I didn't understand the physics lesson and don't know how to determine gravity!

Answer

Gravity is the property of bodies with mass to attract each other. Bodies that have mass are always attracted to each other. The attraction of bodies with very large masses on an astronomical scale creates significant forces that make the world the way we know it.

The force of gravity is the cause of the earth's gravity, which causes objects to fall towards it. Thanks to the force of gravity, the Moon revolves around the Earth, the Earth and other planets revolve around the Sun, solar system— around the center of the Galaxy.

In physics gravity- this is the force with which the body acts on a support or vertical suspension. This force is always directed vertically downwards.

F is the force with which the body acts. It is measured in newtons (N).
m is the mass (weight) of the body. Measured in kilograms (kg)
g is the acceleration due to gravity. It is measured in newtons divided by kilograms (N/kg). Its value is constant and on average over the earth's surface is 9.8 N/kg.

How to determine the force of attraction?

Example:

Let the mass of the suitcase be 15 kg, then to find the force of attraction of the suitcase to the Earth we will use the formula:

F= m*g = 15*9.8 = 147 N.

That is, the force of attraction of the suitcase is 147 newtons.

The value of g for planet Earth is not the same - at the equator it is 9.83 N/kg, and at the poles 9.78 N/kg. Therefore, we take the average value that we used for the calculation. Accurate values ​​for different regions of the planet are used in the aerospace industry, and they are also paid attention to in sports, when training athletes to participate in competitions in other countries.

Historical information: the famous English physicist Isaac Newton was the first to calculate g and derive the formula for gravity, or more precisely the formula for the force with which a body acts on other bodies. It is in his honor that the unit of measurement of force is named. There is a legend that Newton began to explore the issue of gravity after an apple fell on his head.

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 gravity (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).

In relation to the inertial frame of reference (for example, heliocentric CO), the body in free fall will move with 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 universal gravity, 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 crucial during the process of formation of life on Earth, it. In addition to gravity, the Earth is also affected by the gravitational force of the Moon. Due to its close proximity (in cosmic scale), ebbs and flows are 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.

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 designated 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 on 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, free fall accelerations in different areas globe differs 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 free fall is considered to be the same everywhere.

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

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.

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 acted upon by 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 the force of gravity acts on a body, and all other forces are mutually balanced, the body undergoes free fall. According to Newton's second law and formula F t =GMm/R 2 the gravitational acceleration module g is found by the formula

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

From formula (2.29) it follows that the acceleration of free fall 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 is clear 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 located in the gravitational field of the Earth, but not all bodies fall to the Earth. This is explained by the fact that the movement of many bodies is impeded by other bodies, for example supports, suspension threads, etc. Bodies that limit the movement of other bodies are called connections. Under the influence of gravity, the bonds are deformed and the reaction force of the deformed connection, according to Newton’s third law, balances the force of gravity.

The acceleration of gravity is affected by the rotation of the Earth. This influence is explained as follows. The reference systems associated with the Earth's surface (except for the two associated with the Earth's poles) are not, strictly speaking, inertial reference systems - the Earth rotates around its axis, and together with it such reference systems move in circles with centripetal acceleration. This non-inertiality of reference systems is manifested, in particular, in the fact that the value of the acceleration of gravity turns out to be different in different places on the Earth and depends on the geographic latitude of the place where the reference system 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 acceleration due to gravity differ little from each other. Therefore, with not very accurate calculations, we can neglect the non-inertiality of the reference systems associated with the Earth’s surface, as well as the difference in the shape of the Earth from spherical, 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 gravitational acceleration modulus is determined by the formula

g=GM/(R+h) 2.

It has been established that at an altitude of 300 km above the Earth's surface, the acceleration of gravity is 1 m/s2 less than at the Earth's surface.
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, a 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 connection).

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

Р=F t=mg.

If the body moves at an accelerated rate, then its weight depends on the value of this acceleration and on its direction relative to the direction of the acceleration of gravity.

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

F t + F up =ma.

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

The forces Ft and Fup are directed along one vertical straight line. Therefore, if the acceleration of body a is directed downward (i.e., it coincides in direction with the acceleration of free fall g), then in modulus

P=m(g-a)

If the acceleration of the body is directed upward (i.e., opposite to the direction of the acceleration of free fall), 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 the acceleration of free fall is greater than the weight of a body at rest. An 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. freely falling), they are in a state weightlessness. A characteristic feature of this state is the absence of deformations and internal stresses, 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).