In ordinary life, weight is considered synonymous with mass. But in physics, weight and mass are two different things.

Body weight (denoted R) - the force with which the body acts on the support or suspension due to attraction to the Earth.

Astronauts in zero gravity have mass but no weight. Each person reaches
weightlessness, if it lifts both legs off the ground while running.

If the body is at rest or moving uniformly, its weight is calculated by the formula:

Coefficient g differs in different parts of the Earth and on other planets. Man in Minsk
will weigh less than in Moscow. Coefficient g for different places:

At rest and uniform motion, the modules (numerical value) of body weight and gravity
are equal. But if the body is accelerating, decelerating, or moving in a curve, they are different.
When the elevator accelerates and moves down, the body puts less pressure on the floor and the weight decreases, and when
moves up, the pressure on the support and the weight increase. It is felt even by sensations:
when lifting, the body seems to be pressed into the floor. Weight change can be confirmed and
experimentally, if you take a ride in the elevator, standing on the scales.

The change in weight caused by the change in speed is overload.

On a carousel or in a speeding car, the g-force pushes the body into the seat.
Pilots experience enormous overloads: when performing aerobatics, their weight (and
This means that the weight of all organs, bones, blood) grows 10-20 times. Muscle strength is not
increases. The heart muscle of an ordinary person cannot push such a heavy
blood to the head, so at high g-forces he loses consciousness. Therefore, the pilots
trained to withstand 10 times the weight on the centrifuge - this is, in fact, a rapidly rotating
carousel.

1. What is the difference between body weight and body weight?
2. Can body weight be zero?
3. How to find the weight of a body at rest?
4. What is overload?
5. Will the weight of a body on the Moon be different from the weight of the same body on Earth?
6. How will your weight in the capital of the Republic of Belarus differ from your weight in the US capital?

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 make an important remark. 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.

In the past lessons, we have analyzed what the force of universal gravitation is and its special case - the force of gravity, which acts on bodies located on the Earth.

Gravity is the force acting on any material body located near the surface of the Earth or another astronomical body. Gravity plays an important role in our life, since everything that surrounds us is subject to its influence. Today we will analyze another force, which is most often associated with gravity. This force is the weight of the body. The topic of today's lesson is “Body weight. Weightlessness"

Under the action of the elastic force, which is applied to the upper edge of the body, this body, in turn, is also deformed, another elastic force arises due to the deformation of the body. This force is applied to the lower edge of the spring. In addition, it is equal in modulus to the elastic force of the spring and is directed downward. It is this force of elasticity of the body that we will call its weight, that is, the weight of the body is applied to the spring and directed downwards.

After the oscillations of the body on the spring are damped, the system will come to a state of equilibrium in which the sum of the forces acting on the body will be equal to zero. This means that the force of gravity is equal in modulus and opposite in direction to the force of elasticity of the spring (Fig. 2). The latter is equal in modulus and opposite in direction to the weight of the body, as we have already found out. Hence, the modulus of gravity is equal to the weight of the body. This ratio is not universal, but in our example it is true.

Rice. 2. Weight and gravity ()

The above formula does not mean that gravity and weight are the same. These two forces are different in nature. Weight is the elastic force applied to the suspension from the side of the body, and gravity is the force applied to the body from the side of the Earth.

Rice. 3. Weight and gravity of the body on the suspension and on the support ()

Let's find out some features of weight. Weight is the force with which the body presses on the support or stretches the suspension, it follows that if the body is not suspended or not fixed on the support, then its weight is zero. This conclusion seems to contradict our daily experience. However, it has quite fair physical examples.

If the spring with the body suspended from it is released and allowed to fall freely, then the dynamometer pointer will show zero value (Fig. 4). The reason for this is simple: the load and the dynamometer are moving with the same acceleration (g) and the same zero initial speed (V 0). The lower end of the spring moves synchronously with the load, while the spring is not deformed and there is no elastic force in the spring. Consequently, there is no counter force of elasticity, which is the weight of the body, that is, the body does not have weight, or is weightless.

Rice. 4. Free fall of a spring with a body suspended from it ()

The state of weightlessness arises due to the fact that under terrestrial conditions the force of gravity informs all bodies of the same acceleration, the so-called acceleration of free fall. For our example, we can say that the load and the dynamometer are moving with the same acceleration. If only the force of gravity or only the force of universal gravitation acts on the body, then this body is in a state of weightlessness. It is important to understand that in this case only the weight of the body disappears, but not the force of gravity acting on this body.

The state of weightlessness is not exotic, quite often many of you have experienced it - any person jumping or jumping from any height, until the moment of landing, is in a state of weightlessness.

Let us consider the case when the dynamometer and the body attached to its spring move down with some acceleration, but do not freely fall. The dynamometer reading will decrease compared to the readings with a stationary load and spring, which means that the weight of the body has become less than it was at rest. What is the reason for this decrease? Let's give a mathematical explanation based on Newton's second law.

Rice. 5. Mathematical explanation of body weight ()

Two forces act on the body: the downward force of gravity and the upward force of the spring. These two forces impart acceleration to the body. and the equation of motion will look like:

Let's choose the y axis (Fig. 5), since all forces are directed vertically, one axis is enough for us. As a result of projection and transfer of terms, we get - the modulus of the elastic force will be equal to:

ma = mg - F control

F control \u003d mg - ma,

where the left and right sides of the equation are the projections of the forces specified in Newton's second law onto the y-axis. According to the definition, the modulus of the weight of the body is equal to the elastic force of the spring, and, substituting its value, we get:

P \u003d F control \u003d mg - ma \u003d m (g - a)

The weight of the body is equal to the product of the mass of the body and the difference in accelerations. It can be seen from the obtained formula that if the modulus of acceleration of a body is less than the modulus of free fall acceleration, then the weight of the body is less than the force of gravity, that is, the weight of a body moving at an accelerated rate is less than the weight of a body at rest.

Let us consider the case when a body with a weight moves upwards (Fig. 6).

The arrow of the dynamometer will show the value of the body weight greater than the resting load.

Rice. 6. The body with a weight moves rapidly up ()

The body is moving upwards, and its acceleration is directed there, therefore, we need to change the sign of the acceleration projection on the y-axis.

It can be seen from the formula that now the weight of the body is greater than the force of gravity, that is, it is greater than the weight of the resting body.

The increase in body weight caused by its accelerated movement is called overload.

This is true not only for a body suspended on a spring, but also for a body fixed on a support.

Let's consider an example in which a change in a body occurs during its accelerated movement (Fig. 7).

The car moves along the bridge of a convex trajectory, that is, along a curved trajectory. We will consider the shape of the bridge as an arc of a circle. From kinematics, we know that the car is moving with centripetal acceleration, the magnitude of which is equal to the square of the speed divided by the radius of curvature of the bridge. At the moment it is at its highest point, this acceleration will be directed vertically downwards. According to Newton's second law, this acceleration is imparted to the car by the resultant force of gravity and the reaction force of the support.

We choose the coordinate axis y, directed vertically upwards, and write this equation in projection onto the selected axis, substitute the values ​​and carry out transformations:

Rice. 7. The highest point of the car ()

The weight of the car, according to Newton's third law, is equal in absolute value to the reaction force of the support (), while we see that the weight of the car is less than the force of gravity, that is, less than the weight of a stationary car.

The rocket, when launched from the Earth, moves vertically upwards with an acceleration a=20 m/s 2 . What is the weight of the pilot-cosmonaut in the cockpit if his mass is m=80 kg?

It is quite obvious that the acceleration of the rocket is directed upwards and for the solution we must use the body weight formula for the case with g-force (Fig. 8).

Rice. 8. Illustration for the problem

It should be noted that if a body motionless relative to the Earth has a weight of 2400 N, then its mass is 240 kg, that is, the astronaut feels himself three times more massive than he actually is.

We analyzed the concept of body weight, found out the main properties of this quantity and obtained formulas that allow us to calculate the weight of a body moving with acceleration.

If the body moves vertically downwards, while the modulus of its acceleration is less than the free fall acceleration, then the weight of the body decreases compared to the value of the weight of the stationary body.

If the body moves vertically with acceleration, then its weight increases and at the same time the body experiences an overload.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemozina, 2012.
2. Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

Homework

1. Define body weight.
2. What is the difference between body weight and gravity?
3. When does weightlessness occur?

1. Internet portal Physics.kgsu.ru ().
2. Internet portal Festival.1september.ru ().
3. Internet portal Terver.ru ().

Quite a lot of mistakes and non-random reservations of students are connected with the strength of the weight. The phrase “power of weight” itself is not very familiar, because. we (teachers, authors of textbooks and problem books, teaching aids and reference literature) are more accustomed to speaking and writing “body weight”. Thus, the phrase itself leads us away from the concept that weight is force, and leads to the fact that body weight is confused with body weight (we often hear in the store when they are asked to weigh a few kilograms of a product). The second common mistake students make is that they confuse the force of weight with the force of gravity. Let's try to deal with the force of weight at the level of a school textbook.

To begin with, let's look at the reference literature and try to understand the point of view of the authors on this issue. Yavorsky B.M., Detlaf A.A. (1) in a handbook for engineers and students, the weight of a body is the force with which this body acts due to gravity towards the Earth on a support (or suspension) that keeps the body from free fall. If the body and the support are stationary relative to the Earth, then the weight of the body is equal to its gravity. Let's ask some naive questions to the definition:

1. What reporting system are we talking about?

2. Is there one support (or suspension) or several (supports and suspensions)?

3. If the body gravitates not to the Earth, but, for example, to the Sun, will it have weight?

4. If a body in a spaceship moving with acceleration "almost" does not gravitate to anything in observable space, will it have weight?

5. How is the support located relative to the horizon, is the suspension vertical for the case of equality of body weight and gravity?

6. If the body moves uniformly and rectilinearly together with the support relative to the Earth, then the weight of the body is equal to its gravity?

In the reference guide to physics for applicants to universities and self-education, Yavorsky B.M. and Selezneva Yu.A. (2) provide an explanation on the last naive question, leaving the former unaddressed.

Koshkin N.I. and Shirkevich M.G. (3) it is proposed to consider the weight of the body as a vector physical quantity, which can be found by the formula:

The examples below will show that this formula works in cases where no other forces act on the body.

Kuchling H. (4) does not introduce the concept of weight as such at all, identifying it practically with the force of gravity; in the drawings, the force of weight is applied to the body, and not to the support.

In the popular "Physics Tutor" Kasatkina I.L. (5) body weight is defined as the force with which a body acts on a support or suspension due to attraction to the planet. In the following explanations and examples given by the author, answers are given only to the 3rd and 6th of the naive questions.

In most textbooks on physics, definitions of weight are given to some extent similar to the definitions of the authors (1), (2), (5). When studying physics in the 7th and 9th educational grades, perhaps this is justified. In the 10th profile classes with such a definition, when solving a whole class of problems, various kinds of naive questions cannot be avoided (in general, one should not at all strive to avoid any questions).

Authors Kamenetsky S.E., Orekhov V.P. in (6), delimiting and explaining the concepts of gravity and body weight, they write that body weight is a force that acts on a support or suspension. And that's all. You don't have to read between the lines. True, I still want to ask, how many supports and suspensions, and can the body have both support and suspension at once?

And, finally, let's look at the definition of body weight, which is given by Kasyanov V.A. (7) in a 10th grade physics textbook: “body weight is the total body elasticity force acting in the presence of gravity on all connections (supports, suspensions)”. If at the same time we remember that the force of gravity is equal to the resultant of two forces: the force of gravitational attraction to the planet and the centrifugal force of inertia, provided that this planet rotates around its axis, or some other force of inertia associated with the accelerated movement of this planet, then one could agree with this definition. Since, in this case, no one bothers us to imagine a situation where one of the components of gravity is negligible, for example, the case of a spaceship in deep space. And even with these reservations, it is tempting to remove the mandatory presence of gravity from the definition, because situations are possible when there are other forces of inertia that are not related to the movement of the planet or Coulomb forces of interaction with other bodies, for example. Or agree with the introduction of some "equivalent" gravity in non-inertial reference systems and define the force of weight for the case when there is no interaction of the body with other bodies, except for the body that creates gravitational attraction, supports and suspensions.

And yet, let's decide when the weight of the body is equal to the force of gravity in inertial frames of reference?

Suppose we have one support or one suspension. Is the condition sufficient that the support or suspension is motionless relative to the Earth (we consider the Earth to be an inertial frame of reference), or move uniformly and rectilinearly? Take a fixed support, located at an angle to the horizon. If the support is smooth, then the body slides along the inclined plane, i.e. is not resting on a support and is not in free fall. And if the support is so rough that the body is at rest, then either the inclined plane is not a support, or the weight of the body is not equal to the force of gravity (you can, of course, go further and question that the weight of the body is not equal in absolute value and not opposite in direction support reaction force, and then there will be nothing to talk about at all). If, however, we consider the inclined plane as a support, and the sentence in brackets as irony, then, solving the equation for Newton's second law, which for this case will also be the equilibrium condition for the body on the inclined plane, written in projections onto the Y axis, we will obtain an expression for weight other than gravity:

So, in this case, it is not enough to say that the weight of the body is equal to the force of gravity, when the body and the support are motionless relative to the Earth.

Let us give an example with a suspension fixed relative to the Earth and a body on it. A positively charged metal ball on a thread is placed in a uniform electric field so that the thread makes some angle with the vertical. Let's find the weight of the ball from the condition that the vector sum of all forces is equal to zero for a body at rest.

As you can see, in the above cases, the weight of the body is not equal to the force of gravity when the condition of immobility of the support, suspension and body relative to the Earth is met. The features of the above cases are the existence of the friction force and the Coulomb force, respectively, the presence of which actually leads to the fact that the bodies are kept from moving. For vertical suspension and horizontal support, additional forces are not needed to keep the body from moving. Thus, to the condition of immobility of the support, suspension and body relative to the Earth, we could add that the support is horizontal and the suspension is vertical.

But would this addition solve our question? Indeed, in systems with a vertical suspension and a horizontal support, forces can act that reduce or increase the weight of the body. These can be the force of Archimedes, for example, or the force of Coulomb, directed vertically. To summarize for one support or one suspension: the weight of the body is equal to the force of gravity, when the body and the support (or suspension) are at rest (or move uniformly and rectilinearly) relative to the Earth, and only the reaction force of the support (or the elastic force of the suspension) and the force act on the body gravity. The absence of other forces, in turn, implies that the support is horizontal, the suspension is vertical.

Let us consider cases when a body with several supports and/or suspensions is at rest (or moves uniformly and rectilinearly with them relative to the Earth) and no other forces act on it, except for the reaction forces of the support, the elastic forces of the suspensions, and attraction to the Earth. Using the definition of the weight force Kasyanov V.A. (7), we find the total force of elasticity of the body bonds in the first and second cases presented in the figures. The geometric sum of the forces of elastic bonds F, equal in modulus to the weight of the body, based on the equilibrium condition, is really equal to gravity and opposite to it in direction, and the angles of inclination of the planes to the horizon and the angles of deviation of the suspensions from the vertical do not affect the final result.

Let us consider an example (figure below), when in a system that is motionless relative to the Earth, a body has a support and a suspension, and no other forces act in the system, except for the forces of elastic bonds. The result is similar to the above. The weight of the body is equal to the force of gravity.

So, if the body is on several supports and (or) suspensions, and rests together with them (or moves uniformly and rectilinearly) relative to the Earth, in the absence of other forces, except for the force of gravity and the forces of elastic bonds, its weight is equal to the force of gravity. At the same time, the location of supports and suspensions in space and their number do not affect the final result.

Consider examples of finding body weight in non-inertial frames of reference.

Example 1 Find the weight of a body of mass m moving in a spaceship with acceleration but in "empty" space (so far from other massive bodies that their gravity can be neglected).

In this case, two forces act on the body: the force of inertia and the reaction force of the support. If the modulus of acceleration is equal to the acceleration of free fall on the Earth, then the weight of the body will be equal to the force of gravity on the Earth, and the astronauts will perceive the nose of the ship as a ceiling, and the tail as a floor.

The artificial gravity created in this way for the astronauts inside the ship will not differ in any way from the "real" terrestrial one.

In this example, due to its smallness, we neglect the gravitational component of gravity. Then the force of inertia on the spacecraft will be equal to the force of gravity. In view of this, we can agree that the cause of the body weight in this case is gravity.

Let's go back to Earth.

Example 2

With respect to the ground with acceleration but a trolley is moving, on which a body is fixed on a thread of mass m, deviated by an angle from the vertical. Find the weight of the body, neglect the air resistance.

A task with one suspension, therefore, the weight is equal in modulus to the elastic force of the thread.

Thus, you can use any formula to calculate the elastic force, and, therefore, the weight of the body (if the air resistance force is large enough, then it will need to be taken into account as a term for the inertial force).

Let's work with the formula

Therefore, by introducing the "equivalent" force of gravity, we can assert that in this case the weight of the body is equal to the "equivalent" force of gravity. And finally, we can give three formulas for its calculation:

Example 3

Find the weight of a race car driver with mass m in a moving with acceleration but car.

At high accelerations, the reaction force of the seat back support becomes significant, and we will take it into account in this example. The total elastic force of the bonds will be equal to the geometric sum of both reaction forces of the support, which in turn is equal in absolute value and opposite in direction to the vector sum of the forces of inertia and gravity. For this problem, we find the module of the weight force by the formulas:

The effective free fall acceleration is found as in the previous problem.

Example 4

A ball on a thread of mass m is fixed on a platform rotating at a constant angular velocity ω at a distance r from its center. Find the weight of the ball.

Finding the body weight in non-inertial frames of reference in the given examples shows how well the formula for the body weight proposed by the authors in (3) works. Let's complicate the situation a bit in example 4. Let's assume that the ball is electrically charged, and the platform, together with its contents, is in a uniform vertical electric field. What is the weight of the ball? Depending on the direction of the Coulomb force, the weight of the body will decrease or increase:

It so happened that the question of weight naturally reduced to the question of gravity. If we define gravity as the resultant of the forces of gravitational attraction to a planet (or to any other massive object) and inertia, keeping in mind the principle of equivalence, leaving in the fog the origin of the force of inertia itself, then both components of gravity, or one of them, at least cause body weight. If there are other interactions in the system along with the force of gravitational attraction, the force of inertia and the forces of elasticity of the bonds, then they can increase or decrease the weight of the body, lead to a state when the weight of the body becomes equal to zero. And these other interactions can cause weight gain in some cases. Let's charge a ball on a thin non-conducting thread in a spaceship moving uniformly and rectilinearly in a distant "empty" space (we will neglect the forces of gravity because of their smallness). Let's put the ball in the electric field, the thread will be stretched, the weight will appear.

Summarizing the above, we conclude that the weight of the body is equal to the force of gravity (or the equivalent force of gravity) in any system where no other forces act on the body, except for the forces of gravity, inertia and elasticity of the bonds. Gravity, or "equivalent" gravity, is most often the cause of weight force. The force of weight and the force of gravity have a different nature and are applied to different bodies.

Bibliography.

1. Yavorsky B.M., Detlaf A.A. Handbook of physics for engineers and university students, M., Nauka, 1974, 944p.

2. Yavorsky B.M., Selezneva Yu.A. Physics Reference Guide for

entering universities and self-education., M., Nauka, 1984, 383p.

3. Koshkin N.I., Shirkevich M.G. Handbook of elementary physics., M., Nauka, 1980, 208s.

4. Kuhling H. Handbook of Physics., M., Mir, 1983, 520p.

5. Kasatkina I.L. Physics tutor. Theory. Mechanics. Molecular physics. Thermodynamics. Electromagnetism. Rostov-on-Don, Phoenix, 2003, 608s.

6. Kamenetsky S.E., Orekhov V.P. Methods for solving problems in physics in high school., M., Education, 1987, 336s.

7. Kasyanov V.A. Physics. Grade 10., M., Bustard, 2002, 416s.

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

Every body on the planet is affected by the Earth's gravity. 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. The force of gravity always pointing vertically down.

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

F t \u003d 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 is in free fall. According to Newton's second law and the formula F t \u003d GMm / R 2 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 free fall acceleration 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 Fт = mg. In vector form

F t \u003d 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 \u003d GMm / R 2 it can be seen that for this reason the force of gravity and the acceleration of free fall caused by it is greater at the pole than at the equator.

The force of gravity acts on all bodies in the Earth's gravitational field, but not all bodies fall to the Earth. This is due to the fact that the movement of many bodies is hindered by other bodies, such as 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 free fall is affected by the rotation of the Earth. This influence is explained as follows. The frames of reference associated with the surface of the Earth (except for the two associated with the poles of the Earth) are not, strictly speaking, inertial frames of reference - the Earth rotates around its axis, and such frames of reference move along circles with centripetal acceleration along with it. This non-inertiality of reference systems is manifested, in particular, in the fact that the value of the acceleration of free fall turns out to be different in different places on the Earth and depends on the geographical latitude of the place where the reference frame associated with the Earth is located, relative to which the acceleration of gravity is determined.

Measurements carried out at different latitudes showed that the numerical values ​​of the gravitational acceleration differ little from each other. Therefore, with not very accurate calculations, one can neglect the non-inertial reference systems associated with the Earth's surface, as well as the difference in the shape of the Earth from a spherical one, and assume that the acceleration of free fall in any place 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 free fall caused by it decrease with increasing distance from the Earth. At a height h from the Earth's surface, the gravitational acceleration module is determined by the formula

g=GM/(R+h) 2.

It has been established that at a height of 300 km above the Earth's surface, the free fall acceleration 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 a gravitational force applied to a body, weight is an elastic force applied to a support or suspension (i.e., to a connection).

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 moving uniformly and rectilinearly; In this case

P \u003d F t \u003d 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 free fall acceleration.

When a 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 at the same time the body moves vertically up or down relative to the direction of free fall acceleration, then the vector sum of the forces F t and F yn gives the resultant, which causes the acceleration of the body, i.e.

F t + F pack \u003d ma.

According to the above definition of the concept of "weight", we can write that P=-F yp. From the formula: F t + F pack \u003d ma. taking into account the fact that F T =mg, it follows that mg-ma=-F yp . Therefore, P \u003d m (g-a).

The 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., it coincides in direction with the acceleration of free fall g), then modulo

P=m(g-a)

If the acceleration of the body is directed upwards (i.e., opposite to the direction of free fall acceleration), then

P \u003d m \u003d 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 its accelerated movement is called overload.

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

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