What is meant by external forces? External and internal forces acting on the athlete. Their definition and meaning. Law on the conservation of motion of the center of mass of a system

By force is called a measure of the mechanical interaction of material bodies.

Force F- vector quantity and its effect on the body is determined:

• module or numerical value forces (F);
• direction strength (ortom e);
• point of application forces (point A).

The straight line AB along which the force is directed is called the line of action of the force.

The strength can be set:

• geometrically, that is, as a vector with a known module F and a known direction determined by the unit vector e ;
• analytically, that is, its projections F x, F y, F z on the axes of the selected coordinate system Oxyz.

The force application point A must be specified by its coordinates x, y, z.

Force projections are related to its modulus and direction cosines(cosines of angles , , , which the force forms with the coordinate axes Ox, Oy, Oz) with the following relations:

F=(F x 2 +F y 2 +F x 2) ; e x =cos =F x /F; e y =cos =F y /F; e z =cos =F z /F;

Strength F, acting on an absolutely rigid body, can be considered applied to any point on the line of action of the force (such a vector is called sliding). If a force acts on a solid deformable body, then its point of application cannot be transferred, since with such transfer the internal forces in the body change (this vector is called attached).

The SI unit of force is newton (N); A larger unit of 1kN=1000N is also used.

Material bodies can act on each other through direct contact or at a distance. Depending on this, forces can be divided into two categories:

• superficial forces applied to the surface of the body (for example, pressure forces on the body from the side environment);
• volumetric (mass) forces applied to a given part of the body volume (for example, gravitational forces).

Surface and volumetric forces are called distributed forces. In some cases, forces can be considered distributed along a certain curve (for example, the weight forces of a thin rod). Distributed forces are characterized by their intensity (density), that is, the total amount of force per unit length, area or volume. The intensity can be constant ( evenly distributed force) or variable value.

If the small dimensions of the area of ​​action of distributed forces can be neglected, then we consider concentrated force applied to a body at one point (a conditional concept, since it is practically impossible to apply force to one point of the body).

The forces applied to the body under consideration can be divided into external and internal. External are the forces that act on this body from other bodies, and internal are the forces with which the parts of this body interact with each other.

If the movement of a given body in space is limited by other bodies, then it is called unfree. Bodies that limit the movement of a given body are called connections.

Axiom of connections: connections can be mentally discarded and the body considered free if the action of connections on the body is replaced by corresponding forces, which are called reactions of connections.

The reactions of bonds are different in nature from all other forces applied to the body that are not reactions, which are usually called active forces. This difference is that the reaction of the bond is not completely determined by the bond itself. Its magnitude, and sometimes direction, depend on the active forces acting on given body, which are usually known in advance and do not depend on other forces applied to the body. In addition, active forces, acting on a body at rest, can impart to it one or another movement; bond reactions do not have this property, which is why they are also called passive forces.

4. Method of Sections. Internal power factors.
To determine and subsequently calculate additional forces in any section of a beam, we use the method of sections. The essence of the section method is that the beam is mentally cut across into two parts and the equilibrium of any of them is considered, which is under the influence of all external and internal forces attached to this part. Being internal forces for the whole body, they play the role of external forces for the selected part.

Let the body be in equilibrium under the influence of forces: (Figure 5.1, a). Let's cut it with a plane S and discard the right side (Figure 5.1, b). The law of distribution of internal forces over a cross section is, in the general case, unknown. To find it in each specific situation, it is necessary to know how the body in question is deformed under the influence of external forces.

Thus, the section method makes it possible to determine only the sum of internal forces. Based on the hypothesis of a continuous structure of the material, we can assume that the internal forces at all points of a particular section represent a distributed load.

Let us reduce the system of internal forces at the center of gravity to the main vector and the main moment (Figure 5.1, c). Having projected and on the coordinate axis, we obtain a general picture of the stress-strain state of the beam section under consideration (Figure 5.1, d).

5. Axial tension - compression

Under stretching (compression) understand this type of loading in which only longitudinal forces arise in the cross sections of the rod, and other force factors are equal to zero.

Longitudinal force– internal force equal to the sum of the projections of all external forces, taken from one side of the section, to the axis of the rod. Let's accept the following sign rule for longitudinal force : tensile longitudinal force is positive, compressive force is negative

Forces acting on any point mechanical system, are divided into internal and external.

Fi– inner strength

Fe– external force

Internal are called the forces with which the points included in the system act on each other.

External are called forces that are applied to points from the outside, that is, from other points or bodies not included in the system. The division of forces into internal and external is conditional.

mg – external force

Ftr – internal strength

Mechanical system. External and internal forces.

A mechanical system of material points or bodies is a collection of them in which the position or movement of each point (or body) depends on the position and movement of all the others.

We will also consider a material absolutely solid body as a system of material points that form this body and are interconnected in such a way that the distances between them do not change and remain constant all the time.

A classic example of a mechanical system is the solar system, in which all bodies are connected by forces of mutual attraction. Another example of a mechanical system is any machine or mechanism in which all the bodies are connected by hinges, rods, cables, belts, etc. (i.e. various geometric connections). In this case, the bodies of the system are subject to mutual pressure or tension forces transmitted through connections.

A collection of bodies between which there are no interaction forces (for example, a group of airplanes flying in the air) does not form a mechanical system.

In accordance with what has been said, the forces acting on points or bodies of the system can be divided into external and internal.

External forces are those acting on points of a system from points or bodies that are not part of the given system.

Internal forces are those acting on points of a system from other points or bodies of the same system. We will denote external forces by the symbol - , and internal forces by - .

Both external and internal forces can, in turn, be either active or reactions of connections.

Reactions of connections, or simply reactions, are forces that limit the movement of points in the system (their coordinates, speed, etc.). In statics these were forces replacing connections. In dynamics, a more general definition is introduced for them.

All other forces are called active or given forces, everything except reactions.

The necessity of this classification of forces will become clear in the following chapters.

The division of forces into external and internal is conditional and depends on the movement of which system of bodies we are considering. For example, if we consider the movement of the entire solar system in general, the force of attraction of the Earth to the Sun will be internal; when studying the movement of the Earth in its orbit around the Sun, the same force will be considered as external.

Internal forces have the following properties:

1. The geometric sum (principal vector) of all internal forces F12 and F21 of the system is equal to zero. In fact, according to the third law of dynamics, any two points of the system (Fig. 31) act on each other with equal magnitude and oppositely directed forces and, the sum of which is equal to zero. Since a similar result holds for any pair of points in the system, then

2. Sum of moments ( main point) of all internal forces of the system relative to any center or axis is equal to zero. Indeed, if we take an arbitrary center O, then from Fig. 18 it is clear that . A similar result will be obtained when calculating the moments about the axis. Therefore, for the entire system there will be:

However, it does not follow from the proven properties that the internal forces are mutually balanced and do not affect the movement of the system, since these forces are applied to different material points or bodies and can cause mutual movements of these points or bodies. The internal forces will be balanced when the system under consideration is an absolutely rigid body.

30Theorem on the motion of the center of mass.

System weight equals the algebraic sum of the masses of all points or bodies of the system in a uniform gravitational field, for which the weight of any particle of the body is proportional to its mass. Therefore, the distribution of masses in a body can be determined by the position of its center of gravity - geometric point C, the coordinates of which are called the center of mass or center of inertia of a mechanical system

Theorem on the motion of the center of mass of a mechanical system : the center of mass of a mechanical system moves as a material point, the mass of which is equal to the mass of the system, and to which all external forces acting on the system are applied

Conclusions:

A mechanical system or a rigid body can be considered as a material point depending on the nature of its motion, and not on its size.

Internal forces are not taken into account by the theorem on the motion of the center of mass.

The theorem on the motion of the center of mass does not characterize rotational movement mechanical system, but only translational

Law on the conservation of motion of the center of mass of the system:

1. If the sum of external forces (the main vector) is constantly equal to zero, then the center of mass of the mechanical system is at rest or moves uniformly and rectilinearly.

2. If the sum of the projections of all external forces onto any axis is equal to zero, then the projection of the velocity of the center of mass of the system onto the same axis is a constant value.

The equation expresses the theorem on the motion of the center of mass of the system: the product of the mass of the system and the acceleration of its center of mass is equal to geometric sum all external forces acting on the system. Comparing with the equation of motion material point, we obtain another expression of the theorem: the center of mass of the system moves as a material point, the mass of which is equal to the mass of the entire system and to which all external forces acting on the system are applied.

If expression (2) is placed in (3), taking into account the fact that we get:

(4’) – expresses the theorem on the movement of the center of mass of the system: the center of mass of the system moves as a material point on which all the forces of the system act.

Conclusions:

1. Internal forces do not affect the movement of the center of mass of the system.

2. If , the movement of the center of mass of the system occurs at a constant speed.

3., then the movement of the center of mass of the system in projection onto the axis occurs at a constant speed.

These equations are differential equations movements of the center of mass in projections on the axes of the Cartesian coordinate system.

The meaning of the proven theorem is as follows.

1) The theorem provides justification for the methods of point dynamics. From the equations it is clear that the solutions that we obtain by considering a given body as a material point determine the law of motion of the center of mass of this body, i.e. have a very specific meaning.

In particular, if a body moves translationally, then its movement is completely determined by the movement of the center of mass. Thus, a translationally moving body can always be considered as a material point with a mass equal to the mass of the body. In other cases, a body can be considered as a material point only when, practically, to determine the position of the body it is enough to know the position of its center of mass.

2) The theorem allows, when determining the law of motion of the center of mass of any system, to exclude from consideration all previously unknown internal forces. This is its practical value.

So the movement of the car horizontal plane can only occur under the influence of external forces, friction forces acting on the wheels from the road. And braking a car is also possible only with these forces, and not with friction between the brake pads and the brake drum. If the road is smooth, then no matter how much you brake the wheels, they will slide and will not stop the car.

Or after the explosion of a flying projectile (under the influence of internal forces), its parts, fragments, will scatter so that their center of mass will move along the same trajectory.

The theorem on the motion of the center of mass of a mechanical system should be used to solve problems of mechanics that require:

Using the forces applied to a mechanical system (most often to a solid body), determine the law of motion of the center of mass;

According to the given law of motion of bodies included in a mechanical system, find the reactions of external connections;

Based on the given mutual motion of the bodies included in the mechanical system, determine the law of motion of these bodies relative to some fixed reference system.

Using this theorem, you can create one of the equations of motion of a mechanical system with several degrees of freedom.

When solving problems, corollaries from the theorem on the motion of the center of mass of a mechanical system are often used.

Corollary 1. If the main vector of external forces applied to a mechanical system is equal to zero, then the center of mass of the system is at rest or moves uniformly and rectilinearly. Since the acceleration of the center of mass is zero, .

Corollary 2. If the projection of the main vector of external forces onto any axis is zero, then the center of mass of the system either does not change its position relative to this axis or moves uniformly relative to it.

For example, if two forces begin to act on a body, forming a pair of forces (Fig. 38), then its center of mass C will move along the same trajectory. And the body itself will rotate around the center of mass. And it doesn’t matter where the couple of forces are applied.

Dynamic anatomy

ANALYSIS OF POSITIONS AND MOVEMENTS OF THE HUMAN BODY.

The main provisions of this theoretical course were developed by P.F. Lesgaft and was called “Course on the Theory of Bodily Movements”. This course included an analysis of the general laws of human structure, joint movement, and the position of the human body in space during movement.

Analysis of body positions in space involved the study of human movements in a certain sequence:

1. Morphology of movement or position- was based on a purely visual familiarization with the pose, the exercise that was supposed to be performed. At the same time, the position in space of the body and its individual parts - the head, torso, and limbs - was examined in detail.
2. Mechanics of body positions– at the same time, the exercise proposed for implementation was considered from the point of view of the laws of mechanics. And this presupposed mandatory familiarization with the forces that have an effect on the human body.

Any movement, exercise, or position of the body is carried out through the interaction of forces that act on the human body. These forces are divided into external and internal.

EXTERNAL FORCES– forces acting on a person from the outside, during his interaction with external bodies (earth, gymnastic equipment, any objects).

1. GRAVITY is the force with which a body is attracted to the ground. It is equal to the weight or mass of the body, applied to its center and directed vertically downward. The point of application of this force is the general center of gravity of the body - GCT. GCT consists of the centers of gravity of individual body segments.

When the body moves downward gravity is the driving force, those. helps movement;

When driving up– slows down movement (interferes);

When driving along horizontal– has a neutral effect.

2. GROUP REACTION FORCE is the force with which the support area acts on the body.

Moreover, if the body retains vertical position, then the support reaction force is equal to the force of gravity and directed opposite to it, i.e. . up.

When walking, running, or standing long jumps, the reaction force of the support will be directed at an angle to the area of ​​support and, according to the rule of parallelogram of forces, can be decomposed into vertical and horizontal components.

A. VERTICAL COMPONENT OF THE SUPPORT REACTION FORCE– directed upward, opposite to gravity (its mirror image).

B. HORIZONTAL COMPONENT (RESISTS FRICTION FORCE)– directed opposite to the direction of movement. Without friction, movement is impossible. Sometimes this strength is artificially increased - tartan coverings on treadmills.

3. POWER OF RESISTANCE TO THE EXTERNAL ENVIRONMENT- this force can either inhibit movement or promote it.

The braking influence of the environment can be reduced by adopting the most favorable (streamlined) body shape, and the drag force of the environment can be increased by increasing the repulsion surface (for swimmers - fins, for rowers - an oar blade).

4. FORCE OF INERTIA – force that occurs when a body moves with acceleration. Rational use of inertial force allows you to save muscle energy. This power may be centripetal, i.e. directed towards the center of rotation and centrifugal– directed from the center of rotation. These forces are opposite in direction. If they are equal, then the body remains at rest; if not, then the body moves towards the larger of them. For a runner, the force of the tailwind is the driving force, i.e. helps the movement, and the force of the headwind acts as a brake.

In mechanics external forces in relation to a given system of material points (i.e. such a set of material points in which the movement of each point depends on the positions or movements of all other points) those forces are called that represent the action on this system of other bodies (other systems of material points) that we did not include in this system. Internal forces are the forces of interaction between individual material points of a given system. The division of forces into external and internal is completely conditional: when the given composition of the system changes, some forces that were previously external can become internal, and vice versa. So, for example, when considering

the movement of a system consisting of the earth and its satellite the moon, the interaction forces between these bodies will be internal forces for this system, and the gravitational forces of the sun, the remaining planets, their satellites and all the stars will be external forces in relation to the specified system. But if we change the composition of the system and consider the movement of the sun and all the planets as the movement of one common system, then external the forces will be only the forces of attraction exerted by the stars; nevertheless, the forces of interaction between the planets, their satellites and the sun become internal forces for this system. In exactly the same way, if, when a steam locomotive is moving, we select the piston of the steam cylinder as separate system material points subject to our consideration, then the steam pressure on the piston in relation to it will be external force, and the same steam pressure will be one of the internal forces if we consider the movement of the entire locomotive as a whole; in this case, external forces in relation to the entire locomotive, taken as one system, will be: friction between the rails and wheels of the locomotive, gravity of the locomotive, reaction of the rails and air resistance; internal forces will be all the forces of interaction between parts of the locomotive, for example. interaction forces between steam and the cylinder piston, between the slider and its parallels, between the connecting rod and the crank pin, etc. As we see, there is essentially no difference between external and internal forces, but the relative difference between them is determined only depending on which bodies we include in the system under consideration and which we consider not included in the system. However, the indicated relative difference in forces is very significant when studying the motion of a given system; according to Newton's third law (on the equality of action and reaction), the internal forces of interaction between each two material points of the system are equal in magnitude and directed along the same straight line in opposite sides; Thanks to this, when resolving various questions about the motion of a system of material points, it is possible to exclude all internal forces from the equations of motion of the system and thereby make possible the study of the motion of the entire system. This method of eliminating internal, in most cases unknown, coupling forces is essential in deriving various laws of mechanics of a system.

Absolutely elastic impact- a collision of two bodies, as a result of which no deformations remain in both bodies participating in the collision and all the kinetic energy of the bodies before the impact after the impact again turns into the original kinetic energy (note that this is an idealized case).

For an absolutely elastic impact, the law of conservation of kinetic energy and the law of conservation of momentum are satisfied.

Let us denote the velocities of the balls with masses m 1 and m 2 before impact through ν 1 And ν 2, after impact - through ν 1 " And ν 2"(Fig. 1). For a direct central impact, the velocity vectors of the balls before and after the impact lie on a straight line passing through their centers. The projections of the velocity vectors onto this line are equal to the velocity modules. We will take their directions into account using signs: positive ones will be associated with movement to the right, negative ones with movement to the left.

Fig.1

Under these assumptions, the conservation laws have the form

(1)

(2)

Having made the appropriate transformations in expressions (1) and (2), we obtain

(3)

(4)

Solving equations (3) and (5), we find

(7)

Let's look at a few examples.

1. When ν 2=0

(8)
(9)

Let us analyze expressions (8) in (9) for two balls of different masses:

a) m 1 = m 2. If the second ball was hanging motionless before the impact ( ν 2=0) (Fig. 2), then after the impact the first ball will stop ( ν 1 "=0), and the second one will move with the same speed and in the same direction in which the first ball was moving before the impact ( ν 2"=ν 1);

Fig.2

b) m 1 >m 2. The first ball continues to move in the same direction as before the impact, but at a lower speed ( ν 1 "<ν 1). The speed of the second ball after impact is greater than the speed of the first ball after impact ( ν 2">ν 1 ") (Fig. 3);

Fig.3

c) m 1 ν 2"<ν 1(Fig. 4);

Fig.4

d) m 2 >>m 1 (for example, a collision of a ball with a wall). From equations (8) and (9) it follows that ν 1 "= -ν 1; ν 2"≈ 2m 1 ν 2"/m 2 .

2. When m 1 =m 2 expressions (6) and (7) will have the form ν 1 "= ν 2; ν 2"= ν 1; that is, balls of equal mass seem to exchange velocities.

Absolutely inelastic impact- a collision of two bodies, as a result of which the bodies connect, moving further as a single whole. An absolutely inelastic impact can be demonstrated using plasticine (clay) balls that move towards each other (Fig. 5).

Fig.5

If the masses of the balls are m 1 and m 2, their velocities before impact ν 1 And ν 2, then, using the law of conservation of momentum

Where v- the speed of movement of the balls after impact. Then

(15.10)

If the balls move towards each other, they will together continue to move in the direction in which the ball moved with high momentum. In the particular case, if the masses of the balls are equal (m 1 =m 2), then

Let us determine how the kinetic energy of the balls changes during a central absolutely inelastic impact. Since during the collision of balls between them there are forces that depend on their velocities, and not on the deformations themselves, we are dealing with dissipative forces similar to friction forces, therefore the law of conservation of mechanical energy in this case should not be observed. Due to deformation, there is a decrease in kinetic energy, which turns into thermal or other forms of energy. This decrease can be determined by the difference in the kinetic energy of the bodies before and after the impact:

Using (10), we obtain

If the impacted body was initially motionless (ν 2 =0), then

When m 2 >>m 1 (the mass of the stationary body is very large), then ν <<ν 1 and practically all the kinetic energy of the body is converted into other forms of energy upon impact. Therefore, for example, to obtain significant deformation, the anvil must be significantly more massive than the hammer. On the contrary, when hammering nails into a wall, the mass of the hammer should be much greater (m 1 >>m 2), then ν≈ν 1 and almost all the energy is spent on moving the nail as much as possible, and not on residual deformation of the wall.

A completely inelastic impact is an example of the loss of mechanical energy under the influence of dissipative forces.

1. Work of variable force.
Let us consider a material point moving under the influence of force P in a straight line. If effective force is constant and directed along a straight line, and the displacement is equal to s, then, as is known from physics, the work A of this force is equal to the product Ps. Now let's derive a formula for calculating the work done by a variable force.

Let a point move along the Ox axis under the influence of a force, the projection of which onto the Ox axis is a function of f from x. In this case we will assume that f is continuous function. Under the influence of this force, the material point moved from point M (a) to point M (b) (Fig. 1, a). Let us show that in this case the work of A is calculated by the formula

(1)

Let's split the segment [a; b] into n segments of the same length. These are the segments [a; x 1 ], ,..., (Fig. 1.6). Work of force on the entire segment [a; b] is equal to the sum of the work done by this force on the resulting segments. Since f is a continuous function of x, for a sufficiently small segment [a; x 1 ] the work done by the force on this segment is approximately equal to f (a) (x 1 -a) (we neglect the fact that f changes on the segment). Similarly, the work done by the force on the second segment is approximately equal to f (x 1) (x 2 - x 1), etc.; the work done by the force on the nth segment is approximately equal to f (x n-1)(b - x n-1). Consequently, the work of force on the entire segment [a; b] is approximately equal to:

and the accuracy of the approximate equality is higher, the shorter the segments into which the segment [a;b] is divided. Naturally, this approximate equality becomes exact if we assume that n→∞:

Since A n tends to the integral of the function under consideration from a to b as n →∞, formula (1) is derived.
2. Power.

Power P is the rate of work done,

Here v is the speed of the material point to which the force is applied

All forces encountered in mechanics are usually divided into conservative and non-conservative.

A force acting on a material point is called conservative (potential) if the work done by this force depends only on the initial and final positions of the point. The work of a conservative force does not depend either on the type of trajectory or on the law of motion of a material point along a trajectory (see Fig. 2): .

Changing the direction of movement of a point along a small area to the opposite causes a change in sign basic work, hence, . Therefore, the work of a conservative force along a closed trajectory 1 a 2b 1 equals zero: .

Points 1 and 2, as well as sections of closed trajectory 1 a 2 and 2 b 1 can be chosen completely arbitrarily. Thus, the work of a conservative force along an arbitrary closed trajectory L of the point of its application is equal to zero:

In this formula, the circle on the integral sign shows that the integration is carried out along a closed path. Often a closed trajectory L called a closed loop L(Fig. 3). Usually specified by the direction of traversal of the contour L clockwise. The direction of the elementary displacement vector coincides with the direction of the contour traversal L. In this case, formula (5) states: circulation of the vector along a closed loop L is equal to zero.

It should be noted that the forces of gravity and elasticity are conservative, and the forces of friction are non-conservative. In fact, since the friction force is directed in the direction opposite to the displacement or speed, the work of the friction forces along a closed path is always negative and, therefore, not equal to zero.

Dissipative system(or dissipative structure, from lat. dissipatio- “disperse, destroy”) is an open system that operates far from thermodynamic equilibrium. In other words, this is a stable state that arises in a nonequilibrium environment under the condition of dissipation (dissipation) of energy that comes from outside. A dissipative system is sometimes also called stationary open system or nonequilibrium open system.

A dissipative system is characterized by the spontaneous appearance of a complex, often chaotic structure. Distinctive feature such systems - non-conservation of volume in phase space, that is, the failure of Liouville's Theorem.

A simple example Such a system is Benard cells. As more complex examples called lasers, the Belousov-Zhabotinsky reaction and biological life.

The term “dissipative structure” was introduced by Ilya Prigogine.

Latest Research in the field of “dissipative structures” allow us to conclude that the process of “self-organization” occurs much faster in the presence of external and internal “noise” in the system. Thus, noise effects lead to an acceleration of the “self-organization” process.

Kinetic energy

the energy of a mechanical system, depending on the speed of movement of its points. K. e. T material point is measured by half the product of mass m of this point by the square of its speed υ, i.e. T = 1/ 2 mυ 2 . K. e. mechanical system is equal to the arithmetic sum of K. e. all its points: T =Σ 1 / 2 m k υ 2 k . Expression K. e. systems can also be represented in the form T = 1 / 2 Mυ s 2 + Tc, Where M- mass of the entire system, υ c- speed of the center of mass, Tc - K. e. system in its motion around the center of mass. K. e. solid, moving translationally, is calculated in the same way as K. e. a point with mass equal to mass of the whole body. Formulas for calculating K. e. of a body rotating around a fixed axis, see Art. Rotational movement.

Change in K. e. system when it is moved from its position (configuration) 1 to position 2 occurs under the influence of external and internal forces applied to the system and is equal to the sum of work . This equality expresses the theorem on the change of the dynamic energy, with the help of which many problems of dynamics are solved.

At speeds close to the speed of light, K.e. material point

Where m 0- mass of a point at rest, With- speed of light in vacuum ( m 0 s 2- energy of a point at rest). At low speeds ( υ<< c ) the last relation goes into the usual formula 1 / 2 mυ 2.

Kinetic energy.

Kinetic energy - energy of a moving body. (From the Greek word kinema - movement). By definition, the kinetic energy of a body at rest in a given frame of reference vanishes.

Let the body move under the influence constant force in the direction of the force.

Then: .

Because motion is uniformly accelerated, then: .

Hence: .

- kinetic energy is called

It is necessary to know the point of application and direction of each force. It is important to be able to determine which 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 the body is represented 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 the body is represented 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.

Read more about properties of solids.

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 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.