What is the resting body weight. What is the difference between mass and weight and why there is a substitution of concepts? When the difference arises

In this paragraph, we will remind you about the force of gravity, centripetal acceleration and body weight.

Every body on the planet is affected by the gravity of the Earth. The force with which the Earth attracts each body is determined by the formula

The point of application is at the center of gravity of the body. Gravity always points straight down.

The force with which a body is attracted to the Earth under the action of the Earth's gravitational field is called by gravity. According to the law of universal gravitation, on the surface of the Earth (or near this surface), a body of mass m acts on the force of gravity

F t = GMm / R 2

where M is the mass of the Earth; R is the radius of the Earth.
If only gravity acts on the body, and all other forces are mutually balanced, the body makes a free fall. According to Newton's second law and the formula F t = GMm / R 2 the free fall acceleration modulus g is found by the formula

g = F t / m = GM / R 2.

From formula (2.29) it follows that the acceleration of gravity does not depend on the mass m of the falling body, i.e. for all bodies in a given place on the Earth, it is the same. From formula (2.29) it follows that Ft = mg. In vector form

F t = mg

In § 5 it was noted that since the Earth is not a sphere, but an ellipsoid of revolution, its polar radius is less than the equatorial one. From the formula F t = GMm / R 2 it can be seen that for this reason the force of gravity and the acceleration of gravity caused by it at the pole is greater than at the equator.

The force of gravity acts on all bodies in the gravitational field of the Earth, but not all bodies fall to the Earth. This is due to the fact that the movement of many bodies is impeded by other bodies, for example, supports, suspension threads, etc. Bodies that restrict the movement of other bodies are called connections. Under the action of gravity, the bonds are deformed and the reaction force of the deformed bond according to Newton's third law balances the force of gravity.

The acceleration of gravity is influenced by the rotation of the Earth. This influence is explained as follows. Reference frames associated with the Earth's surface (except for two related to the Earth's poles) are not, strictly speaking, inertial reference frames - the Earth rotates around its axis, and together with it moves in circles with centripetal acceleration and such frames of reference. This non-inertia of frames of reference is manifested, in particular, in the fact that the value of the acceleration due to gravity is different in different places of the Earth and depends on the latitude of the place where the frame of reference connected with the Earth is located, relative to which the acceleration of gravity is determined.

Measurements carried out at different latitudes showed that numerical values the accelerations of gravity differ little from each other. Therefore, with not very accurate calculations, one can neglect the non-inertiality of the reference frames associated with the Earth's surface, as well as the difference in the shape of the Earth from the spherical one, and assume that the acceleration of gravity anywhere on the Earth is the same and equal to 9.8 m / s 2.

From the law of universal gravitation it follows that the force of gravity and the acceleration of gravity caused by it decrease with increasing distance from the Earth. At a height h from the Earth's surface, the free fall acceleration modulus is determined by the formula

g = GM / (R + h) 2.

It was found that at an altitude of 300 km above the Earth's surface, the acceleration of gravity is less than at the Earth's surface by 1 m / s2.
Consequently, near the Earth (up to heights of several kilometers), the force of gravity practically does not change, and therefore the free fall of bodies near the Earth is a uniformly accelerated motion.

Body weight. Weightlessness and overload

The force in which, due to attraction to the Earth, the body acts on its support or suspension is called body weight. Unlike gravity, which is gravitational force applied to a body, weight is an elastic force applied to a support or suspension (i.e., to a bond).

Observations show that the weight of the body P, determined on a spring balance, is equal to the force of gravity F t acting on the body only if the balance with the body relative to the Earth is at rest or moves uniformly and rectilinearly; In this case

P = F t = mg.

If the body is moving with acceleration, then its weight depends on the value of this acceleration and on its direction relative to the direction of the acceleration of gravity.

When the body is suspended on a spring balance, two forces act on it: the force of gravity F t = mg and the elastic force F yp of the spring. If in this case the body moves vertically up or down relative to the direction of the acceleration of gravity, then the vector sum of the forces F t and F yn gives the resultant, causing the acceleration of the body, i.e.

F t + F pack = ma.

According to the above definition of the concept of "weight", you can write that P = -F yп. From the formula: F t + F pack = ma. taking into account that F T = mg, it follows that mg-ma = -F yп ... Therefore, P = m (g-a).

Forces F t and F yn are directed along one vertical straight line. Therefore, if the acceleration of the body a is directed downward (i.e. coincides in the direction with the acceleration of gravity g), then the modulus

P = m (g-a)

If the acceleration of the body is directed upward (i.e., opposite to the direction of the acceleration of gravity), then

P = m = m (g + a).

Consequently, the weight of a body whose acceleration coincides in direction with the acceleration of free fall is less than the weight of a body at rest, and the weight of a body whose acceleration is opposite to the direction of acceleration of free fall is greater than the weight of a body at rest. The increase in body weight caused by it accelerated movement are called overload.

In free fall, a = g. From the formula: P = m (g-a)

it follows that in this case P = 0, that is, there is no weight. Consequently, if bodies move only under the action of gravity (i.e., fall freely), they are in the state weightlessness. A characteristic feature This state is the absence of deformations and internal stresses in freely falling bodies, which are caused by gravity in bodies at rest. The reason for the weightlessness of bodies is that the force of gravity imparts equal accelerations to a freely falling body and its support (or suspension).

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 gravity at a given point:

The value of the weight (with a constant mass of the body) is proportional to the acceleration of gravity, 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 geographic coordinates of the measurement point. Another factor affecting the acceleration of gravity and, accordingly, the weight of the body, are gravitational anomalies due to structural features 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 frame of reference 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 generally accepted 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,” even though the 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 with "human body weight".

Notes (edit)

Body weight and body weight: calculation formula

Mass is a measure of the body's inertia, it is how the body reacts to an impact applied to it, or it itself affects other bodies. And body weight 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 in newtons. The weight of the body has a direction, like any force, and is a vector magnitude. And mass has no direction and is a scalar quantity.

The arrow, which denotes the weight of the body in figures 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 weight

g - acceleration due to gravity = 9.81 m / s ^ 2

But despite the coincidence with the formula and the direction of gravity, there is a major difference between gravity and body weight. The force of gravity is applied to the body, that is, roughly speaking, it is she who 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 the force of gravity and the weight of the body is the same 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 height.

Body weight in zero gravity

In a state of weightlessness, the body weight is zero. The body will not press on the support or stretch the suspension and weigh nothing. 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 more mass 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 planet's gravity. We measure body weight with scales, in kilograms, and to measure body weight, which is measured in newtons, we can use a dynamometer, a special device for measuring force.

In everyday life and Everyday life the concepts "mass" and "weight" are absolutely identical, although their semantic meaning is fundamentally different. Asking "What is your weight?" we mean, "How many kilos are you?" However, to the question with which we are trying to find out this fact, the answer is given not in kilograms, but in newtons. We'll have to return to school physics course.

Body weight- the value characterizing the force with which the body exerts pressure on the support or suspension.

For comparison, body mass previously roughly defined as "amount of substance", the modern definition sounds like this:

Weight - a physical quantity that reflects the body's ability 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 enough to understand the fact of the real difference between mass and weight.

In addition, - kilograms, and weights (as a type of force) - Newtons.

And, perhaps, the most important difference between weight and mass is contained in 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 in the form of 9.8 N / kg.

In other words, the weight formula can be understood using the following example:

Weight mass 1 kg is suspended from a stationary dynamometer in order to determine it weight. Since the body, and the dynamometer itself, are at rest, then you can safely multiply its mass by the acceleration of gravity. We have: 1 (kg) x 9.8 (N / kg) = 9.8 N. It is with this force that the weight acts on the suspension of the dynamometer. From here it is clear that the body weight is equal, however, this is not always the case.

Now is the time to make an important note. The weight formula is equal to the gravity only in cases when:

the body is at rest;
the body is not affected by the force of Archimedes (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 does not just push the water out, the body becomes "lighter" by the volume of the displaced water. That is why it is possible to lift a 60 kg girl in water jokingly and laughing, but on the surface it is much more difficult to do it.

At uneven movement body, i.e. when the body together with the suspension moves with acceleration a, changes its appearance and weight formula. The physics of the phenomenon changes insignificantly, but such changes are reflected in the formula:

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 is moving must be greater than the acceleration of gravity. And here again it is important to distinguish weight from mass: negative weight does not affect the mass (the properties of the body remain the same), but it actually becomes directed in the opposite direction.

A good example of an accelerated elevator: when it is accelerated sharply for a short time, it gives the impression of being "pulled to the ceiling." Such a feeling is, of course, quite easy to face. It is much more difficult to feel the state of weightlessness, which is fully felt by astronauts in orbit.

Weightlessness - essentially no weight. For this to be possible, the acceleration with which the body moves must be equal to the notorious acceleration g (9.8 N / kg). The easiest way to achieve this effect is to near-earth orbit... Gravity, i.e. attraction still acts on the body (satellite), but it is negligible. And the acceleration of a satellite drifting in orbit 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.

Part of this effect can be encountered when an airplane takes off. For a second, there is a feeling of being suspended in the air: at this moment the acceleration with which the plane is moving is equal to the acceleration of gravity.

Coming back to differences again weights and masses, it is important to remember that a body weight formula is different from a mass formula that looks like :

m = ρ / V,

that is, the density of a substance divided by its volume.

We feel it as if we are "pressed" into the floor, or as if we are "hanging" in the air. This can be best experienced when riding a roller coaster or in the elevators of high-rise buildings, which abruptly begin to climb and descend.

Example:

Examples of weight gain:

When the elevator suddenly starts moving upward, people in the elevator feel as if they are being "pressed" into the floor.

When the elevator sharply reduces the downward speed, then the people in the elevator, due to inertia, are more "pressed" with their feet into the floor of the elevator.

When a roller coaster is driven over the bottom of the roller coaster, the people in the cart feel as if they are being "pushed" into the seat.

Example:

Weight reduction examples:

When cycling quickly on small hills, the cyclist at the top of the hillock feels a sense of lightness.

When the elevator suddenly begins to move downward, people in the elevator feel that their pressure on the floor decreases, a feeling of free fall arises.

When on a roller coaster ride over the highest point of the roller coaster, people in the cart feel as if they are "thrown" into the air.

When the swing is swinging to the highest point, it is felt that for a short moment the body "hangs" in the air.

The change in weight is associated with inertia - the desire of the body to maintain its initial state. Therefore, a change in weight is always the opposite of an acceleration of movement. When the acceleration is upward, the body weight increases. And if the acceleration of movement is directed downward, the body weight decreases.

In the figure, the blue arrows show the direction of acceleration of the movement.

1) If the elevator is stationary or evenly moving, then the acceleration is zero. In this case, the weight of a person is normal, it is equal to the force of gravity and is determined as follows: P = m ⋅ g.

2) If the elevator is moving upward at an accelerated rate or decreases its speed when moving downward, then the acceleration is directed upward. In this case, the weight of a person increases and is determined as follows: P = m ⋅ g + a.

3) If the elevator moves with acceleration downward or decreases its speed when moving up, then the acceleration is directed downward. In this case, the person's weight decreases and is determined as follows: P = m ⋅ g - a.

4) If a person is in an object that freely falls, then the acceleration of motion is directed downward and is the same as the acceleration of free fall: \ ( a = g \).

In this case, the person's weight is zero: P = 0.

Example:

Given: the mass of a person is \ (80 kg \). A man enters the elevator to go upstairs. The acceleration of the lift is \ (7 \) m s 2.

Each stage of the movement, together with the measurement readings, is shown in the figures below.

1) The elevator stands still, and the weight of the person is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.

2) The lift begins to move upward with an acceleration \ (7 \) m s 2, and the weight of a person increases: P = m ⋅ g a = 80 ⋅ 9.8 7 = 1334 N.

3) The elevator has picked up speed and is moving evenly, while the weight of a person is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.

4) The lift, when moving up, brakes with negative acceleration (deceleration) \ (7 \) m s 2, and the weight of a person decreases: P = m ⋅ g - a = 80 ⋅ 9.8 - 7 = 224 N.

5) The elevator has completely stopped, the weight of a person is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.

In addition to pictures and examples of the assignment, you can watch a video with an experiment conducted by schoolchildren, which shows how the weight of a person's body changes in an elevator. During the experiment, schoolchildren use scales, in which weight instead of kilograms is immediately indicated in \ (newtons, H \). http://www.youtube.com/watch?v=D-GzuZjawNI.

Example:

The state of weightlessness occurs in situations where a person is located in an object that is in free fall. There are special planes that are designed to create a state of zero gravity. They rise to a certain height, and after that the plane is put into free fall for about \ (30 seconds \). During the free fall of the plane, the people in it feel the state of weightlessness. This situation can be seen in this video.

What is the resting body weight. What is the difference between mass and weight and why there is a substitution of concepts? When the difference arises

Body weight. Weightlessness and overload

Notes (edit)

see also

See what "Weight" is in other dictionaries:

Books

Body weight and body weight: calculation formula

Body weight in zero gravity