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. 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. In law gravity 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 \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 acceleration module free fall 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 free fall acceleration turns out to be different in different places Earth and depends on geographical latitude the place where the reference frame associated with the Earth is located, relative to which the acceleration of free fall 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, causing 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. characteristic feature this state is the absence of deformations in freely falling bodies and internal stresses, which are caused in resting bodies by gravity. 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).
Gravity is the force with which a body is attracted to the Earth due to universal gravitation. Gravity causes all bodies that are not acted upon by other forces to move downward with the acceleration of free fall, g. All bodies in the Universe are attracted to each other, and the greater their mass and the closer they are located, the stronger the attraction. To calculate the force of gravity, the mass of the body should be multiplied by a factor, denoted by the letter g, approximately equal to 9.8 N / kg. Thus, gravity is calculated by the formula
The force of gravity is approximately equal to the force of gravitational attraction to the Earth (the difference between the force of gravity and the gravitational force is due to the fact that the reference frame associated with the Earth is not completely inertial).
Friction force.
Friction force - The force that occurs at the point of contact of bodies and prevents their relative movement. The direction of the friction force is opposite to the direction of motion.
Distinguish between static friction force and sliding friction force. If the body slides on any surface, its movement is hindered by sliding friction force.
, where N— support reaction force, a μ is the coefficient of sliding friction. Coefficient μ depends on the material and quality of processing of the contacting surfaces and does not depend on body weight. The coefficient of friction is determined empirically.
The force of sliding friction is always directed opposite to the motion of the body. When the direction of speed changes, the direction of the friction force also changes.
The force of friction begins to act on the body when they try to move it. If an external force F less product μN, then the body will not move - the beginning of the movement, as they say, is hindered by the rest friction force . The body will start moving only when an external force F exceeds the maximum value that the static friction force can have
Friction of rest - frictional force that prevents the movement of one body on the surface of another. In some cases, friction is useful (without friction it would be impossible for a person, animals to walk on the ground, move cars, trains, etc.), in such cases, friction is increased. But in other cases, friction is harmful. For example, because of it, the rubbing parts of mechanisms wear out, excess fuel is consumed in transport, etc. Then friction is fought by applying lubrication or replacing sliding with pitching.
Friction forces do not depend on the coordinates of the relative position of the bodies, they can depend on the speed of the relative motion of the bodies in contact. Friction forces are non-potential forces.
Weight and weightlessness.
Weight - the force of the body's impact on the support (or suspension or other type of attachment) that prevents falling, arising in the field of gravity. In this case, the resulting elastic forces begin to act on the body with the resulting P directed upwards, and the sum of the forces applied to the body becomes equal to zero.
The force of gravity is directly proportional to the mass of the body and depends on the acceleration of free fall, which is maximum at the poles of the Earth and gradually decreases when moving towards the equator. The flattened shape of the Earth at the poles and its rotation around its axis lead to the fact that at the equator the acceleration of free fall is approximately 0.5% less than at the poles. Therefore, the weight of a body measured with a spring balance will be less at the equator than at the poles. Body weight on Earth can vary greatly wide range and sometimes even disappear.
For example, in a falling elevator, our weight will be 0, and we will be in a state of weightlessness. However, the state of weightlessness can be not only in the cabin of a falling elevator, but also on a space station revolving around the Earth. Rotating in a circle, the satellite moves with centripetal acceleration, and the only force that can give it this acceleration is gravity. Therefore, together with the satellite, revolving around the Earth, we move with an acceleration a = g, directed towards its center. And if we, being on the satellite, stood on the spring scales, then P = 0. Thus, on the satellite, the weight of all bodies zero.
It is necessary to know the point of application and the 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 acting in nature. It is impossible to invent non-existent forces 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 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. Gravity always pointing vertically down.
Friction force
Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises as a result of the fact that the surfaces, when viewed under a microscope, are not smooth as they seem. The friction force is determined by the formula:
A force is applied at the point of contact between two surfaces. Directed in the direction opposite to the movement.
Support reaction force
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 support reaction. The name of the force "speaks" react support. This force arises whenever there is an impact on the support. The nature of its occurrence at the molecular level. The object, as it were, deformed the usual position and connections of the molecules (inside the table), they, in turn, tend 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 support reaction occurs.
There is no special formula for finding this force. They designate it with the letter, but this force is just a separate type of elastic 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 the body is represented as a material point, the force can be depicted from the center
Elastic force
This force arises as a result of deformation (changes in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the 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 the body is represented as a material point, the force can be depicted from the center
When connected in series, for example, springs, the stiffness is calculated by 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, its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.
More about properties solids.
Body weight
Body weight is the force with which an object acts on a support. You say it's gravity! The confusion occurs in the following: indeed often body weight equal to strength gravity, but these are completely different forces. Gravity is the force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!
There is no formula for determining weight. This force is denoted by the letter .
The support reaction force or elastic force arises in response to the impact of an object on a suspension or support, therefore the body weight is always numerically the same as the elastic force, but has the opposite direction.
The reaction force of the support and the 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 a support, not on a body. The force of gravity acts on the body.
Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state 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
Note that weight is a force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not weight, but our mass! In this example, our weight is equal to gravity, which is approximately 500N!
Overload- the ratio of weight to gravity
Strength of Archimedes
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 upwards (pushes). Determined by the formula:
In the air, we neglect the force 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 when there is electric charge. These forces, such as the Coulomb force, Ampère force, Lorentz force, are discussed in detail in the Electricity section.
Schematic designation of the forces acting on the body
Often the body is modeled by a material point. Therefore, in the diagrams, various points of application are transferred to one point - to the center, and the body is schematically depicted as a circle or rectangle.
In order to correctly designate the 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, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.
The main thing to remember
1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces
Distinguish between external (dry) and internal (viscous) friction. External friction occurs between solid surfaces in contact, 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 arises 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, the resistance force is proportional to the speed of the body
At high speeds it is proportional to the square of the speed
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 value of free fall acceleration 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 free fall 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 free fall on the latitude of the area is the fact that the Earth rotates around its axis.
When moving away from the surface of the Earth, the force of gravity and the acceleration of free fall change inversely with the square of the distance to the center of the Earth.
Why does a ball thrown in a horizontal direction (Fig. 28) end up on the ground after a while? Why does a stone released from the hands (Fig. 29) fall down? Why does a person jumping up soon find himself down again? All these phenomena have the same reason - the attraction of the Earth. 
The earth attracts all bodies to itself: people, trees, water, houses, the moon, etc.
The force of gravity towards the earth is called gravity. The force of gravity is always directed vertically downwards. It is designated as follows:
F T- gravity.
When a body falls down under the influence of attraction to the Earth, it is affected not only by the Earth, but also by air resistance. In cases where the force of air resistance is negligible compared to the force of gravity, the fall of the body is called free.
For observation free fall various bodies (for example, pellets, feathers, etc.), they are placed in a glass tube (Newton's tube), from which air is pumped out. If at first all these objects are at the bottom of the tube, then after it is quickly turned over, they are on top, after which they begin to fall down (Fig. 30). Watching them fall, you can see that both the lead pellet and the light feather reach the bottom of the tube at the same time. Going beyond same time the same path, these bodies hit the bottom with the same speed. This happens because gravity has the following remarkable property: for every second it increases the speed of any freely falling body (regardless of its mass) always by the same amount.
Measurements show that near the surface of the Earth, the speed of any freely falling body increases by 9.8 m/s for every second of fall. This value is denoted by the letter g and call free fall acceleration.
Knowing the acceleration of free fall, you can find the force with which the Earth attracts any body located near it to itself.
To determine the force of gravity acting on a body, it is necessary to multiply the mass of this body by the acceleration of free fall:
F T = mg.
From this formula it follows that g = F T /m. But F T measured in newtons, a m- in kilograms. Therefore, the value g can be measured in newtons per kilogram:
g= 9.8 N/kg ≈10 N/kg.
As the height above the Earth increases, the free fall acceleration gradually decreases. For example, at an altitude of 297 km it turns out to be not 9.8 N/kg, but 9 N/kg. The decrease in free fall acceleration means that the force of gravity also decreases as the height above the Earth increases. The farther the body is from the Earth, the weaker it attracts it.
1. What causes all bodies to fall to the ground? 2. What force is called gravity? 3. In what case is the fall of a body called free? 4. What is the free fall acceleration near the Earth's surface? 5. What is the formula for gravity? 6. What will happen to the force of gravity, acceleration and time of fall if the mass of the falling body doubles? 7. How do gravity and free fall acceleration change with distance from the Earth?
Experimental tasks. 1. Pick up a piece of paper and release it. Watch him fall. Now crumple this sheet and release again. How will the nature of his fall change? Why? 2. Take a metal circle (for example, a coin) in one hand, and a slightly smaller paper circle in the other. Release them at the same time. Will they fall at the same time? Now take a metal circle in your hand and put a paper circle on top of it (Fig. 31). Release the mugs. Why are they falling at the same time now?
Definition 1
The force of gravity is considered to be applied to the body's center of gravity, determined by suspending the body from a thread at its various points. In this case, the point of intersection of all directions that are marked by a thread will be considered the center of gravity of the body.
The concept of gravity
Gravity in physics is the force acting on any physical body that is near the earth's surface or another astronomical body. The force of gravity on the planet's surface, by definition, will be the sum 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 the Moon), due to their smallness, are not taken into account or are studied separately in the format of temporal changes in the Earth's gravitational field. 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, denoted as the free fall acceleration.
In addition to gravity, bodies moving relative to the Earth's surface are also directly affected by the Coriolis force, which is the force used in studying the motion of a material point with respect to a rotating frame of reference. Attaching the Coriolis force to the physical forces acting on a material point will allow us to take into account the effect of the rotation of the frame of reference on such a movement.
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 symmetrical body with mass $M$ will be determined by the relation:
$F=(G)\frac(Mm)(R^2)$, where:
- $G$ is the gravitational constant,
- $R$ - body radius.
This relation turns out to be valid if we assume a spherically symmetric mass distribution 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 force of inertia $Q$ 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:
$\vec (R_0)$ - 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: thus, there would be no avalanches coming down from the mountains, no rivers, no rains. The Earth's atmosphere can only be maintained by the force of gravity. Planets with less mass, such as the Moon or Mercury, lost their entire atmosphere at a rather rapid pace and became defenseless against aggressive cosmic radiation.
The atmosphere of the Earth played a decisive role in the process of formation of life on Earth, her. In addition to gravity, Earth is also affected by the moon's gravity. Due to its close proximity (on a cosmic scale), the existence of ebb and flow is possible on Earth, and many biological rhythms are consistent with lunar calendar. Gravity, therefore, must be viewed in terms of a useful and important law of nature.
Remark 2
The law of attraction is considered universal and can be applied to any two bodies with a certain mass.
In a situation where the mass of one interacting body is much greater than the mass of the second, we speak of a special case gravitational force, for which there is a special term such as "gravity". It is applicable to tasks focused on determining the force of attraction on the 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 tend towards each other. In problems involving the use of free fall acceleration, this acceleration is denoted by the letter $g$. With the help of his own integral calculus, Newton mathematically managed to prove the constant concentration of gravity in the center of a larger body.