The mass is a fundamental property of the Matière which appears at the same time by the Inertie body and them gravitational interaction. According to the theory of the relativity, the mass constitutes moreover a form of energy.

One can, initially, represent the mass of an object as a measurement of the “quantity of matter” which constitutes it. This intuitive representation, which with the advantage of facilitating the distinction between “mass” and “Weight”, two concepts that one very often confuses in the daily life, corresponds however only roughly to reality, because “mass” and “matter Quantité” are in fact of the concepts basically different one from the other.

The unit SO of mass is the Kilogram (kg) and not the Gram (G). One also uses the ton, equal to 1.000 kg, and the Unit of atomic mass.

Mass and quantity of matter

In any rigor, the mass does not measure the quantity of matter!

The international Système of units establishes a fundamental distinction between the Quantité of matter, measured in mole, and masses it, measured in Kilogram.

Let us take an example. Three moles of Hélium 4 contain exactly the same number of Proton S, Neutron S and electron S, therefore exactly the same quantity of matter, as a mole of Carbone 12, is 6 moles of protons, 6 moles of neutrons and 6 moles of electrons. However it is that the mass of a mole of carbon 12 is worth exactly 12 grams (by definition even of the Nombre of Avogadro) whereas the mass of three moles of helium 4 is worth 3 X 4,0026 = 12,0078 grams. Rigorously identical quantities of matter can thus have different masses.

In the preceding example, the difference in mass observed is explained by the difference between binding the energies nuclear of helium and carbon.

The mass Relativiste (see low the section “Masses and energy”) is another example which shows well that the mass does not correspond to the quantity of matter.

Mass and weight

One should not confuse the mass and the Poids. The weight of a body corresponds mainly to the force which on him the gravitational field exerts.

The relation between the mass and the weight is given by the equation P = Mg , in which P represents the weight (in newtons), m mass (in Kilogram S) and G local intensity of the gravitational field (in N/kg). Since the weight of a body is proportional not only to its mass, but as with the intensity of the gravitational field, any object will be a little lighter at the top of the Everest as to the sea level, and approximately six times lighter on the surface of the the Moon as on the Ground.

With Paris, where G = 9,81 N/kg, a mass of 10 kg weighs thus 98 NR (even if it is usually said, in the daily life, that a object weighs 10 kg).

Inert mass and serious mass

If the mass of an object represents neither the Quantité of matter whose it is made up, nor its weight, which can it represent well? For the knowledge, it is necessary to examine the way in which one measurement mass, i.e. the way in which one compares the mass of an unspecified object with that of a standard of mass.

However the mass intervenes in two distinct physical phenomena and a priori without relationship between them:

  • the Inertia, i.e. resistance that the Corps oppose to any change of their state of movement, with all Accélération. The mass m which characterizes this inertia is defined by the second law of the movement of Newton: F = my .
  • the universal gravitation, i.e. the fact that all the bodies, just as all the Particules which constitute them, attract each other the ones the others. As discovered it Newton, two unspecified particles always exert one on the other a force of attraction directly proportional to the produced their masses and inversely proportional to the square of the distance which separates them: F ∝ m 1 m 2/ D 2.

There thus exist two ways of measuring directly the mass. One can initially compare dynamically two masses by comparing the forces necessary to communicate the same horizontal acceleration to them (in the absence of all Frottement). In this case, gravity does not play any part and measurement does not utilize that inertia: one thus calls inert mass the mass thus measured. One can also compare statically two masses by weighing them using a balances. In this case, inertia does not play any part and measurement does not utilize that gravity: one thus calls serious mass the mass thus measured.

  • the inert mass is a property of the matter which appears by the inertia of the bodies. Concretely, a mass of 20 kg resists twice more acceleration that a mass of 10 kg.

  • the mass engraves is a property of the matter which appears by the gravitation of the bodies. Concretely, a mass of 20 kg creates around it a field of gravity twice more intense than a mass of 10 kg; in addition, in the presence of the same external field of gravity (that of the Earth for example), the mass of 20 kg will undergo a force (the weight) twice larger than the mass of 10 kg.

As it is seen, the mass engraves and the inert mass seem a priori not to have any bond between them and to constitute two properties of the matter completely independent one of the other. However all the experimental results indicate that they are always directly proportional between them.

Let us examine for example the movement of a body in freefall in the immediate vicinity of the Ground. For the needs for the reasoning, we will use different indices to distinguish the inert mass m   i from the mass engraves m   g  .

The movement of a body in freefall obeys the second law of the movement of Newton, which utilizes the inert mass:

F = m   i has ,

where F is the resultant of all the forces applied to the body and has its Accélération.

However the only force applied to a body in freefall is its weight, i.e. the attraction force exerted on the body by the Earth. This force, given by the law of the universal gravitation, depends on the serious mass of each involved body:

F = G   m   g M   g  /  R   2,

where G is a constant universal, M   g the Masse of the Earth and R its ray.

It rises from the two preceding equations that

m   i has = G   m   g M   g  /  R   2.

Let us isolate acceleration:

has = ( m   g  /  m   i)   G   M   g  /  R   2.

By posing G = G   M   g  /  R   2, one obtains finally

has = ( m   g  /  m   i)   G ,
where G represents the intensity of the field of gravity in the vicinity of the Earth.

Since all the experiments seem to show that acceleration in freefall is the same one for all the bodies, the report/ratio m   g  /  m   i (whose in fact the value depends on G ) must be a constant. The intuition that the inert mass and the serious mass represent in fact only one and even property of the matter result in posing m   i   = m   g  .

It is besides this intuition of the equivalence between inert mass and serious mass which led Albert Einstein to suppose that gravity results in fact from the deformation from the space time and allowed him to formulate the laws of the General relativity.

On our scale, this equivalence seems obvious, and it is shown in experiments except for 10-12. However, certain scientific theories as the Théorie of the cords predict that it could cease being checked on scales much finer.

Mass and energy

One can also regard the mass as a form of energy, called energy of mass. The nuclear energy, for example, that it comes from the fusion or the fission, results indeed from the transformation of a certain quantity of mass into energy, according to the famous formula of Einstein: E = mc2 , in which E represents energy, m mass and C the Speed of light.

Thus, when a core of Deuterium and a core of Tritium amalgamate together to form a core of Hélium 4 (with ejection of a Neutron), the final mass is lower than the initial mass and the difference, or mass defect, appears in the form of kinetic energy.

It happens sometimes that Matière completely destroys during a transformation of mass into energy. It is the case for example when a electron enters in collision with a Positron: the two particles disappear completely and all their mass transforms into electromagnetic Rayonnement, in the form of a highly energy Photon gamma. The opposite phenomenon, matérialisation of energy by Creation of pairs, is also possible.

The particle accelerator also make it possible to transform energy into mass. Thus for example, when one accelerates a Proton up to 99% speed of light, its mass becomes approximately 7 times larger than at rest, according to the following formula: m = m o/1/2, in which C is speed of light, v the speed of the proton, m o its Rest mass and m its mass moving, known as mass Relativiste.

Measure mass

The measurement of the mass is called weighing, although this term comes from the word “weight”.

The only manner of measuring directly a mass consists to compare it with another mass; it is the principle of the balances S.

One can also estimate the mass starting from the Poids, i.e. one measures the force which exerts the object to weigh; the device is in fact a Dynamomètre. It is the case more running of the Pèse-personne and of the S balances electronic.

One can also estimate a mass by the disturbance of the field of gravity which it induces. This measurement by Gravimétrie is usable only for the extremely heavy objects, and is used in Géologie to estimate the size of a rock formation, as in Archéologie (gravimetry made it possible to detect a room hidden in a Pyramide).

; Remarks

It should be remembered that the delivers, in France, did not have the same value on all the territory: the of Provence one, the Parisian one or the Breton one did not have the same value completely and today still the Gallon delivers it just like do not have the same value with the USA and the the United Kingdom.

Many goods were sold by volume, by bushels or by Baril S, that is to say 18 bushels (235 liters) - different from the oil barrel which makes only 158,98 liters.

In the European Union, many masses (and volumes), on the consumables, are indicated in estimated Quantité. They are marked like such, of a “E” lower-case.

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