In its broadest sense, body mass refers to the amount of substance contained in the body. Mass is measured in kilograms in the generally accepted International System of Units SI.
Body weight standard
The 1 kilogram mass standard is made of an alloy that is 90% platinum and 10% iridium. This standard is located at the International Bureau of Weights and Measures, near Paris. It has the shape of a cylinder, the height and diameter of which are 39.17 mm.
Often, body weight is called weight, which, strictly speaking, is completely incorrect. The confusion is caused by the fact that the body weighs 1 kg. has a weight of 1 kgf (kilogram-force). This is a non-systemic unit of measurement and is equal to the force required to impart a mass of 1 kg to a body. acceleration equal to the acceleration g of free fall, approximately 9.81 m/(s^2)
Different definitions of mass
Different fields and areas of physics use different definitions of mass:
- based on Newton’s II law, m = f / a, mass is the ratio of the force applied to the body and the acceleration imparted by this force;
- Based on the law of gravity, this is the ratio of the force of gravity to the acceleration of gravity, m = F / g, .
- in general physics and in the theories of relativity, the definition of mass is still used as the ratio of momentum P to velocity v, m = P / v.
Mass is a non-negative scalar quantity. The mass of a photon (a particle that can exist in a vacuum only by moving at the speed of light) is considered equal to zero.
There are many different units of measurement of mass, many of them, like the ounce, carat, pound, barrel, have their own historical origins.
The mass of a body is a scalar physical quantity that characterizes its inertia. Inertia is the ability of the body to change its state. The greater the body weight, the easier it is to change the state of the body.
Let's write down Newton's 2nd law: a = F/m, where a is the acceleration of the body under the influence of force F.
From the expression we see that the greater the mass of the body m, with the same acting force F, the lower the acceleration of the body a. The greater the body mass, the less it changes its state.
Body weight is measured in kilograms.
1 kg is the mass of a body at which, under the influence of a force of F = 1 Newton, the body will acquire an acceleration of a = 1 m/s^2.
Body mass the main mechanical quantity that determines the amount of acceleration imparted to a body by a given force. The motion of bodies is directly proportional to the forces imparting equal accelerations to them and inversely proportional to the accelerations imparted to them by equal forces. Therefore, the connection between M. (T), by force f, and acceleration a, can be expressed by the formula i.e. M. is numerically equal to the ratio between the driving force and the acceleration it produces. The magnitude of this ratio depends solely on the body being moved, therefore the value of M fully characterizes the body from the mechanical side. The view of the real meaning of M. has changed with the development of science; At present, in the system of absolute mechanical units, M. is taken as the amount of matter, as the basic quantity, by which force is then determined. From a mathematical point of view, it makes no difference whether to take M as an abstract factor by which the accelerating force must be multiplied in order to obtain the driving force, or as an amount of matter: both assumptions lead to the same results; from a physical point of view, the latter definition is undoubtedly preferable. Firstly, M., as the amount of substance in the body, has a real meaning, because not only mechanical, but also many physical and chemical properties of bodies depend on the amount of substance in the body. Secondly, the basic quantities in mechanics and physics must be accessible to direct, possibly accurate measurement; We can measure force only with spring force meters - devices that are not only insufficiently accurate, but also not reliable enough, due to the variability of the elasticity of springs over time. Lever scales do not themselves determine the absolute value of weight as force, but only the ratio or equality of weight (see Weight and weighing) of two bodies. On the contrary, lever scales make it possible to measure or compare the mass of bodies, since due to the equality of the acceleration of the fall of all bodies on the same point on the earth, equal masses of two bodies correspond to equal masses. By balancing a given body with the required number of accepted units of mass, we find the absolute value M. him. The unit of M is currently accepted in scientific treatises as the gram (see). A gram is almost equal to M. of one cubic centimeter of water, at the temperature of its highest density (at 4°C M. 1 cubic cm of water = 1.000013 g). The unit of force is also used to determine the unit of force - dyna, or, in short, dyne (see Units of measures). Force f, reporting T grams A units of acceleration, equal to (1 dyne)× m× A = that dynam. Body weight is also determined R, in dynes, according to M. m, and acceleration of free fall g; p = mg din. However, we do not have enough data to directly compare the amounts of different substances, such as wood and copper, to verify whether equal quantities of these substances actually contain equal amounts. As long as we are dealing with bodies of the same substance, we can measure the amounts of substance in them by their volumes, when equal. temperatures, by the weight of the bodies, by the forces that impart equal accelerations to them, since these forces, if uniformly distributed over the body, must be proportional to the number of equal particles. This proportionality of the amount of the same substance to its weight also occurs for bodies of different temperatures, since heating does not change the weight of the body. If we are dealing with bodies made of different substances (one from copper, another from wood, etc.), then we cannot assert either the proportionality of the amounts of substance to the volumes of these bodies, or the proportionality of their forces, giving them equal accelerations, since different substances could have different abilities to perceive motion, just as they have different abilities to magnetize, absorb heat, neutralize acids, etc. Therefore, it would be more correct to say that equal M. of different substances contain equivalent their quantity in relation to mechanical action - but indifferent to other physical and chemical properties of these substances. Only under one condition can one compare the quantities of dissimilar substances by their weight - this is under the condition of extending to them the concept of the relative density of bodies consisting of the same substance, but at different temperatures. To do this, it is necessary to assume that all dissimilar substances consist of exactly the same particles, or initial elements, and all the different physical and chemical properties of these substances are a consequence of the different grouping and convergence of these elements. At present, we do not have enough data to confirm or deny this, although many phenomena even speak in favor of such a hypothesis. Chemical phenomena do not essentially contradict this hypothesis: many bodies consisting of various simple bodies present similar physical and crystalline properties, and vice versa, bodies with the same composition of simple substances present different physical and partly even chemical properties, such as, for example, isomeric bodies having the same percentage composition of the same simple bodies, and allotropic bodies representing varieties of the same simple body (such as coal, diamond and graphite, representing different states of carbon). The force of gravity, the most general of all the forces of nature, speaks in favor of the hypothesis of the unity of matter, since it acts on all bodies equally. That all bodies made of the same substance should fall equally quickly and their weight should be proportional to the amount of substance is understandable; but it does not follow from this that bodies made of different substances also fall at the same speed, since gravity could act differently, for example, on water particles than on zinc particles, just as magnetic force acts differently on different bodies. Observations show, however, that all bodies, without exception, in empty space at the same place on the Earth's surface, fall equally quickly, and therefore gravity acts on all bodies as if they consisted of the same substance and were different. only by the number of particles and their distribution in a given volume. In the chemical phenomena of combination and decomposition of bodies, their sums of weights remain unchanged; their structure and, in general, properties that do not belong to the very essence of the substance are modified. The independence of gravity from the structure and composition of bodies shows that this force penetrates deeper into the essence of matter than all other forces of nature. Therefore, measuring the amount of substance by the weight of bodies has a complete physical basis. P. Fan der Fleet.
Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron. - S.-Pb.: Brockhaus-Efron. 1890-1907 .
See what “Body mass” is in other dictionaries:
body mass- kūno masė statusas T sritis Standartizacija ir metrologija apibrėžtis Tam tikro kūno masė. atitikmenys: engl. body mass vok. Körpermasse, f rus. body weight, f pranc. masse du corps, f… Penkiakalbis aiškinamasis metrologijos terminų žodynas
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body mass- kūno masė statusas T sritis Kūno kultūra ir sportas apibrėžtis Žmogaus svoris. Kūno masė yra labai svarbus žmogaus fizinės brandos, sveikatos ir darbingumo rodiklis, vienas pagrindinių fizinio išsivystymo požymių. Kūno masė priklauso nuo amžiaus … Sporto terminų žodynas
Body mass- One of the main indicators of the level of physical development of a person, depending on age, gender, morphological and functional geno- and phenotypic characteristics. Despite the existence of many systems for assessing “normal” M. t., the concept ... ...
- (weight) in anthropology is one of the main anthropometric characteristics that determine physical development... Big Encyclopedic Dictionary
In combination with other anthropometric characteristics [body length (height) and chest circumference] an important indicator of physical development and health status. Depends on gender, height, is associated with the nature of nutrition, heredity,... ... Great Soviet Encyclopedia
- (weight), in anthropology one of the main anthropometric characteristics that determine physical development. * * * HUMAN BODY MASS HUMAN BODY MASS (weight), in anthropology, one of the main anthropometric characteristics that determine physical ... ... encyclopedic Dictionary
- (weight), in anthropology one of the main. anthropometry, signs that determine physical development … Natural science. encyclopedic Dictionary
Excess body weight- Accumulation of body weight (mainly due to adipose tissue) above normal for a given person, but before the development of obesity. In medical supervision, I. m. t. is understood as exceeding the norm by 1–9%. The problem, however, is establishing... Adaptive physical culture. Concise encyclopedic dictionary
ideal body weight- ideali kūno masė statusas T sritis Kūno kultūra ir sportas apibrėžtis Konkrečių sporto šakų, rungčių, tam tikras funkcijas komandoje atliekančių žaidėjų kūno masės modelis. atitikmenys: engl. ideal body mass vok. ideale Körpermasse, f rus.… …Sporto terminų žodynas
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« Physics - 10th grade"
Inertia of the body.
We have already talked about the phenomenon of inertia.
It is due to inertia that a body at rest does not acquire a noticeable speed under the influence of a force immediately, but only over a certain time interval.
Inertia- the property of bodies to change their speed differently under the influence of the same force.
Acceleration occurs immediately, simultaneously with the onset of the force, but the speed increases gradually.
Even a very strong force is not able to immediately impart significant speed to a body.
This takes time.
To stop the body, it is again necessary that the braking force, no matter how great it is, act for some time.
It is these facts that are meant when they say that bodies inert, i.e. one of the properties of the body is inertia.
Weight.
A quantitative measure of inertia is weight.
Let us give examples of simple experiments in which the inertia of bodies is very clearly manifested.
1. Figure 2.4 shows a massive ball suspended on a thin thread.
Exactly the same thread is tied to the ball below.
If you slowly pull the lower thread, the upper thread will break: after all, both the ball’s weight and the force with which we pull the ball down act on it.
However, if you pull the bottom thread very quickly, it will break, which at first glance is quite strange.
But it's easy to explain.
When we pull the thread slowly, the ball gradually lowers, stretching the upper thread until it breaks.
With a quick jerk with great force, the ball receives great acceleration, but its speed does not have time to increase any significantly during that short period of time during which the lower thread is greatly stretched and breaks.
The upper thread therefore stretches little and remains intact.
2. An interesting experiment is with a long stick suspended on paper rings (Fig. 2.5).
If you hit the stick sharply with an iron rod, the stick breaks, but the paper rings remain unharmed.
3. Finally, perhaps the most spectacular experience.
If you shoot an empty plastic container, the bullet will leave regular holes in the walls, but the container will remain intact.
If you shoot at the same vessel filled with water, the vessel will break into small pieces.
This is explained by the fact that water is poorly compressible and a small change in its volume leads to a sharp increase in pressure.
When a bullet enters the water very quickly, piercing the wall of the vessel, the pressure increases sharply.
Due to the inertia of water, its level does not have time to rise, and the increased pressure tears the vessel into pieces.
The greater the mass of a body, the greater its inertia, the more difficult it is to remove the body from its original state, that is, to make it move or, conversely, to stop its movement.
In kinematics, we used two basic physical quantities - length and time.
For the units of these quantities, appropriate standards have been established, by comparison with which any length and any time interval are determined.
The unit of length is the meter and the unit of time is the second.
All other kinematic quantities do not have unit standards.
The units of such quantities are called derivatives.
When moving to dynamics, we must introduce another basic unit and establish its standard.
In the International System of Units (SI), the unit of mass - one kilogram (1 kg) - is the mass of a standard weight made of an alloy of platinum and iridium, which is stored at the International Bureau of Weights and Measures in Sèvres, near Paris.
Exact copies of this weight are available in all countries.
Approximately 1 kg of water has a mass of 1 liter at room temperature.
We will consider easily feasible ways to compare any mass with the mass of a standard by weighing later.
Source: “Physics - 10th grade”, 2014, textbook Myakishev, Bukhovtsev, Sotsky
Dynamics - Physics, textbook for grade 10 - Cool physics
The concept with which we are familiar from early childhood is mass. And yet, in a physics course, there are some difficulties 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 value is that it determines the amount of substance contained in the body. To denote it, 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, non-systemic ones are often used: gram and ton.
In a school physics course, the answer to the question: “What is mass?” given when studying the phenomenon of inertia. Then it is defined as the ability of a body to resist changes in the speed of its movement. Therefore, the mass is also called inert.
What is weight?
Firstly, this is force, that is, a vector. Mass is a scalar weight that is always attached to a support or suspension and is directed in the same direction as the force of gravity, that is, vertically downward.
The formula for calculating weight depends on whether the support (suspension) is moving. When the system is at rest, the following expression is used:
P = 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.
From this the mass formula can be derived: m = P / g.
When moving downwards, that is, in the direction of the weight, its value decreases. Therefore the formula takes the form:
P = m (g - a). Here “a” is the acceleration of the system.
That is, if 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 upward, we speak of weight gain. In this situation, an overload condition occurs. Because body weight increases, and its formula will look like this:
P = m (g + a).
How is mass related to density?
Solution. 800 kg/m3. In order to use the already known formula, you need to know the volume of the spot. It is easy to calculate if you take the spot as 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 count the mass. It will turn out like this: 535034904 kg.
Answer: the mass of oil is approximately 535036 tons.
Task No. 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/m3. The volume is found using 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 10,000. After calculations, it turns out that the volume of the entire cable is approximately equal to 11,000 m 3.
Now you 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 problem related to mass
Task No. 6. Condition: The largest candle, weighing 89867 kg, had a diameter of 2.59 m. What was its height?
Solution. Wax density is 700 kg/m3. The height will need to be found from That is, V needs to 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.
Exploring the differences between weight and body weight Newton did. He reasoned like this: we know very well that different substances taken in equal volumes weigh differently.
Weight
Newton called the amount of substance contained in a particular object mass.
Weight- something common that is inherent in all objects without exception - it doesn’t matter whether they are shards from an old clay pot or a gold watch.
For example, a piece of gold is more than twice as heavy as an identical piece of copper. Probably, particles of gold, Newton suggested, are capable of packing more densely than particles of copper, and more substance fits in gold than in a piece of copper of the same size.
Modern scientists have established that the different densities of substances are explained not only by the fact that the particles of the substance are packed more densely. The smallest particles themselves - atoms - differ in weight from each other: gold atoms are heavier than copper atoms.
Whether any object lies motionless, or freely falls to the ground, or swings, suspended on a thread, its the mass remains unchanged under all conditions.
When we want to find out how large the mass of an object is, we weigh it on ordinary commercial or laboratory scales with cups and weights. We place an object on one pan of the scale, and weights on the other, and thus compare the mass of the object with the mass of the weights. Therefore, commercial and laboratory scales can be transported anywhere: to the pole and the equator, to the top of a high mountain and into a deep mine. Everywhere and everywhere, even on other planets, these scales will show correctly, because with their help we determine not weight, but mass.
It can be measured at different points on the earth using spring scales. By attaching an object to the hook of a spring scale, we compare the force of gravity of the Earth that this object experiences with the elastic force of the spring. The force of gravity pulls down, (more details:) the force of the spring pulls up, and when both forces are balanced, the scale pointer stops at a certain division.
Spring scales are only correct at the latitude where they are made. At all other latitudes, at the pole and at the equator, they will show different weights. True, the difference is small, but it will still be revealed, because the force of gravity on Earth is not the same everywhere, and the elastic force of the spring, of course, remains constant.
On other planets this difference will be significant and noticeable. On the Moon, for example, an object that weighed 1 kilogram on Earth will weigh 161 grams on spring scales brought from Earth, on Mars - 380 grams, and on huge Jupiter - 2640 grams.
The greater the mass of the planet, the greater the force with which it attracts a body suspended on a spring scale.
That is why a body weighs so much on Jupiter and so little on the Moon.