What is force equal to in physics? Power and concepts associated with it

Christian) - one of the “nine ranks of angels.” According to the classification of Pseudo-Dionysius, the Areopagite is the fifth rank, together with dominions and authorities making up the second triad.

Excellent definition

Incomplete definition ↓

FORCE

non-mechanical, metaphysical). Polychronic orientation of latent absorption, which is complementary to any structure, to this structure itself. For subjective consciousness, S. can only appear as virtuality. There are also no forces in the objective. S. is always a symptom of a cut or cut in existence, a change in the nature of isolating a part from the whole.

Thus, the force-time-motion-structure complex is always a given of incompleteness in permeability, the incomprehensibility of the whole, on the border of a part and its complement. However, it is S., in its meaning, that is the greatest conceptual surrogate. It turns out to be locally here-now represented by the projection of a multiplicity of factors.

The subject does not feel this or that internal psychic force, but even in the most extreme or extreme case - only the pressure of “forces”. The utilization of these pressures in the form of acts and affects also leaves any supposed new forces hidden.

We may well move from ordinary phenomena to microphenomena, real, but lying outside the usual everyday and scientific appearances, but the transition to any kind of micromotority, microkinestheticity is impossible.

The trivial definition of force as a measure of influence is heuristically unacceptable. Everything that is connected with energy appears as a breakthrough of non-existence through one or another system of prohibitions, determined by the structures of a specific given. At the same time, the breakthrough itself is channeled in a certain way. The question is complicated by the fact that structures cannot exist in any capacity if they are not already a given form of an energy breakthrough. At some hypothetical absolute moment there are no structures - they are temporary creations, and beyond

the edge of cycles is inert repetitions.

Excellent definition

Incomplete definition ↓

There are a number of laws that characterize physical processes during mechanical movements of bodies.

The following basic laws of forces in physics are distinguished:

law of gravity;
law of universal gravitation;
laws of friction force;
law of elastic force;
Newton's laws.

Law of Gravity

Note 1

Gravity is one of the manifestations of the action of gravitational forces.

Gravity is represented as a force that acts on a body from the side of the planet and gives it acceleration due to gravity.

Free fall can be considered in the form $mg = G\frac(mM)(r^2)$, from which we obtain the formula for the acceleration of free fall:

$g = G\frac(M)(r^2)$.

The formula for determining gravity will look like this:

$(\overline(F))_g = m\overline(g)$

Gravity has a certain vector of distribution. It is always directed vertically downwards, that is, towards the center of the planet. The body is constantly subject to gravity and this means that it is in free fall.

The trajectory of movement under the influence of gravity depends on:

module of the object's initial velocity;
direction of body speed.

A person encounters this physical phenomenon every day.

Gravity can also be represented as the formula $P = mg$. When accelerating due to gravity, additional quantities are also taken into account.

If we consider the law of universal gravitation, which was formulated by Isaac Newton, all bodies have a certain mass. They are attracted to each other with force. It will be called the gravitational force.

$F = G\frac(m_1m_2)(r^2)$

This force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them.

$G = 6.7\cdot (10)^(-11)\ (H\cdot m^2)/((kg)^2\ )$, where $G$ is the gravitational constant and it has according to the international system SI measurements constant value.

Definition 1

Weight is the force with which a body acts on the surface of the planet after gravity occurs.

In cases where the body is at rest or moves uniformly along a horizontal surface, then the weight will be equal to the support reaction force and will coincide in value with the magnitude of the force of gravity:

At uniformly accelerated motion vertically the weight will differ from the force of gravity based on the acceleration vector. When the acceleration vector is directed in the opposite direction, an overload condition occurs. In cases where the body and the support move with acceleration $a = g$, then the weight will be equal to zero. A state of zero weight is called weightlessness.

The gravitational field strength is calculated as follows:

$g = \frac(F)(m)$

The quantity $F$ is the gravitational force that acts on a material point of mass $m$.

The body is placed at a certain point in the field.

The potential energy of gravitational interaction of two material points with masses $m_1$ and $m_2$ must be at a distance $r$ from each other.

The gravitational field potential can be found using the formula:

$\varphi = \Pi / m$

Here $П$ is the potential energy of a material point with mass $m$. It is placed at a certain point in the field.

Laws of friction

Note 2

The friction force arises during movement and is directed against the sliding of the body.

The static frictional force will be proportional to the normal reaction. The static friction force does not depend on the shape and size of the rubbing surfaces. The static coefficient of friction depends on the material of the bodies that come into contact and generate the friction force. However, the laws of friction cannot be called stable and accurate, since various deviations are often observed in the research results.

The traditional writing of the friction force involves the use of the friction coefficient ($\eta$), $N$ is the normal pressure force.

Also distinguished are external friction, rolling friction force, sliding friction force, viscous friction force and other types of friction.

Law of Elastic Force

The elastic force is equal to the rigidity of the body, which is multiplied by the amount of deformation:

$F = k \cdot \Delta l$

In our classical force formula for searching for elastic force, the main place is occupied by the values of body rigidity ($k$) and body deformation ($\Delta l$). The unit of force is newton (N).

A similar formula can describe the simplest case of deformation. It is commonly called Hooke's law. It states that if anyone tries in an accessible way deform the body, the elastic force will tend to return the shape of the object to its original form.

To understand and accurately describe the process physical phenomenon introduce additional concepts. The elasticity coefficient shows the dependence on:

material properties;
rod sizes.

In particular, the dependence on the size of the rod or area is distinguished cross section and length. Then the elasticity coefficient of the body is written in the form:

$k = \frac(ES)(L)$

In this formula, the quantity $E$ is the elastic modulus of the first kind. It is also called Young's modulus. It reflects the mechanical characteristics of a certain material.

When performing calculations of straight rods, Hooke's law is written in relative form:

$\Delta l = \frac(FL)(ES)$

It is noted that the application of Hooke's law will be effective only for relatively small deformations. If the level of the proportionality limit is exceeded, then the relationship between strains and stresses becomes nonlinear. For some media, Hooke's law cannot be applied even for small deformations.

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 are the forces that are considered in school course physics in the study of 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 the 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 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 designated by the letter , but this power is simply separate species elastic force, so it can be designated 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

At serial connection, for example, spring 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 and its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.

Body weight

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

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

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

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

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

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

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

Overload- ratio of weight to gravity

Archimedes' force

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

In the air we neglect the power of Archimedes.

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

1.Strength- vector physical quantity, which is a measure of the intensity of impact on a given body other bodies, as well as fields Attached to massive force in the body is the reason for 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 magnitude 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 idea of coupled vectors is extremely common, the beginning of which is fixed at a certain point in space or can be located 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 magnitude is directly proportional to the magnitude of the force 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 particle physics, fundamental interactions (gravitational, weak, electromagnetic, strong) are carried out through the exchange of so-called gauge bosons. Experiments in high energy physics conducted in the 70−80s. XX century confirmed the assumption that the weak and electromagnetic interactions are manifestations of the more fundamental electroweak interaction.

The dimension of force is LMT −2, the unit of measurement in the International System of Units (SI) is newton (N, N), in the GHS system it is 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 in the case of mutual compensation of these influences. Such reference systems are called inertial. Newton suggested that everyone massive object has a certain reserve of inertia, which characterizes the “natural state” of movement of this object. This idea rejects 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 statement that a body can move at a constant speed only under the influence of force. The fact that in Newtonian mechanics in inertial frames of reference rest is physically indistinguishable from uniform rectilinear motion is the rationale for Galileo's principle of relativity. Among a set of bodies, it is fundamentally impossible to determine which of them are “in motion” and which are “at rest.” We can talk about motion only relative to some reference system. The laws of mechanics are satisfied equally 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 modern formulation sounds like this: in an inertial reference frame, the rate of change of 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 mass, is speed.

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

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

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

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

In all natural phenomena force, regardless of your origin, appears only in a mechanical sense, that is, as the reason for the violation of the uniform and rectilinear motion of the body in the inertial coordinate system. The opposite statement, i.e. establishing the fact of such 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 modulus 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 us to measure the magnitude of a force. For example, knowledge of the mass of a planet and its centripetal acceleration when moving in orbit allows us to calculate the magnitude of the gravitational attraction force 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 action of body 1 on body 2 is accompanied by the appearance of a force equal in magnitude, but opposite in direction, acting on body 1 from body 2. Mathematically, the law is written So:

This law means that forces always occur 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 acted upon by external forces) cannot move with acceleration. Individual 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 linear motion. However, if external forces act on the system, its center of mass will begin to move with acceleration proportional to the external resultant force and inversely proportional to the mass of the system.

5.Gravity.

Gravity ( gravity) - universal interaction between any types of matter. Within the framework of classical mechanics, it is described by the law of universal gravitation, formulated by Isaac Newton in his work “Mathematical Principles of Natural Philosophy”. Newton obtained the magnitude of the acceleration with which the Moon moves around the Earth, assuming in his calculation that the force of gravity decreases in inverse proportion to the square of the distance from the gravitating body. In addition, he also established that the acceleration caused by 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 gravitation was formulated: any material particles are attracted towards each other with a force directly proportional to the product of 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, you can obtain formulas for calculating the gravitational force of bodies of arbitrary shape. Newton's theory of gravity describes the motion of planets well solar system and many other celestial bodies. However, it is based on the concept of long-range action, contrary to theory relativity. Therefore, the classical theory of gravity is not applicable to describe the motion of bodies moving at speeds close to the speed of light, the gravitational fields of extremely massive objects (for example, black holes), as well as the 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 independent of the reference frame. 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 variable speed, is considered as inertial movement 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 two space-time positions of a given body is maximum. The curvature of space depends on the mass of bodies, as well as on all types of energy present in the system.

6.Electrostatic field (field of stationary charges).

The development of physics after Newton added to the three main quantities (length, mass, time) an electric charge with 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. Thus, in the SI system, the basic unit is the ampere, and the unit of charge, the coulomb, is a derivative of it.

Since the charge, as such, does not exist independently of the body carrying it, the electrical interaction of bodies manifests itself in the form of the same force considered in mechanics, which serves as the cause of acceleration. In relation to the electrostatic interaction of two point charges of magnitude and located in a vacuum, Coulomb's law is used. In the form corresponding to the SI system, it looks like:

where is the force with which charge 1 acts on charge 2, is the vector directed from charge 1 to charge 2 and is equal in magnitude to the distance between the charges, and is the electrical constant equal to ≈ 8.854187817 10 −12 F/m. When charges are placed in a homogeneous and isotropic medium, the interaction force decreases by a factor of ε, where ε is the dielectric constant of the medium.

The force is directed along the line connecting the point charges. Graphically, the electrostatic field is usually depicted as a picture of lines of force, which are imaginary trajectories along which a charged particle without mass would move. These lines start on one charge and end on another.

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, a magnetic field is usually depicted in the form of 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 a magnetic field was with iron filings sprinkled, for example, on a piece of paper placed on a magnet.

Oersted established that the current flowing through a conductor causes a 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 in materials of microscopic closed currents, which together provide the effect of natural or induced magnetism.

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

The unit of measurement 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 between two parallel conductors with 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 it was possible to determine the module 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 in motion relative to each other create magnetic fields, through which the currents created by the movement of charges in the general case come into a state of force interaction.

The fundamental difference between the force that arises during 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 forces of interaction between two charges are directed along the line connecting them. Therefore, the geometry of the problem is two-dimensional and consideration is carried out in a 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 infinitely small element of the first current, interacting with the same element of the second current, generally creates a force acting on it. Moreover, for both currents this picture is completely symmetrical in the sense that the numbering of currents is arbitrary.

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

8.Strong interaction.

The strong force 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 through the exchange of pi mesons between nucleons (protons and neutrons). Pi mesons have a very short lifespan; their lifetime is only enough to provide nuclear forces within the radius of the nucleus, which is why nuclear forces are called short-range. An increase in the number of neutrons “dilutes” the nucleus, reducing electrostatic forces and increasing nuclear ones, but at large quantities neutrons, they themselves, being fermions, begin to experience repulsion due to the Pauli principle. Also, when the nucleons get too close, the exchange of W bosons begins, causing repulsion, due to this atomic nuclei don't "collapse".

Within the hadrons themselves, the strong interaction holds together the quarks - the constituent parts of hadrons. Strong field quanta are gluons. Each quark has one of three “color” charges, each gluon consists of a “color”-“anticolor” pair. Gluons bind quarks in the so-called. “confinement”, due to which free quarks have not been observed in the experiment at the moment. As quarks move away from each other, the energy of gluon bonds increases, and does not decrease as in nuclear interaction. By spending a lot of energy (by colliding hadrons in an accelerator), you can break the quark-gluon bond, but at the same time a jet of new hadrons is released. However, free quarks can exist in space: if some quark managed to avoid confinement during 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 a fundamental short-range interaction. Range 10 −18 m. Symmetrical with respect to the combination of spatial inversion and charge conjugation. All fundamental elements are involved in weak interaction.fermions (leptons And quarks). This is the only interaction that involvesneutrino(not to mention gravity, negligible in laboratory conditions), which explains the colossal penetrating ability of these particles. The weak interaction allows leptons, quarks and theirantiparticles exchange energy, mass, electric charge And quantum numbers- that is, turn into each other. One of the manifestations isbeta decay.

DEFINITION

Force is a vector quantity that is a measure of the action of other bodies or fields on a given body, as a result of which a change in the state of this body occurs. In this case, a change in state means a change or deformation.

The concept of force refers to two bodies. You can always indicate the body on which the force acts and the body from which it acts.

Strength is characterized by:

module;
direction;
application point.

The magnitude and direction of the force are independent of the choice.

The unit of force in the C system is 1 Newton.

In nature, there are no material bodies that are outside the influence of other bodies, and, therefore, all bodies are under the influence of external or internal forces.

Several forces can act on a body at the same time. In this case, the principle of independence of action is valid: the action of each force does not depend on the presence or absence of other forces; the combined action of several forces is equal to the sum of the independent actions of the individual forces.

Resultant force

To describe the motion of a body in this case, the concept of resultant force is used.

DEFINITION

Resultant force is a force whose action replaces the action of all forces applied to the body. Or, in other words, the resultant of all forces applied to the body is equal to the vector sum of these forces (Fig. 1).

Fig.1. Determination of resultant forces

Since the movement of a body is always considered in some coordinate system, it is convenient to consider not the force itself, but its projections onto the coordinate axes (Fig. 2, a). Depending on the direction of the force, its projections can be either positive (Fig. 2, b) or negative (Fig. 2, c).

Fig.2. Projections of force onto coordinate axes: a) on a plane; b) on a straight line (the projection is positive);
c) on a straight line (projection is negative)

Fig.3. Examples illustrating vector addition strength

We often see examples illustrating the vector addition of forces: a lamp hangs on two cables (Fig. 3, a) - in this case, equilibrium is achieved due to the fact that the resultant of the tension forces is compensated by the weight of the lamp; the block slides along an inclined plane (Fig. 3, b) - the movement occurs due to the resultant forces of friction, gravity and support reaction. Famous lines from the fable by I.A. Krylova “and the cart is still there!” - also an illustration of the equality of the resultant of three forces to zero (Fig. 3, c).

Examples of problem solving

EXAMPLE 1

Exercise

Two forces act on the body and . Determine the modulus and direction of the resultant of these forces if: a) the forces are directed in one direction; b) forces are directed in opposite directions; c) the forces are directed perpendicular to each other.

Solution

a) forces are directed in one direction;