How is gravity measured. The force of gravity and the force of universal gravitation

« Physics - Grade 10 "

Why does the moon move around the earth?
What happens if the moon stops?
Why do the planets revolve around the sun?

Chapter 1 discussed in detail how Earth informs all bodies near the surface of the Earth the same acceleration - acceleration free fall. But if the globe imparts acceleration to the body, then, according to Newton's second law, it acts on the body with some force. The force with which the earth acts on the body is called gravity. First we find this force, and then consider the force gravity.

Modulo acceleration is determined from Newton's second law:

In the general case, it depends on the force acting on the body and its mass. Since the acceleration of free fall does not depend on the mass, it is clear that the force of gravity must be proportional to the mass:

The physical quantity is the free fall acceleration, it is constant for all bodies.

Based on the formula F = mg, you can specify a simple and practically convenient method for measuring the masses of bodies by comparing the mass of a given body with the standard unit of mass. The ratio of the masses of two bodies is equal to the ratio of the forces of gravity acting on the bodies:

This means that the masses of bodies are the same if the forces of gravity acting on them are the same.

This is the basis for the determination of masses by weighing on a spring or balance scale. By ensuring that the force of pressure of the body on the scales, equal to the force of gravity applied to the body, is balanced by the force of pressure of the weights on the other scales, equal to the force of gravity applied to the weights, we thereby determine the mass of the body.

The force of gravity acting on a given body near the Earth can be considered constant only at a certain latitude near the Earth's surface. If the body is lifted or moved to a place with a different latitude, then the acceleration of free fall, and hence the force of gravity, will change.

The force of gravity.

Newton was the first to rigorously prove that the reason that causes the fall of a stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. it gravitational force acting between any bodies of the Universe.

Newton came to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from a high mountain (Fig. 3.1) with a certain speed could become such that it would never reach the Earth's surface at all, but would move around it like how the planets describe their orbits in the sky.

Newton found this reason and was able to accurately express it in the form of one formula - the law of universal gravitation.

Since the force of universal gravitation imparts the same acceleration to all bodies, regardless of their mass, it must be proportional to the mass of the body on which it acts:

“Gravity exists for all bodies in general and is proportional to the mass of each of them ... all planets gravitate towards each other ...” I. Newton

But since, for example, the Earth acts on the Moon with a force proportional to the mass of the Moon, then the Moon, according to Newton's third law, must act on the Earth with the same force. Moreover, this force must be proportional to the mass of the Earth. If the gravitational force is truly universal, then from the side of a given body any other body must be acted upon by a force proportional to the mass of this other body. Consequently, the force of universal gravitation must be proportional to the product of the masses of the interacting bodies. From this follows the formulation of the law of universal gravitation.

Law of gravity:

The force of mutual attraction of two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them:

The proportionality factor G is called gravitational constant.

The gravitational constant is numerically equal to the force of attraction between two material points with a mass of 1 kg each, if the distance between them is 1 m. After all, with masses m 1 \u003d m 2 \u003d 1 kg and a distance r \u003d 1 m, we get G \u003d F (numerically).

It must be kept in mind that the law of universal gravitation (3.4) as a universal law is valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.2, a).

It can be shown that homogeneous bodies having the shape of a ball (even if they cannot be considered material points, Fig. 3.2, b) also interact with the force defined by formula (3.4). In this case, r is the distance between the centers of the balls. The forces of mutual attraction lie on a straight line passing through the centers of the balls. Such forces are called central. The bodies whose fall to the Earth we usually consider are much smaller than the Earth's radius (R ≈ 6400 km).

Such bodies, regardless of their shape, can be considered as material points and determine the force of their attraction to the Earth using the law (3.4), keeping in mind that r is the distance from the given body to the center of the Earth.

A stone thrown to the Earth will deviate under the action of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it with more speed, it will fall further.” I. Newton

Definition of the gravitational constant.

Now let's find out how you can find the gravitational constant. First of all, note that G has a specific name. This is due to the fact that the units (and, accordingly, the names) of all quantities included in the law of universal gravitation have already been established earlier. The law of gravitation gives a new connection between known quantities with certain names of units. That is why the coefficient turns out to be a named value. Using the formula of the law of universal gravitation, it is easy to find the name of the unit of gravitational constant in SI: N m 2 / kg 2 \u003d m 3 / (kg s 2).

To quantify G, it is necessary to independently determine all the quantities included in the law of universal gravitation: both masses, force and distance between bodies.

The difficulty lies in the fact that the gravitational forces between bodies of small masses are extremely small. It is for this reason that we do not notice the attraction of our body to surrounding objects and mutual attraction objects to each other, although gravitational forces are the most universal of all forces in nature. Two people weighing 60 kg at a distance of 1 m from each other are attracted with a force of only about 10 -9 N. Therefore, to measure the gravitational constant, rather subtle experiments are needed.

The gravitational constant was first measured by the English physicist G. Cavendish in 1798 using a device called a torsion balance. The scheme of the torsion balance is shown in Figure 3.3. A light rocker with two identical weights at the ends is suspended on a thin elastic thread. Two heavy balls are motionlessly fixed nearby. Gravitational forces act between weights and motionless balls. Under the influence of these forces, the rocker turns and twists the thread until the resulting elastic force becomes equal to the gravitational force. The angle of twist can be used to determine the force of attraction. To do this, you only need to know the elastic properties of the thread. The masses of bodies are known, and the distance between the centers of interacting bodies can be directly measured.

From these experiments, the following value for the gravitational constant was obtained:

G \u003d 6.67 10 -11 N m 2 / kg 2.

Only in the case when bodies of enormous masses interact (or at least the mass of one of the bodies is very large), the gravitational force reaches of great importance. For example, the Earth and the Moon are attracted to each other with a force F ≈ 2 10 20 N.

Dependence of free fall acceleration of bodies on geographic latitude.

One of the reasons for the increase in the acceleration of gravity when moving the point where the body is located from the equator to the poles is that the globe is somewhat flattened at the poles and the distance from the center of the Earth to its surface at the poles is less than at the equator. Another reason is the rotation of the Earth.

Equality of inertial and gravitational masses.

The most striking property of gravitational forces is that they impart the same acceleration to all bodies, regardless of their masses. What would you say about a football player whose kick would equally accelerate an ordinary leather ball and a two-pound weight? Everyone will say that it is impossible. But the Earth is just such an “extraordinary football player” with the only difference that its effect on bodies does not have the character of a short-term impact, but continues continuously for billions of years.

In Newton's theory, mass is the source of the gravitational field. We are in the Earth's gravitational field. At the same time, we are also sources of the gravitational field, but due to the fact that our mass is much less than the mass of the Earth, our field is much weaker and the surrounding objects do not react to it.

The unusual property of gravitational forces, as we have already said, is explained by the fact that these forces are proportional to the masses of both interacting bodies. The mass of the body, which is included in Newton's second law, determines the inertial properties of the body, i.e., its ability to acquire a certain acceleration under the action of a given force. it inertial mass m and.

It would seem, what relation can it have to the ability of bodies to attract each other? The mass that determines the ability of bodies to attract each other is the gravitational mass m r .

It does not follow at all from Newtonian mechanics that the inertial and gravitational masses are the same, i.e. that

m and = m r . (3.5)

Equality (3.5) is a direct consequence of experience. It means that one can simply speak of the mass of a body as a quantitative measure of both its inertial and gravitational properties.

What is strength?

Each of us constantly meets with various cases of the action of bodies on each other. As a result of the interaction, the speed of movement of a body changes.

The body can start moving or stop, or it can change the direction of the speed of its movement.

When we kick the ball, it starts to move

When the ball hits the goal net, it stops

And if we miss and the ball hits the post, then it bounces off it in the other direction, i.e. changes direction of speed.

Often they do not indicate which body and how it acted on this body. They simply say that a force acts on the body or a force is applied to it. That is, considering the example with the ball, it is not always important for us what specifically influenced it. We simply say that the speed of the body has changed under the influence of a force. Therefore, the force can be considered as the cause of the change in the speed of movement.

In physics, force is a physical quantity that characterizes a change in the speed of a body.

In all our examples, we acted on the ball with a certain force, and at the same time its speed changed.

Signs of the action of force on the body

Force is a vector quantity that characterizes the action of bodies on each other, that is, it is a measure of this action.

Four signs of the action of a force on the body are known:

Symptom 1 - the body may change the speed value
(We all love bowling. By pushing the ball with our hands, we can set it in motion. The speed of the ball changes with the action of a human hand. OR when we kick a soccer ball)

Sign 2 - The body may change direction

(This is when the ball hits the bar OR we change the direction of the flying ball with a racket or other object)

Sign 3 - the body may experience a change in body size

(This is inflating an air mattress or a balloon)

Sign 4 - The body may have a change in the shape of the body.

(We can squeeze the eraser in our hands or crumple the basketball during the game or shake our hand)

If there is at least one of these signs, then they say: "A certain force acts on the body."

The force acting on the body can not only change the speed of the whole body, but also of its individual parts. Please note that when we knead a basketball with our hands, the speed does not change for the whole body, but only for some of its parts. For example, we squeeze the ball with our fingers, and only part of its particles begin to move. This is called deformity of the body.

Deformation is a change in the relative position of body particles associated with their movement relative to each other.

Deformation is any change in the shape and size of the body. Another example of deformation - A trampoline attached to supports bends if a person stands on it.

Direction and unit of force

Strength - physical quantity that can be measured.

Known. that the force is the cause of the change in the speed of the body. That is, we can measure how hard we kicked the ball or pushed the bowling ball. However, the force also has a direction, because we can kick the ball in absolutely any direction as well as push the ball, and it depends on us where it will fly or roll.

That is, force is a vector quantity.

It is designated in physics by the letter F with an arrow above it.

The unit of force is the force that changes the speed of a body with a mass of 1 kg by 1 m/s in 1 s.

In honor of the English physicist Newton, this unit is named newton.

Unit of measure of force - Newton, denoted by [H]

Other units are often used - kilonewtons (kN), millinewtons (mN):

1N = 0.001 kN.

Force, like speed, is a vector quantity. It is characterized not only numerical value but also direction.

In the drawing, the force is depicted as a straight line segment with an arrow at the end.

The beginning of the segment - point A is the point of application of force. The length of the segment conditionally denotes the modulus of force on a certain scale.

So, we can say that the result of the action of a force on a body depends on its modulus, direction and point of application.

The force of gravity of the earth

All of us were at football and watched the flights of the soccer ball. One observation can be made: no matter how hard a football player kicks the ball, sooner or later the ball ends up on Earth.

No matter how we rejoiced at the victory of our team and jumped high, high, we still landed back. Any object, being raised above the surface, tends to the Earth.

That is, we come to the conclusion that there is some unchanging force that attracts all objects to the Earth. Why is this happening? What is the name of this phenomenon?

Here is the answer to these questions - A force acts on these bodies - the force of attraction to the Earth. Due to attraction to the Earth, bodies fall, raised above the Earth, and then lowered.

The force of pulling the leg out of quicksand at a speed of 0.1 m/s

equal to the lifting force of the car.

Fun Fact: Quicksand is a Newtonian fluid

which cannot completely absorb a person.

Therefore, people stuck in the sand die of dehydration,

sun exposure or other reasons. .

Gravity and gravitational force

The force of attraction towards the earth is called gravity. The force of gravity acts on all bodies on the surface of the Earth. But not only bodies are attracted to the Earth - they themselves attract the Earth to themselves. As scheduled, twice every day huge waves rise on the seas and oceans - this can be observed on the shore in the form of ebbs and flows. For what? Due to the fact that the moon acts on the Earth. This is interaction. It was first described by the English physicist Isaac Newton. He argued that all bodies in the universe are attracted to each other. I. Newton established that “the greater the mass of interacting bodies, the greater the force with which they interact will be. The forces of attraction between bodies decrease as the distance between them increases. This phenomenon is called the force of universal gravitation.

The attraction of all bodies of the universe to each other is called universal gravitation.

We are all accustomed in life to use the word power in comparative characteristic talking men stronger than women, the tractor is stronger than the car, the lion is stronger than the antelope.

Force in physics is defined as a measure of the change in the speed of a body that occurs when bodies interact. If force is a measure and we can compare the application different strength, which means that it is a physical quantity that can be measured. In what units is force measured?

Force units

In honor of the English physicist Isaac Newton, who did enormous research in the nature of the existence and use of various types of force, 1 newton (1 N) is accepted as a unit of force in physics. What is a force of 1 N? In physics, one does not simply choose units of measurement, but makes a special agreement with those units that have already been adopted.

We know from experience and experiments that if a body is at rest and a force acts on it, then the body under the influence of this force changes its speed. Accordingly, to measure the force, a unit was chosen that would characterize the change in the speed of the body. And do not forget that there is also the mass of the body, since it is known that with the same force the impact on different objects will be different. We can throw the ball far, but the cobblestone will fly away a much shorter distance. That is, taking into account all the factors, we come to the definition that a force of 1 N will be applied to the body if a body with a mass of 1 kg under the influence of this force changes its speed by 1 m / s in 1 second.

Gravity unit

We are also interested in the unit of gravity. Since we know that the Earth attracts to itself all the bodies on its surface, then there is a force of attraction and it can be measured. And again, we know that the force of attraction depends on the mass of the body. The greater the body weight, the stronger earth attracts him. It has been experimentally established that The force of gravity acting on a body of mass 102 grams is 1 N. And 102 grams is approximately one tenth of a kilogram. And to be more precise, if 1 kg is divided into 9.8 parts, then we will just get approximately 102 grams.

If a force of 1 N acts on a body weighing 102 grams, then a force of 9.8 N acts on a body weighing 1 kg. The acceleration of free fall is denoted by the letter g. And g is 9.8 N/kg. This is the force that acts on a body of mass 1 kg, accelerating it every second by 1 m / s. It turns out that a body falling from a great height picks up a very high speed during the flight. Why then snowflakes and rain drops fall pretty easy? They have a very small mass, and the earth pulls them towards itself very weakly. And the air resistance for them is quite large, so they fly to the Earth with not very high, rather the same speed. But meteorites, for example, when approaching the Earth, gain very high speed and upon landing, a decent explosion is formed, which depends on the size and mass of the meteorite, respectively.

Gravity is the amount by which a body is attracted to the earth under the influence of its attraction. This indicator directly depends on the weight of a person or the mass of an object. The more weight, the higher it is. In this article, we will explain how to find the force of gravity.

Factors affecting gravity:

• distance from the ground;
• the geographical location of the body;
• Times of Day.

If the body is not dragged in a horizontal direction, then it is worth taking into account the angle at which the object deviates from the horizon. As a result, the formula will look like this: F=m*g – Fthrust*sin. The force of gravity is measured in newtons. For calculations, use the speed measured in m/s. To do this, divide the speed in km/h by 3.6.

Gravity- this is the force acting on the body from the side of the Earth and informing the body of the acceleration of free fall:

\(~\vec F_T = m \vec g.\)

Any body located on the Earth (or near it), together with the Earth, rotates around its axis, i.e., the body moves in a circle with a radius r with a constant modulo speed (Fig. 1).

A body on the surface of the Earth is affected by the gravitational force \(~\vec F\) and the force from the side earth's surface\(~\vec N_p\).

Their resultant

\(~\vec F_1 = \vec F + \vec N_p \qquad (1)\)

imparts centripetal acceleration to the body

\(~a_c = \frac(\upsilon^2)(r).\)

Let us decompose the gravitational force \(~\vec F\) into two components, one of which will be \(~\vec F_1\), i.e.

\(~\vec F = \vec F_1 + \vec F_T. \qquad (2)\)

From equations (1) and (2) we see that

\(~\vec F_T = - \vec N_p.\)

Thus, the force of gravity \(~\vec F_T\) is one of the components of the force of gravity \(~\vec F\). The second component \(~\vec F_1\) tells the body centripetal acceleration.

At the point Μ on the geographical latitude φ gravity is not directed along the radius of the Earth, but at some angle α to him. The force of gravity is directed along the so-called sheer line (vertically down).

The force of gravity is equal in magnitude and direction to the force of gravity only at the poles. At the equator, they coincide in direction, and the absolute difference is greatest.

\(~F_T = F - F_1 = F - m \omega^2 R,\)

where ω - angular velocity earth rotation, R is the radius of the earth.

\(~\omega = \frac(2 \pi)(T) = \frac(2 \cdot 2.34)(24 \cdot 3600)\) rad/s = 0.727 10 -4 rad/s.

Because ω very small, then F T≈ F. Consequently, the force of gravity differs little in modulus from the force of gravity, so this difference can often be neglected.

Then F T≈ F, \(~mg = \frac(GMm)((h + R)^2) \Rightarrow g = \frac(GM)((h + R)^2)\) .

This formula shows that the free fall acceleration g does not depend on the mass of the falling body, but depends on the height.

Literature

Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsia i vykhavanne, 2004. - C. 39-40.