Mass is a physical quantity definition. Body mass

Let's try to bring some clarity to the vague question - what is body mass?
Let's discard the ancient and often taking place in our time identification of body weight and its weight - after all, we are already smart people and we know that weight is just a force. The force with which any material body is attracted to Mother Earth or some other planet, star and other mega body, near the surface of which the body in question is located.
Let's begin to analyze the idea of ​​humanity about the mass from ancient times.

The term "mass" was apparently invented by ancient housewives, since this word from the ancient Greek "μαζα" is translated as "a piece of dough." Ancient scientists understood by mass a certain amount of matter contained in the physical body, without paying too much attention to it, believing that everything is clear anyway - a piece for themselves, and a piece.
Similar definitions of mass in popular sources of information are found to this day. Such terminology does not bring much clarity to the question of mass, and only raises additional questions - how much of such a substance, and what kind of substance is this?

The first scientific works devoted to an attempt to define the concept of the mass of bodies belong to Newton, who established a connection between the force interaction of bodies and a change in the nature of the movement of these bodies, i.e., acceleration. These (at that time - brilliant) thoughts of Newton were inspired by the experiments of the inquisitive Italian Galileo, who threw various objects down from the top of the Leaning Tower of Pisa, trying to refute the centuries-old delusion of mankind that a heavy body will fall to Earth faster than a lighter one. To the surprise of many onlookers, all the bodies that Galileo dropped landed at the same time.

Newton, having familiarized himself with the experiments of Galileo, went further in his reflections and conclusions - he, in one of his famous laws, indicated that the acceleration due to the action of any external force on a body is proportional to the magnitude of this force.
That is, the same body under the action of forces of different modulus will accelerate in proportion to the magnitude (modulus) of these forces: F \u003d ma, where m is the coefficient of this proportionality for each specific body, called its mass.

Newton, like many of his predecessors, did not dare to completely break the connection between the "piece of dough" and the mass of the body, considering the mass to be some measure of the amount of matter. Nevertheless, he took the first timid steps towards a break between the classical concepts of mass and matter, pointing to the non-material side of mass - its connection with the inertia of bodies, i.e., their eternal desire for peace. And this was already progress in science.

So, Newton was the first to use in his reflections two concepts of mass: as a measure of inertia and as a source of gravitation, i.e., gravity, without, however, separating mass from the amount of matter in the body. However, the interpretation of mass as a measure of the “quantity of matter” was increasingly criticized by physicists, and already in the 19th century it was recognized as unscientific, unphysical and meaningless.

Looking ahead, let's say that the final gap between the concepts of mass and the amount of substance "legally" was formalized in the last century, when the International System of Units SI, along with the seven basic and two additional units of measurement, introduced the unit of measurement of the amount of substance - the mole.

A stunning revolution in the idea of ​​mankind about the world around us was caused by the discoveries of another genius - Albert Einstein. With his theory of relativity, he released another portion of the fog into the concept of mass, refuting the prevailing dogmas about the constancy of the mass of bodies.
It suddenly turned out that the mass depends on the speed of the body, while the material body can never move with the maximum speed - the speed of light, otherwise its mass will become infinitely large. Einstein's conclusions suggested the idea of ​​a close relationship between mass and body energy, and it turned out that the whole world around us is nothing but some form of energy existence, which, as we know today, is a constant thing in magnitude.

Physicists have only to deal with some discrepancies in the mass of particles moving at the speed of light - photons, as well as hypothetical gluons and gravitons. After all, according to the above conclusions, the mass of such particles should be infinite, and that’s out of the question...
The illogical Gordian knot was cut with a careless wave - photons, gluons and gravitons were recognized as non-material particles that do not have mass in the usual sense.

Further reflections in the scientific community about mass even led to some classification of this concept - they distinguish between gravitational (or passive) mass, which characterizes the interaction of a body with external force fields and the ability of bodies to create such fields, and inertial mass, which characterizes the property of bodies to resist an increase in kinetic energy.
If we follow the logic of the most prominent minds of mankind, then the conclusion suggests itself that everything around us seeks to get rid of kinetic energy, that is, the energy of motion, and therefore from excess mass, since their mass grows with the speed of material bodies.
In general, this is not such a simple thing - body weight ... At least - it certainly cannot be compared with a piece of dough.

In some sources of information, the terms rest mass and relativistic mass are found, linking this physical quantity with the speed of the body, as well as the concept of "zero mass", which is possessed by particles moving at the speed of light - photons, gluons and gravitons, united by the common name - luxons. Luxons have no rest mass - they can only exist while moving.

One can safely guess that the reflections of mankind on the nature of the mass of bodies are far from their logical conclusion, since in recent years hypotheses and theories have appeared that try to cross out all the knowledge of mankind about the Universe. Some of these theories believe that the speed of light is not a milestone - there are also superluminal speeds. Within the framework of the special theory of relativity, the existence of particles with an imaginary mass, the so-called tachyons, is theoretically possible. The speed of such particles must be higher than the speed of light.

Other hypotheses introduce the concepts of negative and positive mass, arguing that the existence of material bodies or particles is possible, in which the momentum and energy of motion do not coincide with the direction of movement in space. As you can see, the fantasies of scientists are limitless, and it is impossible to predict what the wording of the concept of “body weight” will be in a dozen or two years.

Summing up the article, one can confidently point out only the ambiguity of such concepts as mass, weight and the amount of matter in the body.
Well, the final answer to the question - what is body weight - for the descendants.

In life, we very often say: “weight 5 kilograms”, “weighs 200 grams” and so on. And yet we do not know that we are making a mistake by saying so. The concept of body weight is studied by everyone in the course of physics in the seventh grade, however, the erroneous use of some definitions has mixed up with us so much that we forget what we have learned and believe that body weight and mass are one and the same.

However, it is not. Moreover, the mass of the body is a constant value, but the weight of the body can change, decreasing down to zero. So what is wrong and how to speak correctly? Let's try to figure it out.

Body weight and body weight: calculation formula

Mass is a measure of the inertia of the body, it is how the body reacts to the impact applied to it, or itself acts on other bodies. And the weight of the body is the force with which the body acts on a horizontal support or vertical suspension under the influence of the Earth's gravity.

Mass is measured in kilograms, and body weight, like any other force, in newtons. The weight of a body has a direction, like any force, and is a vector quantity. Mass has no direction and is a scalar quantity.

The arrow that indicates the weight of the body in the figures and graphs is always directed downward, as well as the force of gravity.

Body weight formula in physics is written as follows:

where m - body weight

g - free fall acceleration = 9.81 m/s^2

But, despite the coincidence with the formula and direction of gravity, there is a serious difference between gravity and body weight. Gravity is applied to the body, that is, roughly speaking, it is it that presses on the body, and the weight of the body is applied to the support or suspension, that is, here the body is already pressing on the suspension or support.

But the nature of the existence of gravity and body weight is the same attraction of the Earth. Strictly speaking, the weight of the body is a consequence of the force of gravity applied to the body. And just like gravity, body weight decreases with height.

Body weight in weightlessness

In a state of weightlessness, the weight of the body is zero. The body will not put pressure on the support or stretch the suspension and will not weigh anything. However, it will still have mass, since in order to give the body any speed, it will be necessary to apply a certain effort, the greater, the greater the mass of the body.

In the conditions of another planet, the mass will also remain unchanged, and the weight of the body will increase or decrease, depending on the force of gravity of the planet. We measure body weight with weights, in kilograms, and to measure body weight, which is measured in Newtons, we can use a dynamometer, a special device for measuring force.

WEIGHT

WEIGHT

(lat. massa, lit. - lump, lump, piece), physical. value, one of the character of matter, which determines its inertial and gravitational. sv. The concept of "M." was introduced into mechanics by I. Newton in determining the momentum (number of motion) of a body - p proportion. speed of free movement of the body v:

where is the coefficient proportionality m - a constant value for a given body, its M. An equivalent definition of M. is obtained from the equation of motion of Newton's classical mechanics:

Here M. is the coefficient. proportionality between the force f acting on the body and the acceleration a caused by it. Defined in this way, M. characterizes the Holy Islands of the body, yavl. a measure of its inertia (the more M. of the body, the less it acquires under the influence of constant force) and called. inertial or inert M.

In Newton's theory of gravity, magnetism acts as the source of the gravitational field. Each body creates gravitation, proportional. M. body, and is affected by the gravitational field created by other bodies, which is also proportional. M. This field causes the attraction of bodies with a force determined by Newton's law of gravity:

where r is the distance between the centers of mass of bodies, G is universal, and m1 and m2 are M. of attracting bodies. From f-ly (3) you can get the relationship between the M. of the body m and its weight P in the Earth's gravitational field:

where g \u003d GM / r2 - (M - M. Earth, r "R, where R is the radius of the Earth). M., defined by relations (3) and (4), called. gravitational.

In principle, it does not follow from anywhere that magnetism, which creates a gravitational field, also determines the inertia of the same body. However, experience has shown that inert and gravitational M. proportion. each other (and with the usual choice of units of measurement, they are numerically equal). This fundam. law of nature called the principle of equivalence. Experimentally, the principle of equivalence was established with very high accuracy - up to 10-12 (1971). Initially, M. was considered (for example, by Newton) as a measure of the number of in-va. Such a definition is quite definite. meaning only for homogeneous bodies, emphasizes the additivity of M. and allows us to introduce the concept of density - M. units. body volume. In the classic physics believed that the M. of the body does not change in any processes (the law of conservation of M. (in-va)).

The concept of "M." acquired a deeper meaning in A. Einstein's theory of relativity (see RELATIVITY THEORY), which considers bodies (or c-c) with very high speeds - comparable to the speed of light c»3 1010 cm/s. In the new mechanics, called. relativistic, the relationship between momentum and speed is given by the relation:

(at low speeds (v

i.e. M. h-tsy (body) grows with an increase in its speed. In relation. In terms of mechanics, the definitions of M. from equations (1) and (2) are not equivalent, since the acceleration ceases to be parallel to the force that caused it, and M. depends on the direction of the velocity of the particle. According to the theory of relativity, M. h-tsy is associated with its energy? ratio:

M. rest m0 determines the internal. the energy of wh-tsy - the so-called. rest energy?0=m0c2. T. energy (and vice versa), so in relation. In mechanics, the laws of conservation of matter and energy do not exist separately - they are merged into a single law of conservation of total (i.e., including rest energy h-c) energy. Their approximate separation is possible only in the classical. physics, when v states release an excess of energy (equal to the binding energy) D?, which corresponds to M. Dm=D?/c2. Therefore, the M. of a composite p-tsy is less than the sum of the M. of the p-ts that form it by the value D? / c2 (so-called). This phenomenon is especially noticeable in nuclear reactions.

The unit of M. in the CGS system of units is , and in the SI - . The mass of atoms and molecules is usually measured in atomic mass units. M. elem. h-c is usually expressed either in units. M. e-on (me), or in energetic. units (indicated by the corresponding hour). So, the M. e-on (me) is 0.511 MeV, the M. proton - 1836.1 me, or 938.2 MeV, etc. The nature of M. is one of the most important problems of physics that have not yet been solved. It is generally accepted that M. elem h-tsy is determined by fields, to-rye are associated with it (el.-magnet., nuclear, etc.). However, quantities. the theory of M. has not yet been created. There is also no theory explaining why M. ale. h-ts form a discr. values, and even more so allowing to determine this spectrum.

Physical Encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

WEIGHT

Fundam. physical quantity that determines the inertial and gravitational. properties of bodies - from macroscopic. objects to atoms and elementary particles - in the non-relativistic approximation, when their speeds are negligible compared to the speed of light With. In this approximation, M. of the body serves as a measure of the substance contained in the body, and the laws of conservation and additivity of M. take place: the mass of isolates. system of bodies does not change with time and is equal to the sum of M. bodies that make up this system. The non-relativistic is the limiting case relativity theory, considering motion at any speed up to the speed of light.

From the point of view of the theory of relativity M. t body characterizes its rest energy, according to the Einstein relation:

In the theory of relativity, as well as in non-relativistic theory, M. isolated. system of bodies does not change with time, but it is not equal to the sum M. of these bodies.

Inertial (or inertial, inertial) properties of M. in non-relativistic (Newtonian) mechanics are determined by the relations:

and the resulting relation

where is the momentum of the body, is the force, is the acceleration. M. is also included in f-lu kinetic. body energy T:

In the Newtonian theory of gravity, M. serves as a source of universal gravitational force, which attracts all bodies to each other. Force with which a body with mass mi attracts a body with mass t 2 , determined by Newton's law of gravity:

where - gravitational constant, a is the radius vector directed from the first body to the second. From f-l (4) and (6) it follows that the acceleration of a body freely falling in gravity. field, does not depend on its M., nor on the properties of the substance of which the body consists. This pattern, tested experimentally in the Earth's field with an accuracy of about 10 -8 and in the Sun's field with an accuracy of about 10 -12, is usually called. equality of inertial and gravitational. (gravitating, heavy) M., although it should be emphasized that we are not talking about the equality of two different M., but about the same physical. size - M., which determines decomp. phenomena. In the special theories of relativity, energy, momentum, and M. are interconnected by relationships that differ from the relationships of nonrelativistic mechanics, but pass into the latter at. An important role in relativistic mechanics is played by the concept of total energy, which is equal for a free body to the sum of its rest energy and kinetic. energy, Essentially the whole mechanics of a relativistic free particle is described by two equations:

Note that the value t, included in the right side of equation (7) is the same M., which is included in the equation of Newtonian mechanics. Unlike energy and momentum, which change when moving from one reference systems to the other, M. remains unchanged: it is a Lorentz invariant.

Relation (3) is also valid in the theory of relativity for arbitrary values ​​of , but relations (2) and (4) no longer hold. In particular, the direction and magnitude of the body's acceleration are determined not only by the force, but also by the speed, so that for not small values ​​it is impossible to introduce one quantity that would serve as a measure of the body's inertia, in this case it is impossible.

It is not in the relativistic case M. and the source of gravity. field, it is the energy-momentum, which generally has 10 components.

From equations (7) and (8) it follows that if the body has zero M., then it always moves at the speed of light and cannot be at rest, and vice versa, if the body moves at the speed of light, its M. should be equal to zero. In the limit, these equations imply that

That is, the Einstein relation (1) and the norelativistic expressions (2) and (5) for the momentum and kinetic are reproduced. energy.

For arbitrary values, from equations (7) and (8) for a body with, one can obtain

T. n. Lorentz factor.

In the special theory of relativity, the laws of conservation of energy and momentum take place. In particular, the energy (momentum R) systems h free particles is equal to the sum of their energies (momentums)

From here and from formula (7) it follows that M. of the system is not equal to the sum of M. of its constituent parts. So, it is easy to check that in the simplest case of two photons with energy each, their total M. is equal to zero if they fly in one direction, and if they fly in opposite directions. This example also illustrates the fact that in the theory of relativity M. systems of bodies is no longer a measure of the amount of matter.

The unit of m in the CGS system is the gram, in the SI it is the kilogram. M. of atoms and molecules is usually measured in atomic mass units. The M. of elementary particles is customarily measured in (or, using the system of units, in which c = 1, - in MeV). For example, M. electron M. proton M. the heaviest of the discovered elementary particles -

Numerous are known. examples of the interconversion of rest energy into kinetic energy. energy and vice versa. Thus, on colliding electron-positron beams, when colliding with energies and oppositely directed momenta, a resting Z-boson is born. During the annihilation of an electron and a positron at rest, all their rest energy is converted into kinetic energy. photon energy. As a result of thermonuclear reactions on the Sun, two electrons and four protons are converted into a helium nucleus and two, and kinetic energy is released. energy

In this case, in the kinetic energy is transferred by about 1% of the sum of M. particles entering into the reaction. During the fission of the uranium nucleus, MeV, which is ~ 10 -3 M. During the combustion of methane

Energy ~ 10 -10 M is released. In the process of photosynthesis, M increases by about the same amount due to the absorption of kinetic energy by the plant. photon energy.

If the particles are not free, as, for example, electrons in a metal or quarks in a nucleon, they have effective weight. Eff. The magnitude of a quark depends on the distance at which it is measured: the smaller the distance, the smaller. quark. There is a fundamental difference between the M. of a quark and the M. of an electron, since a quark, unlike an electron, cannot be in a free state.

The nature of M. elementary particles is one of Ch. physics questions. At the turn of the 19th and 20th centuries. assumed that M. may have an el.-mag. origin. In crust, it is known that e-mag. responsible for only a small fraction of M. electron. It is also known that the contribution to M. nucleons gives , due to gluons, and not M. included in the quarks. But it is not known what causes M. leptons and quarks. There is a hypothesis that here Funds play a role. bosons with zero spin - the so-called. Higgs bosons (see Higgs mechanism). The search for these particles is one of the main problems of high energy physics.

In educational, popular scientific and encyclopedic literature (in particular, in the articles of this encyclopedia devoted to relativistic particle accelerators), archaic terminology, which arose in the beginning, is still widespread. 20th century in the process of creating the theory of relativity. Its starting point is the use of f-ly in the region of non-small values ​​where f-la (8) is valid. As a result, statements arose that the M. of a body grows with an increase in its speed (energy), possesses M., and there is a complete equivalence between M. and energy:

Contrary to what A. Einstein wrote in the article and book, it is often this f-lu, and not f-lu (1) that is called Einstein's f-lo. So, a certain M., as a rule, is denoted t and called M., more rarely - relativistic M. or M. motion. At the same time, the usual M., which was discussed in this article, is called M. of rest or own M. and denoted t 0 . One of the main f-l of the theory of relativity is declared f-la

All this leads to terminology. confusion, creates distorted ideas about the foundations of the theory of relativity, creates the impression that the value plays the role of inertial and gravitational. M. However, this is not true. For example, if the accelerating force is parallel to the velocity of the body, then the "measure of inertia" is the so-called. "longitudinal mass", dr. an example is a relativistic generalization of f-ly (B) on the motion of a light particle (electron or photon) in gravitation. heavy body mass field M(e.g. Earth or Sun). It can be shown (based on the general theory of relativity) that in this case the force acting on a light particle is equal to

where At this f-la passes into (6). At , the quantity playing the role of "gravitational force" turns out to depend not only on the energy of the particle, but also on the mutual direction . If , then "gravity. M." is equal to , and if , then it is equal to

[for a photon _ T. o., it makes no sense to talk about "gravity. M." photon, if for a photon vertically incident on a massive body (eg, the Earth, the Sun) this value is 2 times less than for a photon flying horizontally on the surface of the body. This is the reason why the angle of deflection of a photon in gravity. the solar field turns out to be 2 times larger than it follows from the interpretation of the value as M.

In general, the terminology that uses the concepts of "M. of rest", "M. of motion", f-ly (11), (12), etc. artifacts, makes it difficult to understand the essence of the theory of relativity, makes it difficult to get acquainted with the modern. scientific literature.

Lit.: 1) Einstein A., Ist die Tragheit eines Korpers von seinem Energieinhalt abhangig?, "Ann. Phys.", 1905, Bd 18, S. 639-41; 2) Einstein A., The essence of the theory of relativity, trans. from English, M., 1955, p. 7-44; 3) Landau L. D., Lifshits E. M., Field Theory, 7th ed., M., 1988; 4) Taylor E., Wheeler D., Physics of space - time, trans. from English, 2nd ed., M., 1971. L. B. Okun.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1988 .

• Dictionary of foreign words of the Russian language

See a lot, mob... Dictionary of Russian synonyms and expressions similar in meaning. under. ed. N. Abramova, M .: Russian dictionaries, 1999. mass piece, many, crowd, mob, many ... Synonym dictionary

WEIGHT- (1) one of the main physical characteristics of matter, which is a measure of its inertial (see) and gravitational (see) properties. In the classical (see), the mass is equal to the ratio of the force F acting on the body to the acceleration a acquired by it: m \u003d F / a (see). ... ... Great Polytechnic Encyclopedia

WEIGHT, masses, women. (lat. massa). 1. A lot, a large number. Mass of people. Tired of the mass of impressions. A lot of trouble. 2. more often pl. Wide circles of workers, the population. The working masses. Stay away from the masses. The vital interests of the peasant ... ... Explanatory Dictionary of Ushakov

- - 1) in the natural scientific sense, the amount of matter contained in the body; the resistance of a body to a change in its motion (inertia) is called inertial mass; the physical unit of mass is the inert mass of 1 cm3 of water, which is 1 g (gram ... ... Philosophical Encyclopedia

- (from the Latin massa lump, lump, piece), a fundamental physical quantity that determines the inert and gravitational properties of all bodies from macroscopic bodies to atoms and elementary particles. As a measure of inertia, mass was introduced by I. Newton with ... ... Modern Encyclopedia

One of the main physical characteristics of matter, which determines its inert and gravitational properties. In classical mechanics, the mass is equal to the ratio of the force acting on the body to the acceleration it causes (Newton's 2nd law) in this case, the mass ... ... Big Encyclopedic Dictionary

MASS, better masa female, lat. substance, body, matter; | thickness, the totality of matter in a known body, its materiality. The volume of the atmosphere is vast, and the mass is negligible. Such a mass will crush everything. A mass of goods, a heap, an abyss. | merchant all property... Dahl's Explanatory Dictionary

- (symbol M), a measure of the amount of a substance in an object. Scientists distinguish two types of masses: gravitational mass is a measure of mutual attraction between bodies (earth attraction), expressed by Newton in the law of universal gravitation (see GRAVITATION); inert... Scientific and technical encyclopedic dictionary

The concept with which we are familiar from early childhood is the mass. And yet, in the course of physics, some difficulties are associated with its study. Therefore, it is necessary to clearly define how it can be recognized? And why is it not equal to weight?

Determination of mass

The natural scientific meaning of this quantity is that it determines the amount of matter that is contained in the body. For its designation, it is customary to use the Latin letter m. The unit of measurement in the standard system is the kilogram. In tasks and everyday life, off-system ones are also often used: grams and tons.

In a school physics course, the answer to the question: “What is mass?” given in the study of the phenomenon of inertia. Then it is defined as the ability of a body to resist a change in the speed of its movement. Therefore, the mass is also called inert.

What is weight?

First, it is a force, that is, a vector. Mass, on the other hand, is a scalar weight always attached to a support or suspension and directed in the same direction as gravity, that is, vertically downwards.

The formula for calculating the weight depends on whether this support (suspension) is moving. When the system is at rest, the following expression is used:

P \u003d m * g, where P (in English sources the letter W is used) is the weight of the body, g is the acceleration of free fall. For the earth, g is usually taken equal to 9.8 m / s 2.

The mass formula can be derived from it: m = P / g.

When moving down, that is, in the direction of the weight, its value decreases. So the formula takes the form:

P \u003d m (g - a). Here "a" is the acceleration of the system.

That is, when these two accelerations are equal, a state of weightlessness is observed when the weight of the body is zero.

When the body begins to move upwards, they speak of an increase in weight. In this situation, an overload condition occurs. Because body weight increases, and its formula will look like this:

P \u003d m (g + a).

How is mass related to density?

Solution. 800 kg/m 3 . In order to use the already known formula, you need to know the volume of the spot. It is easy to calculate if we take the spot for a cylinder. Then the volume formula will be:

V = π * r 2 * h.

Moreover, r is the radius, and h is the height of the cylinder. Then the volume will be equal to 668794.88 m 3. Now you can calculate the mass. It will turn out like this: 535034904 kg.

Answer: the mass of oil is approximately equal to 535036 tons.

Task number 5. Condition: The length of the longest telephone cable is 15151 km. What is the mass of copper that went into its manufacture, if the cross section of the wires is 7.3 cm 2?

Solution. The density of copper is 8900 kg/m 3 . The volume is found by a formula that contains the product of the area of ​​​​the base and the height (here, the length of the cable) of the cylinder. But first you need to convert this area into square meters. That is, divide this number by 10000. After calculations, it turns out that the volume of the entire cable is approximately equal to 11000 m 3.

Now we need to multiply the density and volume values ​​​​to find out what the mass is equal to. The result is the number 97900000 kg.

Answer: the mass of copper is 97900 tons.

Another issue related to mass

Task number 6. Condition: The largest candle weighing 89867 kg was 2.59 m in diameter. What was its height?

Solution. Wax density - 700 kg / m 3. The height will need to be found from That is, V must be divided by the product of π and the square of the radius.

And the volume itself is calculated by mass and density. It turns out to be equal to 128.38 m 3. The height was 24.38 m.

Answer: the height of the candle is 24.38 m.

Mass (physical value) Weight, a physical quantity, one of the main characteristics of matter, which determines its inertial and gravitational properties. Accordingly, M. is inert and M. gravitational (heavy, gravitating).

The concept of M. was introduced into the mechanics of I. Newton. In Newton's classical mechanics, M. is included in the definition of momentum ( momentum) body: the momentum p is proportional to the speed of the body v,

p = m.v.

The coefficient of proportionality - a constant value m for a given body - is the M. of the body. An equivalent definition of M. is obtained from the equation of motion of classical mechanics

f = ma.

Here M. is the coefficient of proportionality between the force acting on the body f and the acceleration of the body caused by it a. The mass defined by relations (1) and (2) is called inertial mass, or inertial mass; it characterizes the dynamic properties of the body, is a measure of the inertia of the body: at a constant force, the greater the M. of the body, the less acceleration it acquires, that is, the slower the state of its movement changes (the greater its inertia).

Acting on different bodies with the same force and measuring their accelerations, one can determine the ratios of M. of these bodies: m 1 :m 2 :m 3 ... = a 1 : a 2 : a 3 ...; if one of the M. is taken as a unit of measurement, one can find the M. of the remaining bodies.

In Newton's theory of gravitation, magnetism appears in a different form - as a source of the gravitational field. Each body creates a gravitational field proportional to the M. of the body (and is affected by the gravitational field created by other bodies, the strength of which is also proportional to the M. bodies). This field causes the attraction of any other body to this body with a force determined by Newton's law of gravity:

where r is the distance between the bodies, G is the universal gravitational constant, a m 1 and m 2 ‒ M. attracting bodies. From formula (3) it is easy to obtain a formula for weightР bodies of mass m in the Earth's gravitational field:

P \u003d m g.

Here g = G M / r 2 is the free fall acceleration in the Earth's gravitational field, and r » R is the Earth's radius. The mass determined by relations (3) and (4) is called the gravitational mass of the body.

In principle, it does not follow from anywhere that magnetism, which creates a gravitational field, also determines the inertia of the same body. However, experience has shown that inertial magnetism and gravitational magnetism are proportional to each other (and with the usual choice of units of measurement, they are numerically equal). This fundamental law of nature is called the principle of equivalence. Its discovery is associated with the name of G. Galilee, who established that all bodies on Earth fall with the same acceleration. BUT. Einstein put this principle (which he formulated for the first time) at the basis of the general theory of relativity (cf. gravity). The principle of equivalence has been established experimentally with very high accuracy. For the first time (1890‒1906), a precision check of the equality of inert and gravitational magnetism was carried out by L. Eötvös, who found that M. matched with an error of ~ 10-8 . In 1959–64 the American physicists R. Dicke, R. Krotkov, and P. Roll reduced the error to 10-11 , and in 1971 the Soviet physicists V. B. Braginsky and V. I. Panov reduced the error to 10-12 .

The principle of equivalence makes it possible to most naturally determine the M. of a body weighing.

Initially, mass was considered (for example, by Newton) as a measure of the amount of matter. Such a definition has a clear meaning only for comparing homogeneous bodies built from the same material. It emphasizes the additivity of the M. ‒ The M. of a body is equal to the sum of the M. of its parts. The mass of a homogeneous body is proportional to its volume, so we can introduce the concept density‒ M. units of body volume.

In classical physics, it was believed that the M. of a body does not change in any processes. This corresponded to the law of conservation of matter (substance), discovered by M. V. Lomonosov and A. L. Lavoisier. In particular, this law stated that in any chemical reaction the sum of M. of initial components is equal to the sum of M. of final components.

The concept of M. has acquired a deeper meaning in the mechanics of special. A. Einstein's theory of relativity (see. Relativity theory), which considers the movement of bodies (or particles) with very high speeds - comparable to the speed of light with » 3×1010 cm/sec. In the new mechanics - it is called relativistic mechanics - the relationship between the momentum and the velocity of a particle is given by the relation:

At low speeds (v<< с ) это соотношение переходит в Ньютоново соотношение р = mv . Поэтому величину m 0 называют массой покоя, а М. движущейся частицы m определяют как зависящий от скорости коэфф. пропорциональности между р и v :

With this formula in mind, in particular, they say that the momentum of a particle (body) increases with an increase in its velocity. Such a relativistic increase in the momentum of a particle as its velocity increases must be taken into account when designing particle accelerators high energies. M. rest m 0 (M. in the reference frame associated with the particle) is the most important internal characteristic of the particle. All elementary particles have strictly defined values ​​of m 0 inherent in this kind of particles.

It should be noted that in relativistic mechanics the definition of M. from the equation of motion (2) is not equivalent to the definition of M. as a proportionality factor between the momentum and velocity of a particle, since acceleration ceases to be parallel to the force that caused it, and M. turns out to depend on the direction of the particle's velocity.

According to the theory of relativity, the momentum of a particle m is related to its energy E by the relation:

M. rest determines the internal energy of the particle - the so-called rest energy E 0 \u003d m 0 c 2 . Thus, energy is always associated with M. (and vice versa). Therefore, there is no separate (as in classical physics) law of conservation of M. and the law of conservation of energy - they are merged into a single law of conservation of total (that is, including the rest energy of particles) energy. An approximate division into the law of conservation of energy and the law of conservation of magnetism is possible only in classical physics, when the particle velocities are small (v<< с ) и не происходят процессы превращения частиц.

In relativistic mechanics, magnetism is not an additive characteristic of a body. When two particles combine to form one compound stable state, an excess of energy (equal to binding energy) DE , which corresponds to M. Dm = DE / s 2 . Therefore, the M. of a composite particle is less than the sum of the M. of the particles that form it by the value DE / s 2 (so-called mass defect). This effect is especially pronounced in nuclear reactions. For example, the M. of a deuteron (d) is less than the sum of the M. of a proton (p) and a neutron (n); defect M. Dm is associated with the energy E g of the gamma quantum (g) produced during the formation of a deuteron: p + n ® d + g, E g \u003d Dm c 2 . M.'s defect, which occurs during the formation of a composite particle, reflects the organic connection of M. and energy.

The unit of M. in the CGS system of units is gram, and in International system of units SI - kilogram. The mass of atoms and molecules is usually measured in atomic mass units. It is customary to express the mass of elementary particles either in units of the mass of the electron m e , or in energy units, indicating the rest energy of the corresponding particle. So, the M. of an electron is 0.511 MeV, the M. of a proton is 1836.1 meV, or 938.2 MeV, etc.

The nature of mathematics is one of the most important unsolved problems of modern physics. It is generally accepted that the magnetism of an elementary particle is determined by the fields associated with it (electromagnetic, nuclear, and others). However, the quantitative theory of M. has not yet been created. There is also no theory explaining why the M. of elementary particles form a discrete spectrum of values, and even more so, allowing to determine this spectrum.

In astrophysics, the magnetism of a body that creates a gravitational field determines the so-called gravity radius bodies R gr = 2GM/c 2 . Due to gravitational attraction, no radiation, including light, can go outside, beyond the surface of a body with a radius R £ R gr . Stars of this size would be invisible; so they were called black holes". Such celestial bodies must play an important role in the universe.

Lit .: Jammer M., The concept of mass in classical and modern physics, translated from English, M., 1967; Khaikin S. E., physical foundations of mechanics, M., 1963; Elementary textbook of physics, edited by G. S. Landsberg, 7th ed., vol. 1, M., 1971.

Ya. A. Smorodinsky.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Mass (physical quantity)" is in other dictionaries:

- (lat. massa, lit. lump, lump, piece), physical. value, one of the har to matter, which determines its inertial and gravitational forces. sv. The concept of "M." was introduced into mechanics by I. Newton in the definition of the momentum (number of motion) of the body momentum p proportional. ... ... Physical Encyclopedia

- (lat. massa). 1) the amount of substance in the object, regardless of the form; body, matter. 2) in the hostel: a significant amount of something. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. MASS 1) in physics, quantity ... ... Dictionary of foreign words of the Russian language

- - 1) in the natural scientific sense, the amount of matter contained in the body; the resistance of a body to a change in its motion (inertia) is called inertial mass; the physical unit of mass is the inert mass of 1 cm3 of water, which is 1 g (gram ... ... Philosophical Encyclopedia

WEIGHT- (in the ordinary view), the amount of substance contained in a given body; the exact definition follows from the basic laws of mechanics. According to Newton's second law, "the change in motion is proportional to the acting force and has ... ... Big Medical Encyclopedia

Phys. the value characterizing the dynamic. sv va tepa. I. m. is included in Newton's second law (and, thus, is a measure of the body's inertia). Equal to gravity. mass (see MASS). Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A... Physical Encyclopedia

- (heavy mass), physical. a value that characterizes the body's power as a source of gravity; equal to the inertial mass. (see MASS). Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1983... Physical Encyclopedia

Phys. a value equal to the ratio of mass to count in VA. Unit M. m. (in SI) kg / mol. M \u003d m / n, where M M. m. in kg / mol, m is the mass in va in kg, n is the number in va in moles. Numerical value M. m., vyraz. in kg / mol, equally refers. molecular weight divided by... Big encyclopedic polytechnical dictionary - size, character ka physical. objects or phenomena of the material world, common to many objects or phenomena as qualities. relation, but individual in quantities. relationship for each of them. For example, mass, length, area, volume, electric power. current F ... Big encyclopedic polytechnic dictionary