see also "Physical Portal"

Force as a vector quantity is characterized module , direction and "point" of the application strength. By the last parameter, the concept of force as a vector in physics differs from the concept of a vector in vector algebra, where vectors equal in absolute value and direction, regardless of the point of their application, are considered the same vector. In physics, these vectors are called free vectors. In mechanics, the concept of bound vectors is extremely common, the beginning of which is fixed at a certain point in space or may be on a line that continues the direction of the vector (sliding vectors). .

The concept is also used line of force, denoting the straight line passing through the point of application of the force, along which the force is directed.

The dimension of force is LMT −2, the unit of measurement in the International System of Units (SI) is newton (N, N), in the CGS system - dyne.

History of the concept

The concept of force was used by scientists of antiquity in their works on statics and movement. He was engaged in the study of forces in the process of designing simple mechanisms in the III century. BC e. Archimedes. Aristotle's ideas of power, associated with fundamental inconsistencies, lasted for several centuries. These inconsistencies were eliminated in the 17th century. Isaac Newton using mathematical methods to describe force. Newtonian mechanics remained generally accepted for almost three hundred years. By the beginning of the XX century. Albert Einstein in the theory of relativity showed that Newtonian mechanics is correct only at relatively low speeds and masses of bodies in the system, thereby clarifying the basic provisions of kinematics and dynamics and describing some new properties of space-time.

Newtonian mechanics

Isaac Newton set out to describe the movement of objects using the concepts of inertia and force. Having done this, he established along the way that any mechanical motion is subject to general conservation laws. In Mr. Newton published his famous work "", in which he outlined the three fundamental laws of classical mechanics (the famous laws of Newton).

Newton's first law

For example, the laws of mechanics are exactly the same in the body of a truck when it is driving along a straight section of road at a constant speed and when it is standing still. A person can toss a ball vertically upwards and catch it after some time in the same place, regardless of whether the truck is moving evenly and rectilinearly or at rest. For him, the ball flies in a straight line. However, for an outside observer on the ground, the ball's trajectory looks like a parabola. This is due to the fact that the ball moves relative to the ground during the flight not only vertically, but also horizontally by inertia in the direction of the truck. For a person in the back of a truck, it does not matter whether the latter is moving along the road, or the world around is moving at a constant speed in the opposite direction, and the truck is standing still. Thus, the state of rest and uniform rectilinear motion are physically indistinguishable from each other.

Newton's second law

By definition of momentum:

where is the mass, is the speed.

If the mass of a material point remains unchanged, then the time derivative of the mass is zero, and the equation becomes:

Newton's third law

For any two bodies (let's call them body 1 and body 2), Newton's third law states that the force of the action of body 1 on body 2 is accompanied by the appearance of a force equal in absolute value, but opposite in direction, acting on body 1 from body 2. Mathematically, the law is written like this:

This law means that forces always arise in action-reaction pairs. If body 1 and body 2 are in the same system, then the total force in the system due to the interaction of these bodies is zero:

This means that there are no unbalanced internal forces in a closed system. This leads to the fact that the center of mass of a closed system (that is, one that is not affected by external forces) cannot move with acceleration. Separate parts of the system can accelerate, but only in such a way that the system as a whole remains in a state of rest or uniform rectilinear motion. However, if external forces act on the system, then its center of mass will begin to move with an acceleration proportional to the resulting external force and inversely proportional to the mass of the system.

Fundamental Interactions

All forces in nature are based on four types of fundamental interactions. The maximum speed of propagation of all types of interaction is equal to the speed of light in vacuum. Electromagnetic forces act between electrically charged bodies, gravitational forces act between massive objects. The strong and the weak appear only at very small distances and are responsible for the interaction between subatomic particles, including the nucleons that make up atomic nuclei.

The intensity of the strong and weak interactions is measured in units of energy(electron volts), not units of force, and therefore the application of the term “force” to them is explained by the tradition taken from antiquity to explain any phenomena in the world around us by the action of “forces” specific to each phenomenon.

The concept of force cannot be applied to the phenomena of the subatomic world. This is a concept from the arsenal of classical physics, associated (even if only subconsciously) with Newtonian ideas about forces acting at a distance. In subatomic physics, there are no such forces anymore: they are replaced by interactions between particles that occur through fields, that is, some other particles. Therefore, high energy physicists avoid using the word force, replacing it with the word interaction.

Each type of interaction is due to the exchange of the corresponding carriers of interaction: gravitational - the exchange of gravitons (existence has not been experimentally confirmed), electromagnetic - virtual photons, weak - vector bosons, strong - gluons (and at large distances - mesons). Currently, the electromagnetic and weak interactions are merged into the more fundamental electroweak interaction. Attempts are being made to combine all four fundamental interactions into one (the so-called grand unified theory).

The whole variety of forces manifesting themselves in nature can, in principle, be reduced to these four fundamental interactions. For example, friction is a manifestation of electromagnetic forces acting between atoms of two surfaces in contact, and the Pauli exclusion principle, which prevents atoms from penetrating into each other's area. The force that occurs when a spring deforms, described by Hooke's law, is also the result of electromagnetic forces between particles and the Pauli exclusion principle, forcing the atoms of the crystal lattice of a substance to be held near an equilibrium position. .

However, in practice it turns out not only inexpedient, but also simply impossible according to the conditions of the problem, such a detailed consideration of the issue of the action of forces.

gravity

Gravity ( gravity) - universal interaction between any kind of matter. Within the framework of classical mechanics, it is described by the law of universal gravitation, formulated by Isaac Newton in his work "The Mathematical Principles of Natural Philosophy". Newton obtained the magnitude of the acceleration with which the Moon moves around the Earth, assuming in the calculation that the gravitational force decreases inversely with the square of the distance from the gravitating body. In addition, he also found that the acceleration due to the attraction of one body by another is proportional to the product of the masses of these bodies. Based on these two conclusions, the law of gravity was formulated: any material particles are attracted towards each other with a force that is directly proportional to the product of the masses ( and ) and inversely proportional to the square of the distance between them:

Here is the gravitational constant, the value of which was first obtained in his experiments by Henry Cavendish. Using this law, one can obtain formulas for calculating the gravitational force of bodies of arbitrary shape. Newton's theory of gravitation describes well the motion of the planets of the solar system and many other celestial bodies. However, it is based on the concept of long-range action, which contradicts the theory of relativity. Therefore, the classical theory of gravity is not applicable to describe the motion of bodies moving at a speed close to the speed of light, the gravitational fields of extremely massive objects (for example, black holes), as well as variable gravitational fields created by moving bodies at large distances from them.

Electromagnetic interaction

Electrostatic field (field of fixed charges)

The development of physics after Newton added to the three main (length, mass, time) quantities an electric charge with the dimension C. However, based on the requirements of practice based on the convenience of measurement, an electric current with the dimension I was often used instead of charge, and I = CT − 1 . The unit of charge is the coulomb, and the unit of current is the ampere.

Since the charge, as such, does not exist independently of the body carrying it, the electrical interaction of the bodies manifests itself in the form of the same force considered in mechanics, which causes acceleration. As applied to the electrostatic interaction of two "point charges" in vacuum, Coulomb's law is used:

where is the distance between the charges, and ε 0 ≈ 8.854187817 10 −12 F/m. In a homogeneous (isotropic) substance in this system, the interaction force decreases by a factor of ε, where ε is the dielectric constant of the medium.

The direction of the force coincides with the line connecting the point charges. Graphically, an electrostatic field is usually depicted as a picture of lines of force, which are imaginary trajectories along which a charged particle devoid of mass would move. These lines start on one and end on the other charges.

Electromagnetic field (DC field)

The existence of a magnetic field was recognized back in the Middle Ages by the Chinese, who used the "loving stone" - a magnet, as a prototype of a magnetic compass. Graphically, the magnetic field is usually depicted as closed lines of force, the density of which (as in the case of an electrostatic field) determines its intensity. Historically, a visual way to visualize the magnetic field was iron filings, poured, for example, on a sheet of paper placed on a magnet.

Derived types of forces

Elastic force- the force arising from the deformation of the body and opposing this deformation. In the case of elastic deformations, it is potential. The elastic force has an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. The elastic force is directed opposite to the displacement, perpendicular to the surface. The force vector is opposite to the direction of displacement of molecules.

Friction force- the force arising from the relative motion of solid bodies and opposing this motion. Refers to dissipative forces. The friction force has an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. The friction force vector is directed opposite to the velocity vector.

Medium resistance force- the force arising from the movement of a solid body in a liquid or gaseous medium. Refers to dissipative forces. The resistance force has an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. The resistance force vector is directed opposite to the velocity vector.

Force of normal support reaction- the elastic force acting from the side of support on the body. Directed perpendicular to the surface of the support.

Surface tension forces- forces arising on the surface of the phase section. It has an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. The tension force is directed tangentially to the interface; arises due to the uncompensated attraction of molecules located at the phase boundary by molecules not located at the phase boundary.

Osmotic pressure

Van der Waals forces- electromagnetic intermolecular forces arising from the polarization of molecules and the formation of dipoles. Van der Waals forces decrease rapidly with increasing distance.

inertia force is a fictitious force introduced in non-inertial reference frames in order to fulfill Newton's second law in them. In particular, in the frame of reference associated with a uniformly accelerated body, the force of inertia is directed opposite to the acceleration. From the total inertial force, the centrifugal force and the Coriolis force can be distinguished for convenience.

Resultant

When calculating the acceleration of a body, all the forces acting on it are replaced by one force, called the resultant. This is the geometric sum of all the forces acting on the body. In this case, the action of each force does not depend on the action of others, that is, each force imparts to the body such an acceleration that it would impart in the absence of the action of other forces. This statement is called the principle of independence of action of forces (principle of superposition).

see also

Sources

• Grigoriev V. I., Myakishev G. Ya. - “Forces in nature”
• Landau, L. D., Lifshitz, E. M. Mechanics - 5th edition, stereotypical. - M .: Fizmatlit, 2004. - 224 p. - ("Theoretical Physics", Volume I). - .

Notes

1. Glossary. Earth Observatory. NASA. - "Force - any external factor that causes a change in the movement of a free body or the occurrence of internal stresses in a fixed body."(English)
2. Bronstein I. N. Semendyaev K. A. Handbook of mathematics. M .: Publishing house "Nauka" Editorial board of reference physical and mathematical literature. 1964.
3. Feynman, R. P., Leighton, R. B., Sands, M. Lectures on Physics, Vol 1 - Addison-Wesley, 1963.(English)

> Strength

Description forces in physics: term and definition, laws of force, measurement of units in Newtons, Newton's second law and formula, diagram of the impact of the force of an object.

Force- any action that leads to a change in the object in motion, direction or geometric structure.

Learning task

• Create a relationship between mass and acceleration.

Key Points

• Force is a vector concept that has magnitude and direction. This also applies to mass and acceleration.
• Simply put, force acts as a push or pull, which can be defined by various standards.
• Dynamics is the study of the force that causes objects or systems to move and deform.
• External forces are any external influences that affect the body, while internal forces act from within.

Terms

• Vector velocity is the rate of change of position in time and direction.
• Force is any action that causes an object to change in motion, direction, or geometric structure.
• A vector is a directed quantity characterized by magnitude and direction (between two points).

Example

To study force standards in physics, causes and results, use two rubber bands. Hang one on a hook in a vertical position. Find a small object and attach to the hanging end. Measure the resulting stretch with various objects. What is the relationship between the number of suspended objects and the length of the stretch? What will happen to the glued weight if you move the tape with a pencil?

Force Review

In physics, a force is any phenomenon that causes an object to go through changes in motion, direction, or geometric design. Measured in Newtons. A force is something that causes an object with mass to change its speed or deform. Force is also described in intuitive terms like "push" or "push." Has magnitude and direction (vector).

Characteristics

Newton's second law says that the net force acting on an object is equal to the rate at which its momentum changes. Also, the acceleration of an object is directly proportional to the force acting on it and is in the direction of the net force and inversely proportional to the mass.

Remember that force is a vector quantity. A vector is a one-dimensional array with magnitude and direction. It has mass and acceleration:

Also associated with force are thrust (increases the speed of an object), deceleration (decreases the speed), and torque (changes the speed). Forces that are not applied uniformly in all parts of the object also lead to mechanical stress (deform matter). If in a solid object it gradually deforms it, then in a liquid it changes pressure and volume.

Dynamics

It is the study of the forces that set objects and systems in motion. We understand force as a definite push or pull. They have magnitude and direction. In the figure, you can see several examples of the use of force. Top left - roller system. The force to be applied to the cable must equal and exceed the force generated by mass, objects, or the effects of gravity. Top right shows that any object placed on the surface will affect it. Below is the attraction of magnets.

1. Newton's laws of dynamics

the laws or axioms of motion (as formulated by Newton himself in his Principia Mathematica, 1687): “I. Every body continues to be held in its state of rest, or uniform and rectilinear motion, until and insofar as it is compelled by applied forces to change this state. II. The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts. III. An action always has an equal and opposite reaction, otherwise the interactions of two bodies against each other are equal and directed in opposite directions.

2. What is strength?

Force is characterized by magnitude and direction. Force characterizes the action of other bodies on a given body. The result of the action of a force on a body depends not only on its magnitude and direction, but also on the point of application of the force. The resultant is one force, the result of which will be the same as the result of the action of all real forces. If the forces are codirectional, the resultant is equal to their sum and directed in the same direction. If the forces are directed in opposite directions, then the resultant is equal to their difference and is directed towards the greater force.

Gravity and body weight

Gravity is the force with which a body is attracted to the Earth due to universal gravitation. 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 weight of the body is the force with which the body presses on the support or stretches the suspension due to attraction to the Earth. If the body has neither support nor suspension, then the body has no weight - it is in a state of weightlessness.

Elastic force

The elastic force is the force that occurs inside the body as a result of deformation and prevents the change in shape. Depending on how the shape of the body changes, several types of deformation are distinguished, in particular, tension and compression, bending, shear and shear, torsion.

The more the shape of the body is changed, the greater the elastic force that arises in it.

Dynamometer - a device for measuring force: the measured force is compared with the elastic force that occurs in the spring of the dynamometer.

Friction force

The static friction force is the force that prevents the body from moving.

The reason for the occurrence of friction is that any surfaces have irregularities that engage with each other. If the surfaces are polished, then the friction is caused by the forces of molecular interaction. When a body moves on a horizontal surface, the force of friction is directed against the motion and is directly proportional to the force of gravity:

The sliding friction force is the resistance force when one body slides over the surface of another. The rolling friction force is the drag force when one body rolls over the surface of another; it is much less than the force of sliding friction.

If friction is useful, it is increased; if harmful - reduce.

3. LAWS OF CONSERVATION

LAWS OF CONSERVATION, physical laws, according to which some property of a closed system remains unchanged with any changes in the system. The most important are laws of conservation of matter and energy. The law of conservation of matter states that matter is neither created nor destroyed; during chemical transformations, the total mass remains unchanged. The total amount of energy in the system also remains unchanged; energy is only transformed from one form to another. Both of these laws are only approximately true. Mass and energy can be converted into one another according to the equation E = ts 2. Only the total amount of mass and its equivalent energy remains unchanged. Another conservation law concerns electric charge: it cannot be created and cannot be destroyed either. As applied to nuclear processes, the conservation law is expressed in the fact that the total charge, spin and other QUANTUM NUMBERS of the interacting particles must remain the same for the particles resulting from the interaction. In strong interactions, all quantum numbers are conserved. With weak interactions, some of the requirements of this law are violated, especially with regard to PARITY.

The law of conservation of energy can be explained using the example of a 1 kg ball falling from a height of 100 m. The initial total energy of the ball is its potential energy. When it falls, the potential energy gradually decreases and the kinetic energy increases, but the total amount of energy remains unchanged. Thus, there is a conservation of energy. A - kinetic energy increases from 0 to maximum; B - potential energy decreases from maximum to zero; C - the total amount of energy, which is equal to the sum of the kinetic and poten The law of conservation of matter states that in the course of chemical reactions, matter is not created and does not disappear. This phenomenon can be demonstrated using the classic experiment in which a candle burning under a glass jar (A) is weighed. At the end of the experiment, the weight of the cap and its contents remains the same as at the beginning, although the candle, whose substance consists mainly of carbon and hydrogen, "disappeared" because volatile reaction products (water and carbon dioxide) were released from it. Only after scientists recognized the principle of conservation of matter at the end of the 18th century did a quantitative approach to chemistry become possible.

mechanical work occurs when a body moves under the action of a force applied to it.

Mechanical work is directly proportional to the distance traveled and proportional to the force:

Power

The speed of work in technology is characterized by power.

Power is equal to the ratio of work to the time for which it was done:

Energy is a physical quantity showing how much work a body can do. Energy is measured in joules.

When work is done, the energy of bodies is measured. The work done is equal to the change in energy.

Potential energy is determined by the mutual position of interacting bodies or parts of the same body.

E p \u003d F h \u003d gmh.

Where g \u003d 9.8 N / kg, m - body weight (kg), h - height (m).

Kinetic energy possesses the body as a result of its motion. The greater the mass of the body and the speed, the greater its kinetic energy.

5. the basic law of the dynamics of rotational motion

Moment of power

1. The moment of force about the axis of rotation, (1.1) where is the projection of the force onto a plane perpendicular to the axis of rotation, is the arm of the force (the shortest distance from the axis of rotation to the line of action of the force).

2. The moment of force relative to the fixed point O (the origin). (1.2) It is determined by the vector product of the radius-vector drawn from the point O to the point of application of the force, by this force; is a pseudovector, its direction coincides with the direction of the translational movement of the right screw during its rotation otk ("rule of the gimlet"). Modulus of the moment of force, (1.3) where is the angle between the vectors and, is the shoulder of the force, the shortest distance between the line of action of the force and the point of application of the force.

angular momentum

1. The angular momentum of a body rotating about the axis , (1.4) where is the moment of inertia of the body, is the angular velocity. The angular momentum of the system of bodies is the vector sum of the angular momentum of all bodies of the system: . (1.5)

2. The angular momentum of a material point with momentum relative to the fixed point O (the origin). (1.6) It is determined by the vector product of the radius-vector drawn from the point O to the material point and the momentum vector; is a pseudo-vector, its direction coincides with the direction of the translational motion of the right screw during its rotation otk ("rule of the gimlet"). Modulus of the angular momentum vector, (1.7)

Moment of inertia about the axis of rotation

1. The moment of inertia of a material point , (1.8) where is the mass of the point, is its distance from the axis of rotation.

2. Moment of inertia of a discrete rigid body , (1.9) where is the mass element of the rigid body; is the distance of this element from the axis of rotation; is the number of body elements.

3. Moment of inertia in case of continuous distribution of mass (solid solid body). (1.10) If the body is homogeneous, i.e. its density is the same throughout the volume, then the expression (1.11) is used, where and is the volume of the body.

1. Strength- vector physical quantity, which is a measure of the intensity of the impact on a given body other bodies, and fields . Attached to the massive body force is the cause of its change speed or occurrence in it deformations and stresses.

Force as a vector quantity is characterized module, direction and "point" of the application strength. By the last parameter, the concept of force as a vector in physics differs from the concept of a vector in vector algebra, where vectors equal in absolute value and direction, regardless of the point of their application, are considered the same vector. In physics, these vectors are called free vectors. In mechanics, the concept of connected vectors is extremely common, the beginning of which is fixed at a certain point in space or may be on a line that continues the direction of the vector (sliding vectors).

The concept is also used line of force, denoting the straight line passing through the point of application of the force, along which the force is directed.

Newton's second law states that in inertial reference systems, the acceleration of a material point in direction coincides with the resultant of all forces applied to the body, and in absolute value is directly proportional to the force modulus and inversely proportional to the mass of the material point. Or, equivalently, the rate of change of momentum of a material point is equal to the applied force.

When a force is applied to a body of finite dimensions, mechanical stresses arise in it, accompanied by deformations.

From the point of view of the Standard Model of elementary particle physics, fundamental interactions (gravitational, weak, electromagnetic, strong) are carried out through the exchange of so-called gauge bosons. High-energy physics experiments carried out in the 70s-80s. 20th century confirmed the assumption that the weak and electromagnetic interactions are manifestations of a more fundamental electroweak interaction.

The dimension of force is LMT −2, the unit of measurement in the International System of Units (SI) is the newton (N, N), in the CGS system it is the dyne.

2. Newton's first law.

Newton's first law states that there are frames of reference in which bodies maintain a state of rest or uniform rectilinear motion in the absence of actions on them from other bodies or with mutual compensation of these influences. Such frames of reference are called inertial. Newton suggested that every massive object has a certain amount of inertia, which characterizes the "natural state" of the movement of this object. This idea denies the view of Aristotle, who considered rest to be the "natural state" of an object. Newton's first law contradicts Aristotelian physics, one of the provisions of which is the assertion that a body can move at a constant speed only under the action of a force. The fact that in Newtonian mechanics in inertial frames of reference rest is physically indistinguishable from uniform rectilinear motion is the justification of Galileo's principle of relativity. Among the totality of bodies, it is fundamentally impossible to determine which of them is “in motion” and which are “at rest”. It is possible to speak about motion only in relation to any frame of reference. The laws of mechanics hold the same in all inertial frames of reference, in other words, they are all mechanically equivalent. The latter follows from the so-called Galilean transformations.

3. Newton's second law.

Newton's second law in its modern formulation sounds like this: in an inertial frame of reference, the rate of change in the momentum of a material point is equal to the vector sum of all forces acting on this point.

where is the momentum of the material point, is the total force acting on the material point. Newton's second law states that the action of unbalanced forces leads to a change in the momentum of a material point.

By definition of momentum:

where is the mass, is the speed.

In classical mechanics, at speeds of motion much less than the speed of light, the mass of a material point is considered unchanged, which allows it to be taken out of the sign of the differential under these conditions:

Given the definition of the acceleration of a point, Newton's second law takes the form:

It is said to be "the second most famous formula in physics", although Newton himself never explicitly wrote down his second law in this form. For the first time this form of law can be found in the works of K. Maclaurin and L. Euler.

Since in any inertial frame of reference the acceleration of the body is the same and does not change when moving from one frame to another, then the force is also invariant with respect to such a transition.

In all natural phenomena force, regardless of its origin, appears only in a mechanical sense, that is, as the cause of violation of the uniform and rectilinear motion of the body in the inertial coordinate system. The opposite statement, i.e. the establishment of the fact of such a movement, does not indicate the absence of forces acting on the body, but only that the actions of these forces are mutually balanced. Otherwise: their vector sum is a vector with module equal to zero. This is the basis for measuring the magnitude of a force when it is compensated by a force whose magnitude is known.

Newton's second law allows you to measure the magnitude of force. For example, knowing the mass of a planet and its centripetal acceleration while moving in orbit allows us to calculate the magnitude of the force of gravitational attraction acting on this planet from the Sun.

4. Newton's third law.

For any two bodies (let's call them body 1 and body 2), Newton's third law states that the force of the action of body 1 on body 2 is accompanied by the appearance of a force equal in absolute value, but opposite in direction, acting on body 1 from body 2. Mathematically, the law is written So:

This law means that forces always arise in action-reaction pairs. If body 1 and body 2 are in the same system, then the total force in the system due to the interaction of these bodies is zero:

This means that there are no unbalanced internal forces in a closed system. This leads to the fact that the center of mass of a closed system (that is, one that is not affected by external forces) cannot move with acceleration. Separate parts of the system can accelerate, but only in such a way that the system as a whole remains in a state of rest or uniform rectilinear motion. However, if external forces act on the system, then its center of mass will begin to move with an acceleration proportional to the resulting external force and inversely proportional to the mass of the system.

5. Gravity.

Gravity ( gravity) - universal interaction between any kind of matter. Within the framework of classical mechanics, it is described by the law of universal gravitation, formulated by Isaac Newton in his work "The Mathematical Principles of Natural Philosophy". Newton obtained the magnitude of the acceleration with which the Moon moves around the Earth, assuming in the calculation that the gravitational force decreases inversely with the square of the distance from the gravitating body. In addition, he also found that the acceleration due to the attraction of one body by another is proportional to the product of the masses of these bodies. Based on these two conclusions, the law of gravity was formulated: any material particles are attracted towards each other with a force that is directly proportional to the product of the masses ( and ) and inversely proportional to the square of the distance between them:

Here is the gravitational constant, the value of which was first obtained by Henry Cavendish in his experiments. Using this law, one can obtain formulas for calculating the gravitational force of bodies of arbitrary shape. Newton's theory of gravitation describes well the motion of the planets of the solar system and many other celestial bodies. However, it is based on the concept of long-range action, which contradicts the theory of relativity. Therefore, the classical theory of gravity is not applicable to describe the motion of bodies moving at a speed close to the speed of light, the gravitational fields of extremely massive objects (for example, black holes), as well as variable gravitational fields created by moving bodies at large distances from them.

A more general theory of gravity is Albert Einstein's general theory of relativity. In it, gravity is not characterized by an invariant force that does not depend on the frame of reference. Instead, the free movement of bodies in a gravitational field, perceived by the observer as movement along curved trajectories in three-dimensional space-time with a variable speed, is considered as movement by inertia along a geodesic line in a curved four-dimensional space-time, in which time flows differently at different points. . Moreover, this line is in a sense "the most direct" - it is such that the space-time interval (proper time) between the two space-time positions of a given body is maximum. The curvature of space depends on the mass of the bodies, as well as on all types of energy present in the system.

6. Electrostatic field (field of fixed charges).

The development of physics after Newton added to the three main (length, mass, time) quantities an electric charge with the dimension C. However, based on the requirements of practice, they began to use not a unit of charge, but a unit of electric current as the main unit of measurement. So, in the SI system, the basic unit is the ampere, and the unit of charge is the pendant, a derivative of it.

Since the charge, as such, does not exist independently of the body carrying it, the electrical interaction of the bodies manifests itself in the form of the same force considered in mechanics, which causes acceleration. As applied to the electrostatic interaction of two point charges with values ​​and located in vacuum, the Coulomb's law is used. In the form corresponding to the SI system, it has the form:

where is the force with which charge 1 acts on charge 2; When charges are placed in a homogeneous and isotropic medium, the interaction force decreases by a factor of ε, where ε is the permittivity of the medium.

The force is directed along the line connecting the point charges. Graphically, an electrostatic field is usually depicted as a picture of lines of force, which are imaginary trajectories along which a massless charged particle would move. These lines start on one and end on another charge.

7. Electromagnetic field (direct current field).

The existence of a magnetic field was recognized back in the Middle Ages by the Chinese, who used the "loving stone" - a magnet, as a prototype of a magnetic compass. Graphically, the magnetic field is usually depicted as closed lines of force, the density of which (as in the case of an electrostatic field) determines its intensity. Historically, a visual way to visualize the magnetic field was iron filings, poured, for example, on a sheet of paper placed on a magnet.

Oersted found that the current flowing through the conductor causes the deflection of the magnetic needle.

Faraday came to the conclusion that a magnetic field is created around a current-carrying conductor.

Ampere put forward a hypothesis, recognized in physics, as a model of the process of the emergence of a magnetic field, which consists in the existence of microscopic closed currents in materials, which together provide the effect of natural or induced magnetism.

Ampere found that in a reference frame in vacuum, in relation to which the charge is in motion, that is, it behaves like an electric current, a magnetic field arises, the intensity of which is determined by the magnetic induction vector lying in a plane perpendicular to the direction charge movement.

The unit of magnetic induction is tesla: 1 T = 1 T kg s −2 A −2
The problem was solved quantitatively by Ampere, who measured the force of interaction of two parallel conductors with the currents flowing through them. One of the conductors created a magnetic field around itself, the second reacted to this field by approaching or moving away with a measurable force, knowing which and the magnitude of the current strength, it was possible to determine the modulus of the magnetic induction vector.

The force interaction between electric charges that are not in motion relative to each other is described by Coulomb's law. However, charges that are in motion relative to each other create magnetic fields, through which the currents created by the movement of charges generally come into a state of force interaction.

The fundamental difference between the force arising from the relative motion of charges and the case of their stationary placement is the difference in the geometry of these forces. For the case of electrostatics, the interaction forces of two charges are directed along the line connecting them. Therefore, the geometry of the problem is two-dimensional and the consideration is carried out in the plane passing through this line.

In the case of currents, the force characterizing the magnetic field created by the current is located in a plane perpendicular to the current. Therefore, the picture of the phenomenon becomes three-dimensional. The magnetic field created by an element of the first current, infinitely small in length, interacting with the same element of the second current, in the general case, creates a force acting on it. Moreover, for both currents, this picture is completely symmetrical in the sense that the numbering of the currents is arbitrary.

The law of interaction of currents is used to standardize direct electric current.

8. Strong interaction.

The strong interaction is the fundamental short-range interaction between hadrons and quarks. In the atomic nucleus, the strong force holds together positively charged (experiencing electrostatic repulsion) protons, this happens through the exchange of pi-mesons between nucleons (protons and neutrons). Pi-mesons live very little, their lifetime is only enough to provide nuclear forces within the radius of the nucleus, therefore nuclear forces are called short-range. An increase in the number of neutrons "dilutes" the nucleus, reducing electrostatic forces and increasing nuclear ones, but with a large number of neutrons, being fermions, they themselves begin to experience repulsion due to the Pauli principle. Also, when the nucleons are too close together, the exchange of W-bosons begins, causing repulsion, thanks to which the atomic nuclei do not “collapse”.

Within the hadrons themselves, the strong force holds together the quarks that make up the hadrons. The quanta of the strong field are gluons. Each quark has one of three "color" charges, each gluon consists of a pair of "color" - "anticolor". Gluons bind quarks in the so-called. "confinement", due to which free quarks have not been observed in the experiment at the moment. When the quarks move apart from each other, the energy of gluon bonds increases, and does not decrease as in the case of nuclear interaction. Having spent a lot of energy (by colliding hadrons in the accelerator), one can break the quark-gluon bond, but in this case, a jet of new hadrons is ejected. However, free quarks can exist in space: if a quark managed to avoid confinement during the Big Bang, then the probability of annihilating with the corresponding antiquark or turning into a colorless hadron for such a quark is vanishingly small.

9. Weak interaction.

The weak interaction is the fundamental short-range interaction. Range 10 −18 m. Symmetrical with respect to the combination of spatial inversion and charge conjugation. The weak interaction involves all the fundamentalfermions (leptons and quarks). This is the only interaction that involvesneutrino(not to mention gravity, negligible under laboratory conditions), which explains the colossal penetrating power of these particles. The weak interaction allows leptons, quarks and theirantiparticles exchange energy, weight, electric charge and quantum numbers- that is, turn into each other. One of the manifestationsbeta decay.

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.

Learn more about the properties of 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 the weight of the body is equal to the force of gravity, but these forces are completely different. 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. Occur in the presence of an 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.