What is scales in physics. Academy of Entertaining Sciences. Physics. Video
I regularly encounter the fact that people do not understand the difference between weight and mass. This is generally understandable, since we are all our lives in the Earth's gravitational field, which does not stop its action, and these quantities are constantly connected for us. And this connection is also linguistically reinforced by the fact that we recognize the mass with the help of scales, "weigh" ourselves or, say, the products in the store.
But let's still try to untie these concepts.
In subtlety (such as the different g in different places Land and other things) we will not go into. I note that all this is included in the school physics course, so if all of the following is obvious to you, do not swear at those who did not have time to understand these things, but at the same time at those who decided to explain this for the hundredth time.) I hope that there will be people for whom this note will replenish their apparatus for understanding the world around them.
So let's go. The mass of a body is a measure of its inertia. That is, a measure of how difficult it is to change the speed of this body modulo (accelerate or decelerate) or in direction. In the SI system, it is measured in kilograms (kg). It is usually denoted by the letter m. It is an invariable parameter, both on Earth and in space.
Gravity, measured in SI units in Newtons (N). This is the force with which the Earth attracts the body, and is equal to the product m * g. The coefficient g is 10 m/s2, called the acceleration free fall. With this acceleration, the body begins to move relative to the earth's surface, devoid of support (in particular, if the body started from a stationary state, its speed will increase by 10 m/s every second).
Now let's consider a body of mass m lying motionless on a table. For definiteness, let the mass be 1 kg. Gravity mg mg acts on this body vertically downwards (actually, the vertical itself is determined precisely by the direction of gravity), equal to 10 N. In technical system units, this force is called kilogram-force (kgf).
The table does not allow our body to accelerate, acting on it with a force N directed vertically upwards (it is more correct to draw this force from the table, but so that the lines do not overlap, I will also draw from the center of the body):
N is called the reaction force of the support, balances the force of gravity (in this case equal in absolute value to the same 10 Newtons), so that the resultant force F (the sum of all forces) is zero: F = mg - N = 0.
And the fact that the forces are balanced, we see from Newton's second law F = m * a, according to which if the acceleration of the body a is zero (that is, it either rests, as in our case, or moves uniformly and rectilinearly), then the resultant force F is also equal to zero.
Now we can finally say what weight is - this is the force with which the body acts on the stand or suspension. According to Newton's third law, this force is opposite to the force N and equal to it in absolute value. That is, in this case it is the same 10 N = 1 kgf. Perhaps it will seem to you that all this is unnecessarily complicated, and you should have said right away that weight and gravity are one and the same? After all, they coincide both in direction and in magnitude.
No, in fact they differ significantly. The force of gravity acts constantly. The weight changes depending on the acceleration of the body. Let's give examples.
1. You start up on a high-speed elevator (high-speed, so that the acceleration phase is more effective / noticeable). Your mass is, say, 70 kg (you can recalculate all the numbers below for your mass). Your weight in a stationary elevator (before the start) is 700 N (or 70 kgf). At the moment of acceleration upwards, the resulting force F is directed upwards (it is this that accelerates you), the reaction force N exceeds the force of gravity mg, and since your weight (the force with which you act on the floor of the elevator) is modulo N, you experience the so-called overload. If the elevator were accelerating with an acceleration g, then you would experience a weight of 140 kgf, that is, an overload of 2g, 2 times the weight at rest. In fact, in normal mode, there are no such overloads in elevators, acceleration usually does not exceed 1 m/s2, which leads to an overload of only 1.1g. The weight in our case will be 77 kgf. When the elevator has accelerated to the desired speed, the acceleration is zero, the weight returns to the initial 70 kgf. When decelerating, the weight, on the contrary, decreases, and if the acceleration modulo is 1 m/s2, then the overload will be 0.9g. When moving in reverse side(down) the situation is reversed: when accelerating, the weight decreases, on a flat section, the weight is restored, when decelerating, the weight increases.
2. You are running and your resting weight is still 70 kgf. At the moment of running, when you push off the ground, your weight exceeds 70 kgf. In the meantime, you are flying (one leg is off the ground, the other has not yet touched), your weight zero(because you are not affecting either the stand or the gimbal). This is weightlessness. Indeed, it is quite short. Thus, running is an alternation of overloads and weightlessness.
Let me remind you that the force of gravity in all these examples did not disappear, did not change, and amounted to your "hard-earned" 70 kgf = 700 N.
Now let's significantly lengthen the phase of weightlessness: imagine that you are on the ISS (international space station). At the same time, we have not eliminated gravity - it still acts on you - but since both you and the station are in the same orbital motion, you are in weightlessness relative to the ISS. You can imagine yourself anywhere in outer space, it's just that the ISS is a little more realistic.)
What will be your interaction with objects? Your mass is 70 kg, you take an object with a mass of 1 kg in your hand, throw it away from you. In accordance with the law of conservation of momentum, the 1-kg object, as less massive, will receive the main speed, and the throw will be approximately as "easy" as on Earth. But if you try to push off from an object weighing 1000 kg, then you will actually push yourself away from it, since in this case you yourself will receive the main speed, and in order to accelerate your 70 kg, you will have to develop more force. To roughly imagine what it is like, you can now go up to the wall and push off from it with your hands.
Now you are out of the station and into outer space and want to manipulate some kind of massive object. Let its mass be five tons.
To be honest, I would be very careful when handling a five-ton object. Yes, weightlessness and all. But only its small speed relative to the ISS is enough to press your finger or something more seriously. These five tons are difficult to move: disperse, stop.
And, as one person suggested, I don’t want to imagine myself between two objects weighing 100 tons each. Their slightest oncoming movement, and they will easily crush you. In complete, which is characteristic, weightlessness.)
And finally. If you have fun flying around the ISS and hit a wall / bulkhead, then you will be hurt exactly the same as if you were running at the same speed and hit the wall / jamb in your apartment. Because the impact reduces your speed (that is, it gives you acceleration with a minus sign), and your mass is the same in both cases. So, according to Newton's second law, the impact force will be proportional.
I am glad that in films about space ("Gravity", "Interstellar", the series "The Expanse") more and more realistically (albeit not without flaws like George Clooney, hopelessly flying away from Sandra Bullock) display the basic things described in this post.
I summarize. The mass is "inalienable" from the object. If an object is difficult to accelerate on Earth (especially if you have tried to minimize friction), then it is just as difficult to accelerate it in space. As for the scales, when you stand on them, they simply measure the force with which they are squeezed, and for convenience they display this force not in Newtons, but in kgf. At the same time, without adding the letter "c" so as not to confuse you.)
. (In the case of several supports, weight is understood as the total force acting on all supports; however, for liquid and gaseous supports, in the case of immersion of the body in them, an exception is often made, i.e. then the forces of the body acting on them are excluded from the weight and included in the force Archimedes). The unit of weight in the International System of Units (SI) is the newton, sometimes the CGS unit is the dyne.
Weight P of a body at rest in an inertial reference frame , coincides with the force of gravity acting on the body, and is proportional to the mass and acceleration of free fall at a given point:
The value of the weight (with the body mass unchanged) is proportional to the free fall acceleration, which depends on the height above the earth's surface (or the surface of another planet, if the body is near it, and not the Earth, and the mass and size of this planet), and, due to the non-sphericity of the Earth, and also due to its rotation (see below), from the geographical coordinates of the measurement point. Another factor affecting the acceleration of free fall and, accordingly, the weight of the body, are gravitational anomalies due to structural features of the earth's surface and subsoil in the vicinity of the measurement point.
When the body-support (or suspension) system moves relative to the inertial reference frame with acceleration, the weight ceases to coincide with the force of gravity:
At the same time, a strict distinction between the concepts of weight and mass is accepted mainly in physics, and in many everyday situations the word "weight" continues to be used when, in fact, we are talking about "mass". For example, we say that an object "weighs one kilogram" despite the fact that a kilogram is a unit of mass. In addition, the term "weight" in the meaning of "mass" is traditionally used in the cycle of human sciences - in combination "human body weight".
Notes
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Synonyms:See what "Weight" is in other dictionaries:
weight- weight, a and y, pl. h. a, ov ... Russian spelling dictionary
weight- weight/ … Morphemic spelling dictionary
Exist., m., use. often Morphology: (no) what? weight and weight, what? weight, (see) what? weight what? weight, what? about weight; pl. What? weight, (no) what? weights, why? scales, (see) what? weight than? weights about what? about scales 1. The weight of any physical ... ... Dictionary Dmitrieva
A (y); m. 1. Phys. Gravity. 2. Expand. and special Quantity, mass of whom, what l., determined by weighing. B. goods, luggage. lung fighter, heavy weight. A container weighing one hundred kilograms. Gain, lose weight. Gain, lose weight... encyclopedic Dictionary
WEIGHT, weights (y), pl. weight (special), male 1. The gravity of the body to the ground, the pressure of the body on some kind of surface (physical). 2. Expressed in numerical terms, the severity of the body (determined using weights). Determine weight. Bag weighing 5 kg. How much is in it... Explanatory Dictionary of Ushakov
See authority, importance, dignity, value worth its weight in gold, with weight ... Dictionary of Russian synonyms and expressions similar in meaning. under. ed. N. Abramova, M .: Russian dictionaries, 1999. weight mass; prestige, prestige, prestige, influence, ... ... Synonym dictionary
WEIGHT, the force of GRAVITATIONAL attraction of the body. Body weight is equal to the product body mass to the free fall acceleration. The mass remains constant, but the weight depends on the location of the object on the Earth's surface. As height increases, weight decreases... Scientific and technical encyclopedic dictionary
Quantity of goods to be delivered or offered for delivery. A distinction is also made between the shipping weight indicated in the shipping documents and the unloaded weight indicated in the weight check report. Dictionary of business terms. Akademik.ru. 2001 ... Glossary of business terms
weight- WEIGHT, a, m. Iron. Significance, dignity of someone or something. You are now the boss, you now have the weight of a pregnant elephant. You me with your weight is not the soul. To hold the weight to behave pompously, with excessive importance, with emphasized dignity. From high… … Dictionary of Russian Argo
IN modern science weight and mass different concepts. Weight is the force with which a body acts on a horizontal support or vertical suspension. Mass is a measure of the inertia of a body.
Weight measured in kilograms, and weight in newtons. Weight is the product of mass and free fall acceleration (P = mg). The value of weight (with a constant body mass) is proportional to the acceleration of free fall, which depends on the height above the earth's (or other planet's) surface. And if, even more precisely, then weight is a particular definition of Newton's 2nd law - force is equal to the product of mass and acceleration (F = ma). Therefore, it is calculated in Newtons, like all forces.
Weight is a permanent thing, weight, strictly speaking, depends, for example, on the height at which the body is located. It is known that with an increase in height, the acceleration of free fall decreases, and the weight of the body decreases accordingly, under the same measurement conditions. Its mass remains constant.
For example, under conditions of weightlessness, all bodies have zero weight, and each body has its own mass. And if in the state of rest of the body the readings of the weights will be zero, then when the weights of the bodies with the same speeds are hit, the impact will be different.
Interestingly, as a result daily rotation There is a latitudinal decrease in weight of the Earth: at the equator, it is approximately 0.3% less than at the poles.
Nevertheless, a strict distinction between the concepts of weight and mass is accepted mainly in physics, and in many everyday situations, the word "weight" continues to be used when actually talking about "mass". By the way, when you see the inscriptions on the product: “net weight” and “gross weight”, do not be alarmed, NET is the net weight of the product, and GROSS is the weight with packaging.
Strictly speaking, when going to the market, addressing the seller, one should say: “Please weigh a kilogram” ... ”or“ Give me 2 newtons of doctor's sausage. Of course, the term "weight" has already taken root as a synonym for the term "mass", but this does not eliminate the need to understand that it's not the same thing at all.
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In everyday life and Everyday life the concepts of "mass" and "weight" are absolutely identical, although their semantic meaning is fundamentally different. Asking "What is your weight?" we mean "How many kilograms are you in?". However, the question with which we are trying to find out this fact is not answered in kilograms, but in newtons. I'll have to go back to my high school physics course.
Body weight- a value that characterizes the force with which the body exerts pressure on the support or suspension.
For comparison, body mass formerly roughly defined as "amount of substance", the modern definition reads as follows:
Weight - a physical quantity that reflects the ability of a body to inertia and is a measure of its gravitational properties.
The concept of mass is generally somewhat broader than that presented here, but our task is somewhat different. It is quite enough to understand the fact of the actual difference between mass and weight.
In addition, - kilograms, and weights (as a form of force) - newtons.
And, perhaps, the most important difference between weight and mass contains the weight formula itself, which looks like this:
where P is the actual weight of the body (in Newtons), m is its mass in kilograms, and g is the acceleration, which is usually expressed as 9.8 N / kg.
In other words, the weight formula can be understood with this example:
Weight weight 1 kg suspended from a fixed dynamometer, in order to determine its weight. Since the body, and the dynamometer itself, are at rest, we can safely multiply its mass by the free fall acceleration. We have: 1 (kg) x 9.8 (N / kg) \u003d 9.8 N. It is with this force that the weight acts on the suspension of the dynamometer. From this it is clear that the weight of the body is equal. However, this is not always the case.
It's time to do important note. The weight formula equals gravity only in cases where:
- the body is at rest;
- the body is not affected by the Archimedes force (buoyancy force). A curious fact concerning it is known that a body immersed in water displaces a volume of water equal to its weight. But it doesn't just push the water out, the body becomes "lighter" by the amount of water displaced. That is why it is possible to lift a girl weighing 60 kg in water jokingly and laughing, but on the surface it is much more difficult to do.
With uneven movement of the body, i.e. when the body together with the suspension move with acceleration a, changes its appearance and weight formula. The physics of the phenomenon changes slightly, but such changes are reflected in the formula as follows:
P=m(g-a).
As can be replaced by the formula, the weight can be negative, but for this the acceleration with which the body moves must be greater than the acceleration of free fall. And here again it is important to distinguish weight from mass: negative weight does not affect mass (the properties of the body remain the same), but it actually becomes directed in the opposite direction.
A good example is with an accelerated elevator: when it accelerates sharply, for a short time it creates the impression of "pulling to the ceiling." Of course, it is quite easy to face such a feeling. It is much more difficult to feel the state of weightlessness, which is fully felt by astronauts in orbit.
Weightlessness - Basically no weight. In order for this to be possible, the acceleration with which the body moves must be equal to the notorious dampening g (9.8 N/kg). The easiest way to achieve this effect is in near-Earth orbit. Gravity, i.e. attraction still acts on the body (satellite), but it is negligible. And the acceleration of a drifting satellite also tends to zero. This is where the effect of the absence of weight arises, since the body does not come into contact with either the support or the suspension at all, but simply floats in the air.
Partially, this effect can be encountered during takeoff of the aircraft. For a second, there is a feeling of suspension in the air: at this moment, the acceleration with which the plane is moving is equal to the acceleration of free fall.
Back to differences weight And masses, It is important to remember that the body weight formula is different from the mass formula, which looks like :
m= ρ/V,
that is, the density of a substance divided by its volume.
Today we will raise a seemingly insignificant, but in fact a very important topic. Namely, we will analyze what is the difference between mass and weight. A school graduate knows that weight and mass are not the same thing. But even the most titled physicist will not say to the seller: "Give me back" a kilogram of apples. He will say "weigh", referring to the amount of apple product, not its severity. Let's solve the mystery of this state of affairs.
Flipping through a physics textbook
Weight is strength variable, measured in newtons, means the impact on the support of a lying object or the tension of the suspension. Mass is the amount of matter inside the body, calculated in kilograms, tons, pounds, etc., is a constant value.
For stationary objects, the values of these parameters are directly proportional. When weighing, the force with which the product presses on the stand is determined, and the scoreboard shows its mass. Very convenient for sellers and buyers.
When there is a difference
- The farther from the center of the Earth, the smaller g, and the lighter the body.
- Inertia. When an airplane or rocket takes off, the pilot experiences overload. It was the inertia of the start that was added to its gravity, and the pressure on the support (chair) increased. On the contrary, when the elevator moves down, the passenger becomes lighter, puts less pressure on the floor.
- The falling object weighs nothing, since K = g - g = 0. This is a state of weightlessness, although the mass remains the same.
- In the conditions of other planets, gravity changes. On the Moon, g = 1.62, and on Mars, 3.86. The same body on the Moon is 6 times lighter, on Mars - 2.5 times lighter than on Earth.
Why does confusion happen
Man perceives the world through sensations. We cannot feel mass, but we can feel weight. The girl is holding a book. In this case, the palm is a support. The book presses, the hand resists. The reader feels an effort to hold the book. Counteraction - the only way definition of mass, given to us by nature. Hence the reason for the substitution of concepts, the discrepancy between the norms of the language and physical phenomena.
