The formula for calculating the force of gravity. Gravity, formulas

Absolutely all bodies in the Universe are affected by a magical force that somehow attracts them to the Earth (more precisely to its core). There is nowhere to escape, nowhere to hide from the all-encompassing magical gravity: the planets of our solar system are attracted not only to the huge Sun, but also to each other, all objects, molecules and the smallest atoms are also mutually attracted. known even to small children, having devoted his life to the study of this phenomenon, he established one of the greatest laws - the law of universal gravitation.

What is gravity?

The definition and formula have long been known to many. Let us recall that gravity is a certain quantity, one of the natural manifestations of universal gravitation, namely: the force with which any body is invariably attracted to the Earth.

Gravity is denoted by the Latin letter F gravity.

Gravity: formula

How to calculate the direction towards a specific body? What other quantities do you need to know for this? The formula for calculating gravity is quite simple; it is studied in the 7th grade of a secondary school, at the beginning of a physics course. In order to not only learn it, but also understand it, one should proceed from the fact that the force of gravity, which invariably acts on a body, is directly proportional to its quantitative value (mass).

The unit of gravity is named after the great scientist - Newton.

It is always directed strictly downwards, towards the center of the earth's core, thanks to its influence all bodies fall downwards equally accelerated. We observe the phenomena of gravity in everyday life everywhere and constantly:

objects, accidentally or deliberately released from the hands, necessarily fall down to the Earth (or to any surface that prevents free fall);
a satellite launched into space does not fly away from our planet to an indefinite distance perpendicularly upward, but remains rotating in orbit;
all rivers flow from the mountains and cannot be turned back;
sometimes a person falls and gets injured;
tiny specks of dust settle on all surfaces;
the air is concentrated near the surface of the earth;
hard to carry bags;
Rain drips from the clouds, snow and hail fall.

Along with the concept of "gravity" the term "body weight" is used. If a body is placed on a flat horizontal surface, then its weight and gravity are numerically equal, thus, these two concepts are often replaced, which is not at all correct.

Acceleration of gravity

The concept of “acceleration of gravity” (in other words, is associated with the term “force of gravity”. The formula shows: in order to calculate the force of gravity, you need to multiply the mass by g (acceleration of gravity).

"g" = 9.8 N/kg, this is a constant value. However, more accurate measurements show that due to the rotation of the Earth, the value of the acceleration of St. n. is not the same and depends on latitude: at the North Pole it = 9.832 N/kg, and at the hot equator = 9.78 N/kg. It turns out that in different places on the planet, different forces of gravity are directed towards bodies of equal mass (the formula mg still remains unchanged). For practical calculations, it was decided to allow for minor errors in this value and use the average value of 9.8 N/kg.

The proportionality of such a quantity as gravity (the formula proves this) allows you to measure the weight of an object with a dynamometer (similar to an ordinary household business). Please note that the device only shows strength, since the regional g value must be known to determine the exact body weight.

Does gravity act at any distance (both close and far) from the earth's center? Newton hypothesized that it acts on a body even at a significant distance from the Earth, but its value decreases in inverse proportion to the square of the distance from the object to the Earth's core.

Gravity in the Solar System

Is there a Definition and formula regarding other planets that remain relevant. With only one difference in the meaning of "g":

on the Moon = 1.62 N/kg (six times less than on Earth);
on Neptune = 13.5 N/kg (almost one and a half times higher than on Earth);
on Mars = 3.73 N/kg (more than two and a half times less than on our planet);
on Saturn = 10.44 N/kg;
on Mercury = 3.7 N/kg;
on Venus = 8.8 N/kg;
on Uranus = 9.8 N/kg (almost the same as ours);
on Jupiter = 24 N/kg (almost two and a half times higher).

Gravity is the force with which the Earth attracts a body located near its surface. .

The phenomena of gravity can be observed everywhere in the world around us. A ball thrown up falls down, a stone thrown horizontally will end up on the ground after some time. An artificial satellite launched from the Earth, due to the effects of gravity, does not fly in a straight line, but moves around the Earth.

Gravity always directed vertically downward, towards the center of the Earth. It is denoted by the Latin letter F t (T- heaviness). The force of gravity is applied to the center of gravity of the body.

To find the center of gravity of an arbitrary shape, you need to hang a body on a thread at its different points. The point of intersection of all directions marked by the thread will be the center of gravity of the body. The center of gravity of bodies of regular shape is at the center of symmetry of the body, and it is not necessary that it belong to the body (for example, the center of symmetry of a ring).

For a body located near the surface of the Earth, the force of gravity is equal to:

where is the mass of the Earth, m- body weight, R- radius of the Earth.

If only this force acts on the body (and all others are balanced), then it undergoes free fall. The acceleration of this free fall can be found by applying Newton's second law:

(2)

From this formula we can conclude that the acceleration of gravity does not depend on the mass of the body m, therefore, it is the same for all bodies. According to Newton's second law, gravity can be defined as the product of the mass of a body and its acceleration (in this case, the acceleration due to gravity g);

Gravity, acting on the body, is equal to the product of the mass of the body and the acceleration of gravity.

Like Newton's second law, formula (2) is valid only in inertial frames of reference. On the Earth's surface, inertial reference systems can only be systems associated with the Earth's poles, which do not take part in its daily rotation. All other points of the earth's surface move in circles with centripetal accelerations and the reference systems associated with these points are non-inertial.

Due to the rotation of the Earth, the acceleration of gravity at different latitudes is different. However, the acceleration of free fall in different regions of the globe varies very little and differs very little from the value calculated by the formula

Therefore, in rough calculations, the non-inertiality of the reference system associated with the Earth’s surface is neglected, and the acceleration of gravity is considered to be the same everywhere.

Definition

Under the influence of the force of gravity towards the Earth, all bodies fall with equal accelerations relative to its surface. This acceleration is called the acceleration of gravity and is denoted by: g. Its value in the SI system is considered equal to g = 9.80665 m/s 2 - this is the so-called standard value.

The above means that in the reference frame that is associated with the Earth, any body with mass m is acted upon by a force equal to:

which is called gravity.

If a body is at rest on the surface of the Earth, then the force of gravity is balanced by the reaction of the suspension or support, which keeps the body from falling (body weight).

Difference between gravity and the force of attraction to the Earth

To be precise, it should be noted that as a result of the non-inertiality of the reference frame that is associated with the Earth, the force of gravity differs from the force of attraction to the Earth. The acceleration that corresponds to orbital motion is significantly less than the acceleration that is associated with the daily rotation of the Earth. The reference frame associated with the Earth rotates relative to the inertial frames with angular velocity =const. Therefore, when considering the movement of bodies relative to the Earth, one should take into account the centrifugal force of inertia (F in), equal to:

where m is the mass of the body, r is the distance from the Earth’s axis. If the body is not located high from the surface of the Earth (in comparison with the radius of the Earth), then we can assume that

where R Z is the radius of the earth, is the latitude of the area.

In this case, the acceleration of free fall (g) relative to the Earth will be determined by the action of forces: the force of attraction to the Earth () and the force of inertia (). In this case, gravity is the resultant of these forces:

Since the force of gravity imparts to a body with mass m an acceleration equal to , then relation (1) is valid.

The difference between gravity and the force of attraction to the Earth is small. Because .

Like any force, gravity is a vector quantity. The direction of the force, for example, coincides with the direction of the thread stretched by the load, which is called the plumb direction. The force is directed towards the center of the Earth. This means that the plumb line is also directed only at the poles and the equator. At other latitudes, the angle of deviation () from the direction to the center of the Earth is equal to:

The difference between Fg -P is maximum at the equator, it is 0.3% of the magnitude of the force Fg. Since the globe is oblate near the poles, F g has some variations in latitude. So it is 0.2% less at the equator than at the poles. As a result, the acceleration g varies with latitude from 9.780 m/s 2 (equator) to 9.832 m/s 2 (poles).

With respect to the inertial reference frame (for example, heliocentric CO), a body in free fall will move with an acceleration (a) different from g, equal in magnitude:

and coinciding in direction with the direction of the force.

Units of gravity

The basic SI unit of gravity is: [P]=H

In GHS: [P]=din

Examples of problem solving

Example

Exercise. Determine how many times the force of gravity on Earth (P 1) is greater than the force of gravity on the Moon (P 2).

Solution. The gravity modulus is determined by the formula:

If we mean the force of gravity on Earth, then we use m/s^2 as the acceleration of gravity. To calculate the force of gravity on the Moon, using reference books we will find the acceleration of gravity on this planet; it is equal to 1.6 m/s^2.

Thus, to answer the question posed, one should find the relation:

Let's carry out the calculations:

Answer.

Example

Exercise. Obtain an expression that relates latitude and the angle formed by the gravity vector and the gravitational force vector towards the Earth.

Solution. The angle that is formed between the directions of the force of attraction to the Earth and the direction of gravity can be estimated by considering Fig. 1 and applying the sine theorem. Figure 1 shows: – the centrifugal force of inertia, which arises due to the rotation of the Earth around its axis, – the force of gravity, – the force of attraction of a body to the Earth. Angle is the latitude of an area on Earth.

Definition 1

The force of gravity is considered to be applied to the center of gravity of a body, determined by hanging the body by a thread from its various points. In this case, the point of intersection of all directions that are marked by the thread will be considered the center of gravity of the body.

Gravity concept

In physics, gravity is considered to be a force acting on any physical body located near the earth’s surface or another astronomical body. The force of gravity on the surface of the planet, by definition, will consist of the gravitational attraction of the planet, as well as the centrifugal force of inertia provoked by the daily rotation of the planet.

Other forces (for example, the attraction of the Sun and Moon) due to their smallness are not taken into account or are studied separately in the format of temporary changes in the Earth’s gravitational field. The force of gravity imparts equal acceleration to all bodies, regardless of their mass, while representing a conservative force. It is calculated based on the formula:

$\vec (P) = m\vec(g)$,

where $\vec(g)$ is the acceleration imparted to the body by gravity, designated as the acceleration of gravity.

In addition to gravity, bodies moving relative to the Earth's surface are also directly affected by the Coriolis force, which is a force used in studying the motion of a material point in relation to a rotating reference frame. Attaching the Coriolis force to the physical forces acting on a material point will make it possible to take into account the effect of rotation of the reference system on such motion.

Important formulas for calculation

According to the law of universal gravitation, the force of gravitational attraction acting on a material point with its mass $m$ on the surface of an astronomical spherically symmetric body with mass $M$ will be determined by the relation:

$F=(G)\frac(Mm)(R^2)$, where:

$G$-gravitational constant,
$R$ is the radius of the body.

This relationship turns out to be valid if we assume a spherically symmetric distribution of mass over the volume of the body. Then the force of gravitational attraction is directed directly to the center of the body.

The modulus of the centrifugal inertial force $Q$ acting on a material particle is expressed by the formula:

$Q = maw^2$, where:

$a$ is the distance between the particle and the axis of rotation of the astronomical body that is being considered,
$w$ is the angular velocity of its rotation. In this case, the centrifugal force of inertia becomes perpendicular to the axis of rotation and directed away from it.

In vector format, the expression for the centrifugal force of inertia is written as follows:

$\vec(Q) = (mw^2\vec(R_0))$, where:

$\vec (R_0)$ is a vector perpendicular to the axis of rotation, which is drawn from it to the specified material point located near the surface of the Earth.

In this case, the force of gravity $\vec (P)$ will be equivalent to the sum of $\vec (F)$ and $\vec (Q)$:

$\vec(P) = \vec(F) = \vec(Q)$

Law of Attraction

Without the presence of gravity, the origin of many things that now seem natural to us would be impossible: for example, there would be no avalanches coming down from the mountains, river flows, or rains. The Earth's atmosphere can be maintained solely by gravity. Planets with a lower mass, for example, the Moon or Mercury, lost their entire atmosphere at a fairly rapid pace and became defenseless against streams of aggressive cosmic radiation.

The Earth's atmosphere played a decisive role in the process of formation of life on Earth, its. In addition to gravity, the Earth is also affected by the gravitational force of the Moon. Due to its close proximity (on a cosmic scale), ebb and flow of tides is possible on Earth, and many biological rhythms coincide with the lunar calendar. Gravity, therefore, must be viewed as a useful and important law of nature.

Note 2

The law of attraction is considered universal and can be applied to any two bodies that have a certain mass.

In a situation where the mass of one interacting body turns out to be much greater than the mass of the second, we speak of a special case of gravitational force, for which there is a special term, such as “gravity”. It is applicable to problems focused on determining the force of gravity on Earth or other celestial bodies. When substituting the value of gravity into the formula of Newton's second law, we get:

Here $a$ is the acceleration of gravity, forcing the bodies to strive towards each other. In problems involving the use of gravity acceleration, such acceleration is denoted by the letter $g$. Using his own integral calculus, Newton was able to mathematically prove the constant concentration of gravity in the center of a larger body.

It is necessary to know the point of application and direction of each force. It is important to be able to determine exactly what forces act on the body and in what direction. Force is denoted as , measured in Newtons. In order to distinguish between forces, they are designated as follows

Below are the main forces operating in nature. It is impossible to invent forces that do not exist when solving problems!

There are many forces in nature. Here we consider the forces that are considered in the school physics course when studying dynamics. Other forces are also mentioned, which will be discussed in other sections.

Gravity

Every body on the planet is affected by 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. Gravity always directed vertically downwards.

Friction force

Let's get acquainted with the force of friction. This force occurs when bodies move and two surfaces come into contact. The force occurs because surfaces, when viewed under a microscope, are not as smooth as they appear. The friction force is determined by the formula:

The force is applied at the point of contact of two surfaces. Directed in the direction opposite to movement.

Ground reaction force

Let's imagine a very heavy object lying on a table. The table bends under the weight of the object. But according to Newton's third law, the table acts on the object with exactly the same force as the object on the table. The force is directed opposite to the force with which the object presses on the table. That is, up. This force is called the ground reaction. The name of the force "speaks" support reacts. This force occurs whenever there is an impact on the support. The nature of its occurrence at the molecular level. The object seemed to deform the usual position and connections of the molecules (inside the table), they, in turn, strive to return to their original state, “resist.”

Absolutely any body, even a very light one (for example, a pencil lying on a table), deforms the support at the micro level. Therefore, a ground reaction occurs.

There is no special formula for finding this force. It is denoted by the letter , but this force is simply a separate type of elasticity force, so it can also be denoted as

The force is applied at the point of contact of the object with the support. Directed perpendicular to the support.

Since we represent the body as a material point, force can be represented from the center

Elastic force

This force arises as a result of deformation (change in the initial state of the substance). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress a spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.

Hooke's law

The elastic force is directed opposite to the deformation.

Since we represent the body as a material point, force can be represented from the center

When connecting springs in series, for example, the stiffness is calculated using the formula

When connected in parallel, the stiffness

Sample stiffness. Young's modulus.

Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material and its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.

Body weight

Body weight is the force with which an object acts on a support. You say, this is the force of gravity! The confusion occurs in the following: indeed, often the weight of a body is equal to the force of gravity, but these forces are completely different. Gravity is a force that arises as a result of interaction with the Earth. Weight is the result of interaction with support. The force of gravity is applied at the center of gravity of the object, while weight is the force that is applied to the support (not to the object)!

There is no formula for determining weight. This force is designated by the letter.

The support reaction force or elastic force arises in response to the impact of an object on the suspension or support, therefore the weight of the body is always numerically the same as the elastic force, but has the opposite direction.

The support reaction force and weight are forces of the same nature; according to Newton's 3rd law, they are equal and oppositely directed. Weight is a force that acts on the support, not on the body. The force of gravity acts on the body.

Body weight may not be equal to gravity. It may be more or less, or it may be that the weight is zero. This condition is called weightlessness. Weightlessness is a state when an object does not interact with a support, for example, the state of flight: there is gravity, but the weight is zero!

It is possible to determine the direction of acceleration if you determine where the resultant force is directed

Please note that weight is force, measured in Newtons. How to correctly answer the question: “How much do you weigh”? We answer 50 kg, not naming our weight, but our mass! In this example, our weight is equal to gravity, that is, approximately 500N!

Overload- ratio of weight to gravity

Archimedes' force

Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upward (pushes). Determined by the formula:

In the air we neglect the power of Archimedes.

If the Archimedes force is equal to the force of gravity, the body floats. If the Archimedes force is greater, then it rises to the surface of the liquid; if it is less, it sinks.

Electrical forces

There are forces of electrical origin. Occurs in the presence of an electrical charge. These forces, such as the Coulomb force, Ampere force, Lorentz force, are discussed in detail in the section Electricity.

Schematic designation of forces acting on a body

Often a body is modeled as a material point. Therefore, in diagrams, various points of application are transferred to one point - to the center, and the body is depicted schematically as a circle or rectangle.

In order to correctly designate forces, it is necessary to list all the bodies with which the body under study interacts. Determine what happens as a result of interaction with each: friction, deformation, attraction, or maybe repulsion. Determine the type of force and correctly indicate the direction. Attention! The amount of forces will coincide with the number of bodies with which the interaction occurs.

The main thing to remember

1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces

There are external (dry) and internal (viscous) friction. External friction occurs between contacting solid surfaces, internal friction occurs between layers of liquid or gas during their relative motion. There are three types of external friction: static friction, sliding friction and rolling friction.

Rolling friction is determined by the formula

The resistance force occurs when a body moves in a liquid or gas. The magnitude of the resistance force depends on the size and shape of the body, the speed of its movement and the properties of the liquid or gas. At low speeds of movement, the drag force is proportional to the speed of the body

At high speeds it is proportional to the square of the speed

Let's consider the mutual attraction of an object and the Earth. Between them, according to the law of gravity, a force arises

Now let's compare the law of gravity and the force of gravity

The magnitude of the acceleration due to gravity depends on the mass of the Earth and its radius! Thus, it is possible to calculate with what acceleration objects on the Moon or on any other planet will fall, using the mass and radius of that planet.

The distance from the center of the Earth to the poles is less than to the equator. Therefore, the acceleration of gravity at the equator is slightly less than at the poles. At the same time, it should be noted that the main reason for the dependence of the acceleration of gravity on the latitude of the area is the fact of the Earth’s rotation around its axis.

As we move away from the Earth's surface, the force of gravity and the acceleration of gravity change in inverse proportion to the square of the distance to the center of the Earth.