form:
E = m * c 2
The square of the speed of light c is the conversion coefficient between mass and energy. This expression suggests that both quantities, in fact, are one and the same characteristic of matter.
The recorded expression was confirmed experimentally in the study of nuclear reactions and reactions of elementary particles.