In life, we very often say: “weighs 5 kilograms,” “weighs 200 grams,” and so on. And at the same time we don’t know that we are making a mistake in saying this. The concept of body weight is studied by everyone in the physics course in the seventh grade, but the erroneous use of some definitions has become so mixed up among us that we forget what we have learned and believe that body weight and mass are one and the same thing.
However, it is not. Moreover, body weight is a constant value, but body weight can change, decreasing down to zero. So what is the mistake 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 a body, it is how the body reacts to an impact applied to it, or itself affects other bodies. And the weight of a 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, is measured in newtons. The weight of a body has a direction, like any force, and is a vector quantity. But mass has no direction and is a scalar quantity.
The arrow that indicates body weight in pictures and graphs is always directed downward, just like the force of gravity.
Body weight formula in physics is written as follows:
where m is body mass
g - gravitational 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. The force of gravity is applied to the body, that is, roughly speaking, it presses on the body, and the weight of the body is applied to the support or suspension, that is, here the body presses on the suspension or support.
But the nature of the existence of gravity and the weight of a body is the same as the attraction of the Earth. Strictly speaking, the weight of a body is a consequence of the force of gravity applied to the body. And, just like gravity, body weight decreases with increasing altitude.
Body weight in zero gravity
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 force, the greater the greater the mass of the body.
Under the conditions of another planet, the mass will also remain unchanged, and the weight of the body will increase or decrease, depending on the strength of the planet’s gravity. We measure body mass with scales, in kilograms, and to measure body weight, which is measured in Newtons, you can use a dynamometer, a special device for measuring force.
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.
amount of something Weight One of the main physical characteristics of matter, determining its inert and gravitational properties Spec Weight a collection of something Weight Pasty, shapeless substance, thick mixture Weight Something large, concentrated in one place Weight Broad sections of the working populationMass in the Encyclopedic Dictionary:
Massa - (Massa) - a city in the Center. Italy, in the region Tuscany, administrative center of the province. Massa e Carrara. 67 thousand inhabitants (1985). Production of products from Carrara marble. Metallurgy, chemical industry. one of the main physical characteristics of matter, determining its inert and gravitational properties. In classical mechanics weight equal to the ratio of the force acting on the body to the acceleration it causes (Newton’s 2nd law) - in this case weight called inert; in addition, the mass creates a gravitational field - gravitational, or heavy, weight. Inert and heavy masses are equal to each other (equivalence principle). (Massa) Isaac (1587-1635) - Dutch merchant. Lived in Moscow at the beginning of the 17th century. Author of "Brief news about Muscovy at the beginning of the 17th century."
The meaning of the word Mass according to the dictionary of medical terms:
Weight- Woodlongan diagram (E. Masse, French surgeon and anatomist of the 19-20 centuries; Woodlonghan, French surgeon and anatomist of the 19-20 centuries) - diagram of craniocerebral topography for determining the projection of the central and lateral grooves, according to which their location corresponds to straight lines , connecting certain points on the horizontal (equator) and sagittal (meridian) arcs drawn through the bridge of the nose and the greater occipital tubercle. Synonyms for the word Mass: mass, see piece, a lot, crowd, mob
The meaning of the word Mass according to Ushakov’s dictionary:
WEIGHT
masses, w. (Latin massa). 1. Many, large quantities. Weight to the people. Tired of the mass of impressions. Weight hassle. 2. more often plural. Wide circles of workers and population. The working masses. Don't break away from the masses. The vital interests of the peasant masses....The Soviets are the most powerful organs of the revolutionary struggle of the masses... Stalin. Connection with the masses, strengthening this connection, readiness to listen to the voice of the masses - this is the strength and invincibility of the Bolshevik leadership. Stalin.... Changes in the electoral system mean increased control of the masses in relation to Soviet bodies and increased responsibility of Soviet bodies in relation to the masses (from the resolution of the plenum of the Central Committee of the All-Union Communist Party of Bolsheviks, March 1937). 3. Heap, bulk. A dark one was approaching the shore weight armadillo. || A concentrated portion of something, an overwhelming amount. The bulk of the artillery is located on the flank. 4. A mixture, a dough-like substance that is a semi-finished product in various industries (technical). Wood pulp. Porcelain mass. Paper pulp. (sheets of paper are made from the cut). 5. Weight and inertia inherent in matter and energy (physical). For the most part - for the most part.
The meaning of the word Mass according to Dahl's dictionary:
Weight
better masa lat. substance, body, matter; | thickness, the totality of matter in a known body, its materiality. The volume of the atmosphere is vast, and weight insignificant. Such a mass will crush everything. A mass of goods, a heap, an abyss. | Merchant all property of the insolvent debtor. Massive, imposing, thick and durable; rough finish; clumsy, heavy in appearance; majestic, thicker in size. -ness, property, state of massive.
Definition of the word “Mass” according to TSB:
Weight- Massa
Isaac (1587, Haarlem, Netherlands, - after May 1635, there or in Lisse), Dutch merchant and resident in Russia in 1614-34. Lived in Moscow in 1601-09, 1612-34. I studied the Russian language and collected a lot of materials on the history of the country of the late 16th - early 17th centuries and its geography. Around 1611 he wrote an essay about events in Russia at the end of the 16th - beginning of the 17th centuries - important on the history of the peasant war led by I. I. Bolotnikov and other events of 1601-1609. M.'s articles on the history and geography of Siberia were one of the first works about Siberia in Western European literature. M. published a number of maps of Russia and its individual regions.
Works: Brief news about Muscovy at the beginning of the 17th century, M., 1937. Massa - Massa (from Latin massa - block, mass)
1) a large quantity, a large accumulation of something. 2) Semi-liquid or pasty, shapeless substance; mixture (semi-finished product) in various industries (for example, paper pulp). 3) See Mass in physics. Mass is a physical quantity, one of the main characteristics of matter, determining its inertial and gravitational properties. Accordingly, a distinction is made between inert material and gravitational material (heavy, gravitating).
The concept of magnetism was introduced into mechanics by I. Newton. In Newton's classical mechanics, magnetism is included in the definition of momentum (quantity of motion (See Quantity of Motion)) of a body: momentum p is proportional to the speed of movement of the body v,
p = mv. (1)
The proportionality coefficient - a constant value m for a given body - is the M of the body. An equivalent definition of magnetism is obtained from the equation of motion of classical mechanics
f = ma. (2)
Here M. is the coefficient of proportionality between the force ƒ acting on the body and the acceleration of the body a caused by it. The mass defined by relations (1) and (2) is called inertial mass, or inertial mass; it characterizes the dynamic properties of a body and is a measure of the body’s inertia: with a constant force, the greater the M of the body, the less acceleration it acquires, that is, the slower the state of its motion changes (the greater its inertia).
By acting on different bodies with the same force and measuring their accelerations, it is possible to determine the M ratios 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, the M. of the remaining bodies can be found.
In Newton's theory of gravity, magnetism appears in a different form - as a source of the gravitational field. Each body creates a gravitational field proportional to the magnetism of the body (and is influenced by the gravitational field created by other bodies, the strength of which is proportional to the magnetism of the body). This field causes the attraction of any other body to this body with a force determined by Newton’s law of gravity:
15/15031047.tif, (3)
where r is the distance between the bodies, G is the universal gravitational constant, a m 1 and m 2 are the M of attracting bodies. From formula (3) it is easy to obtain a formula for the Weight P of a body of mass m in the Earth’s gravitational field:
P = m g. (4)
Here g = G · M / rІ is the acceleration of gravity in the gravitational field of the Earth, and r ≈ R is the radius of the Earth. 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. Galileo, who established that all bodies on Earth fall with the same acceleration. A. Einstein put this principle (formulated by him for the first time) into the basis of the general theory of relativity (see Gravity). The equivalence principle has been established experimentally with very high accuracy. For the first time (1890-1906), a precision test of the equality of inertial and gravitational magnetism was carried out by L. Eotvos, who found that the magnetisms coincide with an error of ∼ 10 −8. In 1959-64, American physicists R. Dicke, R. Krotkov and P. Roll reduced the error to 10 −11, and in 1971 Soviet physicists V. B. Braginsky and V. I. Panov - to 10 −12.
The principle of equivalence makes it possible to most naturally determine the body's weight by weighing.
Initially, M. was considered (for example, by Newton) as a measure of the quantity of a substance. This definition has a clear meaning only for comparing homogeneous bodies built from the same material. It emphasizes the additivity of M. - The M. of a body is equal to the sum of M. of its parts. The mass of a homogeneous body is proportional to its volume, so we can introduce the concept of density - the mass of a unit of volume of a body.
In classical physics it was believed that the magnetism of a body does not change in any processes. This corresponded to the law of conservation of matter (matter), discovered by M. V. Lomonosov and A. L. Lavoisier. In particular, this law stated that in any chemical reaction the sum of M of the initial components is equal to the sum of M of the final components.
The concept of M. acquired a deeper meaning in the mechanics of specialties. theory of relativity by A. Einstein (see Relativity theory), which considers the movement of bodies (or particles) at very high speeds - comparable to the speed of light c
≈ 3·10 10 cm/sec. In new mechanics - it is called relativistic mechanics - the relationship between momentum and velocity of a particle is given by the relation:
15/15031048.tif (5)
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