So what is the Force?
Physics characterizes Force as follows:
“Force is power, energy, charge, the ability to withstand applied loads and stresses.”
"energy" is a quantitative measure that reflects strength, i.e. the speed of movement, with the help of which the interaction of all types of matter is determined.
In accordance with various forms of matter - different forms of energy (motion) are considered: - mechanical, internal, electromagnetic, chemical, nuclear, etc.
The following formula is an expression of the amount of energy or force:
E \u003d m with 2;
Where E - energy, m - weight, with - speed.
Based on the formula, force and energy depend not so much on mass as on the speed of movement of this mass, or rather on the primary action (impulse of force).
Not only material bodies, such as a flying bullet or a thrown stone, can move, but movement can also be said about a sunbeam moving along a wall when a mirror is turned, or about the movement of a shadow cast by an illuminated object. Therefore, movement can be associated both with the movement of material bodies, and with the transmission from one place to another of any signal, such as a sound, light or radio signal.
To study movement, first of all, it is necessary to learn how to describe the movements of material bodies in relation to any other physical bodies.
Any movement, as well as the rest of the body (as a special case of movement) are relative. When answering the question whether a body is at rest or moving and how exactly it moves, it is necessary to indicate with respect to which bodies the movement of a given body is considered, otherwise no statement about movement can make sense.
In all cases, the physical bodies in relation to which the movement is considered are called the reference frame, and the movement of the bodies itself is called "relocation".
When studying movements on the Earth's surface, the Earth itself is usually taken as the reference frame. When studying the motion of the Earth or other planets in space, the Sun and stars are taken as reference systems.
Such a reference system is adopted in the study of the laws of dynamics.
If we do not find out the reason for the occurrence of movements, then in this case we will consider the kinematics of these movements.
In order to know the displacement of the body, it is enough to know its initial position, as well as the numerical value and sign of the distance traveled. In the same way, knowing the initial position of the body, the numerical value of its speed and the direction of movement of this body, we can answer the question of where this body will be in one second, in two seconds, etc. But if the body moves as you like, then these data are not enough for us.
Rice. 1. Marking of a curvilinear trajectory.
Moving an AB point between its positions A and B
does not lie on the path.
If the trajectory of the body's motion is a curved line, then we will continue to call the body's displacement the segment connecting its initial and final positions. If we mark the curvilinear trajectory and “bind” the individual positions of the moving point to the corresponding points in time (see Fig. 1), then it turns out that the curvilinear motion consists of a large number of rectilinear ones, and the total speed of the curvilinear motion will be determined by the average speed, which is a derivative of sections with rectilinear movement, the speed of movement on which is uneven and depends on the curvature (angle) of movement.
However, this is only a rough, approximate concept of the nature of the movement. The thing is that, when determining the average speed, we kind of replace the movement during each period of time with uniform movement and consider that the speed changes abruptly from one period of time to another. However, in reality, these sections can have different lengths and directions, and, accordingly, the speed on them will vary greatly.
As a rule, the average speed of uniform motion is called instantaneous speed or simply speed. If the movement is uniform, then its instantaneous speed at any moment of time is equal to the speed of this uniform movement, in other words: - the instantaneous speed of uniform movement is constant. The instantaneous speed of uneven movement is a variable that takes on different values at different times. From this it becomes clear that the instantaneous speed of curvilinear motion is changing throughout the motion.
If the instantaneous speed of a moving body increases, then the movement is called accelerated; if the instantaneous speed decreases, then the movement is called slow.
Among the various accelerated movements, there are often movements in which the instantaneous speed for any equal time intervals increases by the same amount. Such movements are called uniformly accelerated. Uniformly accelerated movements are disturbed by friction and air resistance
Uniformly accelerated motion is quantitatively characterized by a change in speed over time, which is called acceleration.
If the movement is not uniformly accelerated, then the concept of average acceleration is introduced, which characterizes the change in speed over a certain period of time on the section of the path traveled during this period of time. On separate segments of this section, the average acceleration can have different values.
As a rule, the trajectories of movement of different points of the body are different.
The simplest motion of a body is a motion in which all points of the body move in the same way, describing the same trajectories. Such a movement is called progressive.
During translational motion, any straight line drawn in the body remains parallel to itself.
Another simple type of movement is the rotational movement of the body, or rotation. During rotational motion, all points of the body move along circles, the centers of which lie on a straight line, which is called the axis of rotation.
Both reciprocating and rotational movements have their own specific boundaries (edges), direction (axis, vector) and rhythm (amplitude, frequency) of movements.
Rice. 2. Continuous vibrations
It is these 2 movements that underlie all types of movements, be it mechanical, sound, electrical, light, etc. electromagnetic, chemical, etc.
It is these movements that represent the oscillations of the pendulum, which can be undamped or damped.
H 
rice. 3. Damped vibrations
undamped oscillations occur in an oscillatory system in the absence of friction and are called eigenoscillations of the system (Fig. 2).
However, in Nature there are various kinds of friction forces, air resistance, etc., which slow down the process of movement and cause damping of oscillations (stopping movement) (Fig. 3).
At 
Rice. 4. Aperiodic motions
by increasing the friction in one way or another, one can reach such high attenuations that the system stops after the first swing, or even to the first transition through the equilibrium position (Fig. 4). Such strongly damped motions of an oscillatory system are called aperiodic.
Considering the oscillations of a load on a spring, it is easy to observe an increase in damping with increasing friction. If the load is placed in water, then the damping of the oscillations will increase sharply compared to the damping in air; in oil it will be even greater than in water: the motion will turn out to be aperiodic or close to aperiodic.
So let's recap:
Force is Energy.
The speed of matter movement - determines the amount of Force (Energy).
At the heart of any movement is the initial impulse, which is called instantaneous speed.
The quantitative expression of instantaneous speed is called acceleration.
There are only 2 fundamental types of movements - translational and rotational, all other movements are their various combinations.
These movements can be undamped, damped and aperiodic.
Mechanical, sound, electromagnetic, chemical, etc. the phenomena that are usually represented by the concept of energy are the movement of matter in various states of aggregation.
So, in any case, for any kind of movement, any material body or substance should be taken as a reference system.
The human body is not a special exception to the rule, it is also a material body that has a complex combination of substances from the smallest cells to large tissue structures. Therefore, our organism should be considered on the basis of those laws of Nature, according to which our World exists.
Mechanical interaction is one of the types of interaction of matter that can cause a change in the mechanical movement of material bodies.
Force characterizes the quantitative aspect of mechanical interaction. Thus, when it is said that forces act on a body, it means that other bodies (or physical fields) act on it. Not always, however, the force really leads to a change in the motion of the body; such a change can be blocked by the action of other forces. With that said, we write:
Force (Newtonian) is a measure of mechanical action on some material body from another material body (or physical field); it characterizes the intensity and direction of this impact. This, of course, is not a definition, but only an explanation of the concept of force. Since the concept of force is fundamental, its exact meaning is revealed in the axioms of mechanics.
For now, we note this. The reservation “Newtonian” is made because in dynamics we will meet with other quantities, also called forces, which, however, are not measures of mechanical interaction. In the same semester, we will talk about Newtonian forces, and for brevity we will call them simply forces.
Further, the word “measure” in mechanics and physics is understood as a physical quantity that serves to quantitatively describe any property or relationship. In this case, we are talking about the description of a mechanical interaction (and, as you know, there are other interactions – thermal, chemical, and others).
In elementary particle physics, there are four fundamental interactions: strong, electromagnetic, weak and gravitational. These four interactions are the basis of all observed phenomena - both related to mechanics and other branches of natural science.
However, in the macrocosm fundamental interactions are manifested, as a rule, indirectly, and we have to deal with a much wider list of interactions (not necessarily fundamental). If we talk about mechanical interactions, then we can talk about forces of various origins.
Examples of forces: gravity forces, elastic forces, Archimedean forces, environmental resistance forces, etc. In most problems of mechanics, however, the physical nature of certain forces is usually of no interest.
We also, explaining the concept of force, spoke about the intensity and direction of the impact. This means that force is a vector quantity. Namely, this is a vector applied to a certain point of a material body. Therefore, we can talk about such characteristics of power.
Strength is characterized by:
1) value (modulus);
3) application point.
Unfortunately, in the exam, one often encounters a complete disregard for this rule. In the best case, the examiner in this situation will do this: he will sigh and ask the student to quickly put down the designations of the vectors in the text of the answer to the question posed. If the student fails to put down the symbols correctly, this is the first step towards getting a “deuce”. So please don't ignore the line in your notes if it's written on the board.
Parentheses with a comma in the middle denote the scalar product of vectors (the comma separates the factors). Note that in many books, the dot product is denoted differently - by a point between vectors, and the point can usually be omitted.
But we will adhere to just such designations (they are also quite common). Among other things, they avoid confusion (after all, the scalar product of vectors must be distinguished from the usual product of two scalars).
So far we have only talked about the vector of force. But the concept of force is not reduced to the concept of its vector. The point of application of the force is also important: after all, if the force vector of the same magnitude and direction is applied at another point of the body, then its movement may change.
In geometry, the following terminology is adopted. A free vector (or simply a vector) is a vector characterized only by its modulus and direction. An associated vector is a vector that is also characterized by an application point. Sometimes such designations are used.
u---.A denotes the bound vector obtained if the free vector u--- is applied at point A. Note that here the point is not written in the middle of the line (as when multiplying numbers), but on its bottom line. Thus, the following conclusion can be drawn. So, force is a coupled vector (full notation: F----.A).
Where we need to emphasize the presence of a certain point of application of force, we will use this full designation. Where the point of application of the force will be specified in advance, we will use the abbreviated notation, denoting the force simply F---- (ie, in the same way as the force vector). The following must be said about the point of application of force: If the force acts on a material point, then this point itself serves as the point of application.
If a force acts on a material body, then the point of application is the point of the body (it can change over time). In the general case, the point of application of the force cannot lie outside the body. If the body is absolutely rigid, then this restriction can be removed; but we will talk about this later.
The question arises: how can one set the point of application of force in practice? Any point can be specified, for example, by its radius vector drawn from some pole. A pole is an arbitrarily selected point (the position of which is usually assumed to be known).
Since it says “usually”, then you can completely ignore the text in brackets. It often happens like this: they took a certain point and declared it a pole (and from now on it will be considered as such). But to set the position of the point of application of force, we just need to know the position of the pole. You can - but not necessarily - take the origin of the coordinate system as a pole.
Both designations are used, but the first is preferable: the vector is denoted by one letter, and the letter “r” reminds us that we are talking about the radius vector, or six scalars (Fx, Fy, Fz, xA, yA, zA). This is convenient, and this is often done. But you can also set the force in another way, which we will consider in the next paragraph.
1. Force - the action of one body on another, resulting in acceleration. Those. force is a measure of the interaction of forces, as a result of which bodies are deformed or acquire acceleration. Force is a vector quantity; it is characterized by a numerical value, direction of action and point of application to the body.
2. Is it possible, based on the formula F = ma, to assert that the force applied to the body depends on the mass of the body and its acceleration?
2. No, you can't.
3. Is it possible, based on the expression m = F / a, to assert that the mass of a body depends on the force applied to it and on its acceleration?
3. No, you can't.
4. Is it possible, based on the equality a = F / m, to assert that the acceleration of a body depends on the force applied to it and on the mass of the body?
4. Yes. Only for inertial frames of reference.
5. How is Newton's first law formulated, if we use the concept of force?
5. There are such frames of reference, relative to which a progressively moving body keeps its speed constant if the resultant of all forces applied to the body is equal to zero.
6. What is the resultant force?
6. A force equal to the geometric sum of all forces applied to the body (point) is called the resultant or resultant force.
2. GENERAL CHARACTERISTICS OF THE CONCEPT "POWER"
2.1 History of the concept of "power"
Force is a vector physical quantity, which is a measure of the intensity of the interaction of bodies. The force applied to a massive body is the cause of a change in its speed or the occurrence of deformations in it.
Force, as a vector quantity, is characterized by its modulus and direction. Newton's second law states that in inertial frames of reference the acceleration of the movement of a material point coincides in direction with the applied force; modulo is directly proportional to the modulus of force and inversely proportional to the mass of a material point. Or, equivalently, in inertial frames of reference, the rate of change of momentum of a material point is equal to the applied force. Deformations are a consequence of the occurrence of internal stresses in the body.
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.
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 1970s and 1980s 20th century confirmed the assumption that the weak and electromagnetic interactions are manifestations of a more fundamental electroweak interaction.
The dimension of force in systems of quantities LMT - dim F = L M T−2, the unit of force in the International System of Units (SI) is newton (N, N).
2.2 Newton's laws
Isaac Newton set out to describe the movement of objects using the concepts of inertia and force. Having done this, he simultaneously established that any mechanical movement is subject to general conservation laws. In 1687, Newton published his famous work "Mathematical Principles of Natural Philosophy", in which he outlined the three fundamental laws of classical mechanics (Newton's famous laws).
2.2.1 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 margin 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 Newton's mechanics, rest is physically indistinguishable from uniform rectilinear motion, is the rationale for 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.
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.
2.2.2 Newton's second law
Although Newton's second law is traditionally written as: F=ma, Newton himself wrote it a little differently, using differential calculus.
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.
It is believed to be "the second most famous formula in physics", although Newton himself never explicitly wrote down his second law in this form.
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 phenomena of nature, force, regardless of its origin, manifests itself only in a mechanical sense, i.e. 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. 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.
symmetry. In recent decades, a large number of new devices for measuring intraocular pressure have appeared. The purpose of this work was to assess the reliability and objectivity of the readings of a new domestic device - a digital portable tonometer of intraocular pressure through the eyelid TGDts-01 "PRA" (Fig. 1). Rice. 1. Digital portable tonometer of intraocular pressure through the eyelid...
Electromechanical class. Measurement of current strength Ammeter - a device for measuring current strength in amperes (Fig. 1). The scale of ammeters is graduated in microamperes, milliamps, amperes or kiloamperes in accordance with the measurement limits of the device. The ammeter is connected to the electrical circuit in series with that section of the electrical circuit (Fig. 2), the current strength in which is measured; for increase...
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The concept of "strength" is primarily physical. In mechanics, it expresses the measure of the interaction of bodies, the reason for their movement. Therefore, in the physical sense - as a vector quantity - force is understood in the case when the quantitative side of human interaction is considered, say, with a support, projectile or other external object. In other words, in this case, the result of the movement, its working effect, is evaluated through force.
If we are talking about the source of movement, then, speaking of force, they mean the ability of a person to do work, and this ability acts as the reason for the movement of the body or its individual links. In this case, we mean the traction force of human muscles, that is, a physiological phenomenon.
And, finally, the concept of "strength" is used as one of the qualitative characteristics of a person's voluntary movements that solve a specific motor task. Here, strength, together with such criteria as speed, endurance, dexterity, etc., acts as a pedagogical concept that evaluates the qualitative side of the movement being performed (Yu. V. Verkhoshansky, 1977).
Force a person is defined as his ability to overcome external resistance through muscular efforts (Theory and Methods of Physical Education, 1976). That is, the concept of “strength” means any ability of a person to overcome mechanical and biomechanical forces that impede action by muscle tension, to counteract them, thereby ensuring the effect of action (despite the obstructing forces of gravity, inertia, environmental resistance, etc.).
Depending on the conditions, nature and magnitude of the manifestation of muscle strength in sports practice, it is customary to distinguish several varieties of strength qualities.
In the case when the athlete's efforts are not accompanied by movement, they speak of static (isometric) mode muscle work ("static strength"). In static mode, tense muscles do not change their length. Static force is characterized by its two features of manifestation (V. V. Kuznetsov, 1975; cited by: Zh. K. Kholodov, V. S. Kuznetsov, 2003):
1) with muscle tension due to active volitional efforts of a person (active static force);
2) when attempting external forces or under the influence of a person's own weight, forcibly stretch a tense muscle (passive static force).
But most often, strength is manifested in movement, in the so-called dynamic mode("dynamic force").
Dynamic muscle work occurs either in overcoming mode, either in yielding. In the first case, the working muscles contract and shorten (for example, when squeezing the barbell), in the second, being in a tense state, they stretch and lengthen (for example, during depreciation bending of the legs at the moment of landing after a jump). In addition, dynamic work can occur at different speeds, with different accelerations and decelerations, as well as with a uniform manifestation of force. The latter at different speeds is called isotonic regimen, and at a constant speed - isokinetic(N. G. Ozolin, 2003).
According to the nature of the efforts in the dynamic force, three varieties are distinguished (according to V. Kuznetsov; cited by: S. M. Vaitsekhovsky, 1971):
- explosive force - manifestation of strength with maximum acceleration, which is typical, for example, for the so-called speed-strength exercises: jumping, throwing, sprinting, individual elements of wrestling, boxing, sports games, etc.;
- fast force - manifestation of strength with non-maximal acceleration, for example, when performing fast (but not extremely fast) movements in running, swimming, cycling, etc.;
- slow force , manifested with relatively slow movements, with practically no acceleration. Typical examples are barbell presses, push-ups on the rings or bar.
When evaluating the amount of effort in a particular exercise or simple movement, the terms are used "absolute" and "relative" strength.
