The movement of the body is called a directed segment of a straight line that connects the initial position of the body with its subsequent position. Displacement is a vector quantity.
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Basic concepts of kinematics
Kinematics called a section of mechanics in which the movement of bodies is considered without clarifying the reasons for this movement.
Mechanical movement bodies are called the change ᴇᴦο position in space relative to other bodies over time.
Mechanical movement relatively... The movement of the same body relative to different bodies is different. To describe the movement of a body, it is necessary to indicate in relation to which body the movement is considered. This body is called reference body.
The coordinate system associated with the reference body and the clock for counting time form frame of reference , which allows you to determine the position of a moving body at any time.
In the International System of Units (SI), the unit of length is meter, and per unit of time - second.
Every body has a certain size. Different parts of the body are in different places in space. However, in many problems of mechanics there is no need to indicate the positions of individual parts of the body. If the dimensions of the body are small in comparison with the distances to other bodies, then this body can be considered ᴇᴦο material point... This can be done, for example, when studying the motion of planets around the Sun.
If all parts of the body move in the same way, then such a movement is called progressive ... For example, the cabins in the attraction "Giant wheel", a car on a straight section of the path, etc. move progressively. During the translational movement of the body, ᴇᴦο can also be considered as a material point.
A body whose dimensions can be neglected under these conditions is called material point .
The concept of a material point plays an important role in mechanics.
Moving over time from one point to another, the body (material point) describes some line, which is called body trajectory .
The position of a material point in space at any time ( law of motion ) can be determined either by using the dependence of coordinates on time x = x(t), y = y(t), z = z(t) (coordinate method), or using the time dependence of the radius vector (vector method), drawn from the origin of coordinates to a given point (Fig. 1.1.1).
The movement of a body is called a directed segment of a straight line connecting the initial position of the body with ᴇᴦο the subsequent position. Displacement is a vector quantity.
The movement of the body is called a directed segment of a straight line that connects the initial position of the body with its subsequent position. Displacement is a vector quantity. - concept and types. Classification and features of the category "Displacement of a body is a directed line segment connecting the initial position of the body with its subsequent position. Displacement is a vector quantity." 2015, 2017-2018.
Question 1: Radius vector: Displacement vector
- radius vector is a vector drawn from a reference point ABOUT to the point under consideration M.
- moving (or radius vector change) is the vector that connects the start and end of the path.
radius vector in a rectangular Cartesian coordinate system:
Where -called point coordinates.
Question 2: Travel speed. Average and instant speeds.
Travel speed(vector) - shows how the displacement changes per unit of time.
Average: Instant: 
The instantaneous speed is always tangential to the path,
and the middle one coincides with the displacement vector.
Projection: Module: 
Question 3: Path. Its communication with the speed module.
S– way Is the length of the trajectory (scalar,\u003e 0).
S-area of \u200b\u200bthe figure bounded by the curve v (t) and the straight lines t 1 and t 2.
Question 4: Acceleration: Acceleration module.
Acceleration -meaning - shows how the speed changes per unit of time.
Projection: Module: 
Mean:
Question 5: Non-uniform motion of a point along a curved path.
If a point moves along a curved trajectory, then it is advisable to decompose the acceleration into components, one of which is directed tangentially and is called tangential or tangential acceleration, and the other is directed along the normal to the tangent, i.e. along the radius of curvature, to the center of curvature and is called normal acceleration.
It characterizes the change in speed in the direction, - in magnitude.
Where r - radius of curvature.
A point moving along a curved path always has normal acceleration, and tangential only when the speed changes in magnitude.
(2, 3) Topic 2. KINEMATIC EQUATIONS OF MOTION.
Question 1. Get the kinematic equations of motion r (t) and v (t).
Two differential and related two integral vector equations:
→ 
and - kinematic equations of an equal variable points at.
Question 2. Get the kinematic equations of motion x (t), y (t), v x (t) and v y (t), for a thrown body.
Question 3. Get the kinematics. equations of motion x (t), y (t), v x (t) and v y (t), for a body thrown at an angle.
 |   |  |
Question 4. Get the equation of motion for a body thrown at an angle.
Topic 3. KINEMATICS OF ROTATION.
Question 1. Kinematic characteristics of rotational motion.
angular movement - angle of rotation of the radius vector.
angular velocity - shows how the angle of rotation of the radius vector changes.
angular acceleration - shows how the angular velocity changes per unit of time.
Question 2. The relationship between the linear and angular characteristics of the movement of a point
Question 3: Get the kinematic equationsw (t) and f(t).
Then the kinematic equations after integration will take a simpler form: 
- kin. equations of uniform acceleration (+) and equally slow (-) rotational motion.
(4, 5, 6) Topic 4. KINEMATICS ATT.
Question 1: Definition of ATT. ATT translational and rotational movements.
ATTis called a body, the deformations of which can be neglected under the conditions of this problem.
All ATT movements can be decomposed into translational and rotational, relative to some instantaneous axis. Translational motion -this is a movement in which a straight line drawn through any two points of the body moves parallel to itself. When moving forward, all points of the body make the same movements. Rotational movement - This is a movement in which all points of the body move in circles, the centers of which lie on the same straight line, called the axis of rotation.
As the kinematic equation of the ATT rotational motion, it is sufficient to know the equation j (t)for the angle of rotation of the radius vector drawn from the axis of rotation to any point of the body (if the axis is stationary). That is, the fundamentally kinematic equations of motion for a point and ATT do not differ.
Topic 5. LAWS OF NEWTON.
Topic 6. LAW OF PRESERVATION OF THE IMPULSE.
Topic 7. WORK. POWER. ENERGY.
Question 7. The laws of conservation in relation to an absolutely elastic impact of two balls.
Absolutely resilient impact - this is such a blow, which conserves the kinetic energy of the entire system.
Topic 10. FORCE FIELDS
Question 3. Length reduction.
l 0 Is the length of the rod in the system with respect to which it is at rest (in our case, in TO), l -the length of this segment in the system relative to which it moves ( K ¢). since and find a connection between land l 0: 
.
Thus, from SRT it follows that the sizes of moving bodies should be reduced in the direction of their motion, but there is no real reduction, because all ISOs are equal.
Question 2: ideal gas
The simplest model of real gases is ideal gas... FROM m andcroscopic point of view is a gas for which the gas laws are satisfied ( pV \u003d const, p / T \u003d const, V / T \u003d const). FROM m andcroscopic point of view, it is a gas for which it is possible to neglect: 1) the interaction of molecules with each other and 2) the intrinsic volume of gas molecules in comparison with the volume of the vessel in which the gas is located.
The equation connecting the state parameters is called equation of state gas. One of the simplest equations of state is
( ; ; 
) mendeleev - Clapeyron equation.
(n -concentration, k -boltzmann constant) - the equation of state for an ideal gas in a different form.
Topic 15. BASIC CONCEPTS OF THERMODYNAMICS
Question 1. Basic concepts. Reversible and irreversible processes.
Reversible process -this is a process of transition of the system from the state AND in state IN, at which the reverse transition from IN to ANDthrough the same intermediate states and at the same time no changes occur in the surrounding bodies. The system is called isolatedif it does not exchange energy with the environment. On the graph, states are indicated by dots, and processes by lines.
The quantities that depend only on the state of the system and do not depend on the processes by which the system came to this state are called state functions... The quantities whose values \u200b\u200bin a given state depend on the preceding processes are called process functions - it's warmth Q and work A, their change is often denoted as dQ, dAor . ( d- Greek letter - delta)
Job and heat - these are two forms of energy transfer from one body to another. When doing work, the relative position of bodies or body parts changes. The transfer of energy in the form of heat is carried out at the contact of bodies - due to the thermal motion of molecules.
TO internal energyinclude: 1) the kinetic energy of the thermal motion of molecules (but not the kinetic energy of the entire system as a whole), 2) the potential energy of interaction of molecules with each other, 3) the kinetic and potential energy of the vibrational motion of atoms in a molecule, 4) the binding energy of electrons with a nucleus in an atom , 5) the energy of interaction of protons and neutrons inside the atomic nucleus. These energies are very different in magnitude from each other, for example, the energy of thermal motion of molecules at 300 K is ~ 0.04 eV, the binding energy of an electron in an atom is ~ 20-50 eV, and the interaction energy of nucleons in a nucleus is ~ 10 MeV. Therefore, these interactions are considered separately.
Internal energy of ideal gas Is the kinetic energy of the thermal motion of its molecules. It only depends on the temperature of the gas. Her change has the same expression for all processes in ideal gases and depends only on the initial and final gas temperatures. 
is the internal energy of an ideal gas.
Topic 16.
Question 1. Entropy
The second beginning of thermodynamics, like the first beginning, is a generalization of a large number of experimental facts and has several formulations.
Let us first introduce the concept of "entropy", which plays a key role in thermodynamics. E ntropia - S - one of the most important thermodynamic functions that characterize the state or possible changes in the state of a substance is a multifaceted concept.
1)Entropy is a function of state... The introduction of such quantities is valuable because for any process the change in the state function is the same, therefore, a complex real process can be replaced by “invented” simple processes. For example, the real process of transition of the system from state A to state B (see Fig.) Can be replaced by two processes: isochoric А®С and isobaric С®В.
Entropy is defined as follows.
For reversible processes in ideal gases, one can obtain formulas for calculating the entropy in various processes. Let us express dQ from the beginning I and substitute it into the expression for dS .
general expression for the change in entropy in reversible processes.
By integrating, we obtain expressions for the change in entropy in various isoprocesses in ideal gases.
Question 2,3,4. Isobaric, isochoric, isothermal
In all entropy calculations, only the difference between the entropies of the final and initial states of the system matters
2)Entropy is a measure of energy dissipation.
 | we write down the I beginning of thermodynamics for a reversible isothermal process, taking into account that dQ \u003d T × dSand express the work dА |
| thermodynamic function is called free energy quantity is called bound energy | |
| From the formulas, we can conclude that not the entire supply of internal energy of the system can be transferred to work U... Part of the energy TS cannot be translated into work, it dissipates in the environment. And this "bound" energy is the greater, the greater the entropy of the system. Therefore, entropy can be called a measure of energy dissipation. |
3)Entropy is a measure of system disorder
Let us introduce the notion of thermodynamic probability: Suppose we have a box divided into ncompartments. Moves freely in the drawer in all compartments Nmolecules. The first compartment will contain N 1 molecules in the second compartment N 2 molecules, ...,
in n-th compartment - N n molecules. Number of ways wthat can be distributed Nmolecules by nstates (compartments) is called thermodynamic probability... In other words, the thermodynamic probability shows how many microdistributions, you can get this macrodistribution It is calculated by the formula:
 |
For an example calculation w Consider a system consisting of three molecules 1, 2, and 3, which move freely in a box with three compartments.
In this example N \u003d 3 (three molecules) and n \u003d 3(three compartments), the molecules are considered distinguishable.
In the first case, macrodistribution is a uniform distribution of molecules over the compartments; it can be carried out by 6 microdistributions. The probability of such a distribution is the greatest. Uniform distribution can be called "disorder" (by analogy with scattered things in a room) In the latter case, when molecules are collected in only one compartment, the probability is the smallest. Simply put, we know from everyday observation that air molecules are more or less evenly distributed in a room, and it is almost completely improbable that all the molecules are gathered in one corner of the room. However, theoretically, such a possibility exists.
Boltzmann postulated that entropy is directly proportional to the natural logarithm of thermodynamic probability:
Therefore, entropy can be called a measure of the disorder of the system.
Question 6: Now we can formulate the second law of thermodynamics.
| 1) For any processes occurring in a thermally insulated system, the entropy of the system cannot decrease: |
| The “\u003d” sign refers to reversible processes, the “\u003e” sign refers to irreversible (real) processes. In open systems, entropy can change in any way. |
| In other words, in closed real systems, only those processes are possible in which the entropy increases. Entropy is related to thermodynamic probability, therefore, its increase in closed systems means an increase in the "disorder" of the system, i.e. molecules tend to come to the same energy state and over time all molecules must have the same energy. From this it was concluded that our Universe is striving for thermal death. "The entropy of the world tends to the maximum" (Clausius). Since the laws of thermodynamics are derived from human experience on the scale of the Earth, the question of their applicability on the scale of the Universe remains open. |
| 3) “It is impossible to build a perpetual motion machine of the second kind, i.e. such a periodically operating machine, the action of which would consist only in lifting the load and cooling the heat reservoir "(Thomson, Planck) |
| There must also be a body, which "will" have to give up some of the heat. It is impossible to simply take away heat from some body and turn it into work, because such a process is accompanied by a decrease in the entropy of the heater. Therefore, one more body is needed - a refrigerator, the entropy of which will increase so that DS \u003d 0... Those. heat is taken from the heater, due to this, work can be done, but part of the heat is "lost", i.e. transferred to the refrigerator. |
Question 7. CIRCULAR PROCESSES (CYCLES)
Circular process or cycle is called a process in which the system, after going through a series of states, returns to its original state. If the process is done clockwise, it is called direct, counterclock-wise - reverse... Because internal energy is a function of state, then in a circular process
The device in which heat is expended and work is obtained is called heat engine... All heat engines operate in a direct cycle consisting of various processes. A device operating in a reverse cycle is called refrigeration machine... Work is expended in the refrigerating machine, and as a result, heat is taken away from the cold body, i.e. additional cooling of this body occurs.
Consider carnot cycle for an ideal heat engine.It is assumed that the working fluid is an ideal gas, there is no friction. This cycle, consisting of two isotherms and two adiabats, is not really feasible, but it played a huge role in the development of thermodynamics and heat engineering and made it possible to analyze the efficiency of heat machines.
| 1-2 isothermal expansion |  | the heat transferred goes to gas work | |
2-3 adiabatic expansion  |  | gas does work due to internal energy | |
| 3-4 isothermal compression |  | external forces compress the gas, transferring heat to the environment | |
4-1 adiabatic compression  |  | work is done on the gas, its internal energy increases | |
( - from the equations of adiabats) | complete work per cycle; full on the chart ANDequal to the area covered by the curve 1-2-3-4-1 | ||
Thus, per cycle, the gas was informed Q 1 heat transferred to the refrigerator Q 2 warmth and got work AND.
From the obtained expression it follows that: 1) the efficiency is always less than one,
2) the efficiency does not depend on the type of working fluid, but only on the temperature of the heater and refrigerator, 3) to increase the efficiency, it is necessary to increase the heater temperature and reduce the temperature of the refrigerator. In modern engines, combustible mixtures are used as a heater - gasoline, kerosene, diesel fuel, etc., which have certain combustion temperatures. The environment usually serves as a refrigerator. Therefore, it is possible to really increase the efficiency only by reducing friction in various units of the engine and machine.
Topic 18 Question 1. AGGREGATE STATES OF SUBSTANCE
Molecules are complex systems of electrically charged particles. The bulk of the molecule and all of its positive charge are concentrated in nuclei, their dimensions are on the order of 10 - 15 - 10 - 14 m, and the size of the molecule itself, including the electron shell, is about 10 - 10 m. In general, the molecule is electrically neutral. The electric field of its charges is mainly concentrated inside the molecule and sharply decreases outside it. When two molecules interact, the forces of attraction and repulsive forces are simultaneously manifested, they depend differently on the distance between the molecules (see Fig. - dotted lines). The simultaneous action of intermolecular forces gives the dependence of the force Ffrom distance rbetween molecules, characteristic of two molecules, and atoms, and ions (solid curve). At large distances, the molecules practically do not interact; at very small distances, repulsive forces prevail. At distances equal to several diameters of molecules, attractive forces act. Distance r obetween the centers of two molecules, on which F \u003d 0,is the equilibrium position. Since force is associated with potential energy F \u003d -dE pot / dr, then integration will give the dependence of the potential energy on r(potential curve) .
The equilibrium position corresponds to the minimum potential energy - U min... For various molecules, the shape of the potential curve is similar, but the numerical values r oand U minare different and determined by the nature of these molecules.
In addition to the potential, the molecule also has kinetic energy. The minimum potential energy for each type of molecule is different, and the kinetic energy depends on the temperature of the substance ( E kin~ kT). Depending on the ratio between these energies, a given substance can be in one or another state of aggregation. For example, water can be solid (ice), liquid, and vapor.
Inert gases U min are small, so they become liquid at very low temperatures. Metals have large values U min therefore, they are in a solid state up to the melting point - this can be hundreds and thousands of degrees.
Question 3.
Wetting leads to the fact that the liquid on the walls of the vessel "creeps" along the wall, and its surface is curved. In a wide vessel, this curvature is almost imperceptible. In narrow tubes - capillaries - this effect can be observed visually. Due to the forces of surface tension, additional (compared to atmospheric) pressure is created Dpdirected towards the center of curvature of the liquid surface.
Additional pressure near curved liquid surface D p leads to the rise (when wetting) or lowering (when not wetting) the liquid in the capillaries.
In equilibrium, the additional pressure is equal to the hydrostatic pressure of the liquid column. From the Laplace formula for a circular capillary D p \u003d 2s /R, hydrostatic pressure r = r g h... Equating Dp = r, find h.
The formula shows that the smaller the capillary radius, the higher the rise (or fall) of the liquid.
The phenomenon of capillarity is extremely common in nature and technology. For example, the penetration of moisture from the soil into plants is carried out by lifting it through capillary channels. Capillary phenomena also include such a phenomenon as the movement of moisture along the walls of a room, leading to dampness. Capillarity plays a very important role in oil production. The pore sizes in the rock containing oil are extremely small. If the produced oil turns out to be non-wetting in relation to the rock, it will clog the tubules and will be very difficult to extract. By adding some substances to a liquid, even in a very small amount, it is possible to significantly change its surface tension. Such substances are called surfactants. radius vector in a rectangular Cartesian coordinate system:
Where -called point coordinates.
Trajectory (from Late Latin trajectories - referring to movement) is the line along which a body (material point) moves. The trajectory of movement can be straight (the body moves in one direction) and curvilinear, that is, mechanical movement can be rectilinear and curvilinear.
Linear trajectory in a given coordinate system, it is a straight line. For example, we can assume that the vehicle's trajectory on a flat road without turns is straight.
Curvilinear motion Is the movement of bodies in a circle, ellipse, parabola or hyperbola. An example of curved movement is the movement of a point on the wheel of a moving car, or the movement of a car in a bend.
The movement can be tricky. For example, the trajectory of the body at the beginning of the path can be rectilinear, then curved. For example, at the beginning of the journey, a car moves along a straight road, and then the road begins to "wind" and the car starts curving.
Way
Way Is the length of the trajectory. The path is a scalar value and is measured in SI units in meters (m). Path calculation is performed in many physics problems. Some examples will be discussed later in this tutorial.
Displacement vector
Displacement vector (or simply moving) Is a directed line segment connecting the initial position of the body with its subsequent position (Fig.1.1). Displacement is a vector quantity. The displacement vector is directed from the start point of the movement to the end point.
Displacement vector modulus (that is, the length of the segment that connects the start and end points of the movement) can be equal to the distance traveled or less than the distance traveled. But the absolute value of the displacement vector can never be larger than the distance traveled.
The magnitude of the displacement vector is equal to the traveled path when the path coincides with the path (see the Trajectory and Path sections), for example, if the car moves from point A to point B along a straight road. The modulus of the displacement vector is less than the distance traveled when the material point moves along a curved trajectory (Fig. 1.1).
Figure: 1.1. Displacement vector and path traveled.
In fig. 1.1:
Another example. If the car drives in a circle once, it turns out that the starting point of movement coincides with the end point of movement, and then the displacement vector will be equal to zero, and the distance traveled will be equal to the circumference. Thus, the path and movement is two different concepts.
Vector addition rule
The displacement vectors are added geometrically according to the vector addition rule (triangle rule or parallelogram rule, see Fig. 1.2).
Figure: 1.2. Addition of displacement vectors.
Figure 1.2 shows the rules for adding vectors S1 and S2:
a) Addition according to the triangle rule
b) Addition according to the parallelogram rule
Displacement vector projections
When solving problems in physics, the projection of the displacement vector on the coordinate axes is often used. The projections of the displacement vector on the coordinate axes can be expressed in terms of the difference between the coordinates of its end and origin. For example, if a material point has moved from point A to point B, then the displacement vector (Fig. 1.3).
Let's choose the OX axis so that the vector lies with this axis in the same plane. Drop the perpendiculars from points A and B (from the start and end points of the displacement vector) to the intersection with the OX axis. Thus, we get the projections of points A and B on the X-axis. Let's designate the projections of points A and B, respectively, A x and B x. The length of the segment A x B x on the OX axis - this is displacement vector projection on the OX axis, that is
S x \u003d A x B x
IMPORTANT!
Let me remind you for those who do not know mathematics very well: do not confuse the vector with the projection of the vector onto any axis (for example, S x). A vector is always denoted by a letter or several letters with an arrow above it. In some electronic documents, the arrow is not put, as this can cause difficulties when creating an electronic document. In such cases, be guided by the content of the article, where the word "vector" can be written next to the letter, or in some other way they indicate to you that this is a vector, and not just a segment.
Figure: 1.3. Displacement vector projection.
The projection of the displacement vector onto the OX axis is equal to the difference between the coordinates of the end and the beginning of the vector, that is
S x \u003d x - x 0 The projections of the displacement vector on the axes OY and OZ are similarly determined and written: S y \u003d y - y 0 S z \u003d z - z 0
Here x 0, y 0, z 0 - initial coordinates, or coordinates of the initial position of the body (material point); x, y, z - end coordinates, or coordinates of the subsequent position of the body (material point).
The projection of the displacement vector is considered positive if the direction of the vector and the direction of the coordinate axis coincide (as in Figure 1.3). If the direction of the vector and the direction of the coordinate axis do not coincide (opposite), then the projection of the vector is negative (Fig. 1.4).
If the displacement vector is parallel to the axis, then the modulus of its projection is equal to the modulus of the Vector itself. If the displacement vector is perpendicular to the axis, then the modulus of its projection is zero (Fig. 1.4).
Figure: 1.4. Displacement vector projection modules.
The difference between the subsequent and initial values \u200b\u200bof some quantity is called the change in this quantity. That is, the projection of the displacement vector onto the coordinate axis is equal to the change in the corresponding coordinate. For example, for the case when the body moves perpendicular to the X axis (Fig. 1.4), it turns out that the body DOES NOT MOVE relative to the X axis. That is, the movement of the body along the X axis is zero.
Consider an example of body motion on a plane. The initial position of the body is point A with coordinates x 0 and y 0, that is, A (x 0, y 0). The final position of the body is point B with coordinates x and y, that is, B (x, y). Let's find the body movement module.
From points A and B, we omit the perpendiculars on the coordinate axes OX and OY (Fig. 1.5).
Figure: 1.5. Body movement on a plane.
Let's define the projections of the displacement vector on the OX and OY axes:
S x \u003d x - x 0 S y \u003d y - y 0
In fig. 1.5 it can be seen that triangle ABC is rectangular. From this it follows that when solving the problem, one can use pythagorean theorem, with which you can find the modulus of the displacement vector, since
AC \u003d s x CB \u003d s y
By the Pythagorean theorem
S 2 \u003d S x 2 + S y 2
Where can you find the modulus of the displacement vector, that is, the length of the body path from point A to point B:
And finally, I suggest you consolidate the knowledge gained and calculate a few examples at your discretion. To do this, enter any numbers in the coordinate fields and click the CALCULATE button. Your browser must support JavaScript scripts and script execution must be enabled in your browser settings, otherwise the calculation will not be performed. In real numbers, the integer and fractional parts must be separated by a dot, for example, 10.5.
Weight Is a property of the body that characterizes its inertia. Under the same influence from the surrounding bodies, one body can quickly change its speed, while the other under the same conditions - much more slowly. It is customary to say that the second of these two bodies is more inert, or, in other words, the second body has a greater mass.
If two bodies interact with each other, then as a result the speed of both bodies changes, that is, in the process of interaction, both bodies acquire accelerations. The ratio of the accelerations of the two given bodies turns out to be constant under any impacts. In physics, it is accepted that the masses of interacting bodies are inversely proportional to the accelerations acquired by the bodies as a result of their interaction.
Power Is a quantitative measure of the interaction of bodies. Force is the cause of the change in body speed. In Newtonian mechanics, forces can have a different physical nature: friction force, gravity force, elastic force, etc. Force is vector quantity... The vector sum of all forces acting on the body is called resultant force.
To measure forces, you must set standard of strength and way of comparison other forces with this standard.
A spring stretched to a certain specified length can be taken as a standard of force. Power module F 0, with which this spring, at a fixed tension, acts on a body attached to its end, is called the standard of strength... The way to compare other forces with the standard is as follows: if the body under the action of the measured force and the reference force remains at rest (or moves uniformly and rectilinearly), then the forces are equal in modulus F = F 0 (fig. 1.7.3).
If the measured force F more (in modulus) than the reference force, then two reference springs can be connected in parallel (Fig. 1.7.4). In this case, the measured force is 2 F 0. The forces 3 can be measured similarly F 0 , 4F 0, etc.
Measurement of forces less than 2 F 0 can be performed according to the scheme shown in Fig. 1.7.5.
The reference force in the International System of Units is called newton (H).
A force of 1 N imparts an acceleration of 1 m / s 2 to a body weighing 1 kg
In practice, there is no need to compare all measured forces with a standard. To measure the forces, use springs calibrated as described above. These calibrated springs are called dynamometers ... The force is measured by the tension of the dynamometer (Fig. 1.7.6).
Newton's laws of mechanics -three laws underlying the so-called. classical mechanics. Formulated by I. Newton (1687). The first law: "Every body continues to be held in its state of rest or uniform and rectilinear motion, until and since it is forced by the applied forces to change this state." The second law: "The change in the momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts." The third law: "Action is always equal and opposite opposition, otherwise, the interactions of two bodies against each other are equal and directed in opposite directions." 1.1. Law of Inertia (Newton's First Law)
: a free body, which is not acted upon by forces from other bodies, is in a state of rest or uniform rectilinear motion (the concept of velocity here is applied to the center of mass of a body in the case of non-translational motion). In other words, inertia is inherent in bodies (from the Latin inertia - “inactivity”, “inertia”), that is, the phenomenon of speed conservation, if external influences on them are compensated. Reference frames in which the law of inertia is fulfilled are called inertial reference frames (IFR). For the first time, the law of inertia was formulated by Galileo Galilei, who, after many experiments, concluded that no external reason is needed for a free body to move at a constant speed. Prior to this, a different point of view (dating back to Aristotle) \u200b\u200bwas generally accepted: a free body is at rest, and a constant force must be applied to move at a constant speed. Subsequently, Newton formulated the law of inertia as the first of his three famous laws. Galileo's principle of relativity: in all inertial reference frames, all physical processes proceed in the same way. In a frame of reference brought to a state of rest or uniform rectilinear motion relative to an inertial frame of reference (conventionally - “at rest”) all processes proceed in the same way as in a resting frame. It should be noted that the concept of an inertial reference system is an abstract model (some ideal object considered instead of a real object. Examples of an abstract model are an absolutely rigid body or a weightless thread), real reference frames are always associated with an object and the correspondence of the actually observed motion of bodies in such systems the calculation results will be incomplete. 1.2 Law of motion
- a mathematical formulation of how a body moves or how a more general movement occurs. In the classical mechanics of a material point, the law of motion represents three dependences of three spatial coordinates on time, or the dependence of one vector quantity (radius vector) on time, type. The law of motion can be found, depending on the problem, either from the differential laws of mechanics, or from the integral ones. Law of energy conservation
- the basic law of nature, which states that the energy of a closed system is conserved in time. In other words, energy cannot arise from nothing and cannot disappear into nowhere, it can only pass from one form to another. The law of conservation of energy is found in various branches of physics and manifests itself in the conservation of various types of energy. For example, in classical mechanics, the law manifests itself in the conservation of mechanical energy (the sum of potential and kinetic energies). In thermodynamics, the law of conservation of energy is called the first law of thermodynamics and speaks of the conservation of energy together with thermal energy. Since the law of conservation of energy does not refer to specific quantities and phenomena, but reflects a general, applicable everywhere and always, regularity, it is more correct to call it not a law, but the principle of conservation of energy. A special case - The law of conservation of mechanical energy - the mechanical energy of a conservative mechanical system is preserved in time. Simply put, in the absence of forces such as friction (dissipative forces), mechanical energy does not arise from nothing and cannot disappear anywhere. Ek1 + En1 \u003d Ek2 + En2 The law of conservation of energy is an integral law. This means that it consists of the action of differential laws and is a property of their combined action. For example, it is sometimes said that the impossibility of creating a perpetual motion machine is due to the law of conservation of energy. But this is not the case. In fact, in each project of a perpetual motion machine, one of the differential laws is triggered and it is he who makes the engine inoperative. The law of conservation of energy simply generalizes this fact. According to Noether's theorem, the law of conservation of mechanical energy is a consequence of the homogeneity of time. 1.3. The law of conservation of momentum (Law of conservation of the amount of motion, 2nd Newton's law)
states that the sum of the momenta of all bodies (or particles) of a closed system is a constant value. From Newton's laws, it can be shown that when moving in empty space, the momentum is conserved in time, and in the presence of interaction, the rate of its change is determined by the sum of the applied forces. In classical mechanics, the momentum conservation law is usually derived as a consequence of Newton's laws. However, this conservation law is also true in cases where Newtonian mechanics is not applicable (relativistic physics, quantum mechanics). Like any of the conservation laws, the momentum conservation law describes one of the fundamental symmetries, the homogeneity of space Newton's third law
explains what happens to two interacting bodies. Take for example a closed system consisting of two bodies. The first body can act on the second with some force F12, and the second - on the first with the force F21. How do the forces compare? Newton's third law states: the force of action is equal in magnitude and opposite in direction to the force of reaction. Let us emphasize that these forces are applied to different bodies, and therefore are not compensated at all. The law itself: Bodies act on each other with forces directed along the same straight line, equal in magnitude and opposite in direction:. 
1.4. Forces of inertia
Newton's laws, strictly speaking, are valid only in inertial reference frames. If we honestly write the equation of motion of a body in a non-inertial frame of reference, then it will look different from Newton's second law. However, often, to simplify the consideration, some fictitious “force of inertia” is introduced, and then these equations of motion are rewritten in a form very similar to Newton's second law. Mathematically, everything is correct (correct) here, but from the point of view of physics, a new fictitious force cannot be considered as something real, as a result of some real interaction. Let us emphasize once again: “the force of inertia” is just a convenient parametrization of how the laws of motion differ in inertial and non-inertial frames of reference. 1.5. Viscosity law
Newton's law of viscosity (internal friction) is a mathematical expression that relates the stress of internal friction τ (viscosity) and the change in the velocity of the medium v \u200b\u200bin space (deformation rate) for fluid bodies (liquids and gases): where the value of η is called the coefficient of internal friction or dynamic coefficient of viscosity (the CGS unit is poise). The kinematic coefficient of viscosity is the value μ \u003d η / ρ (the CGS unit is Stokes, ρ is the density of the medium). Newton's law can be obtained analytically by means of physical kinetics, where viscosity is usually considered simultaneously with thermal conductivity and the corresponding Fourier law for thermal conductivity. In the kinetic theory of gases, the coefficient of internal friction is calculated by the formula 
Where< u > is the average speed of the thermal motion of molecules, λ is the average free path.
a vector connecting the initial position of the body to its subsequent position. and got the best answer
Answer from Winter37 [guru]
Mechanical movement is a change in the position of a body in space over time relative to other bodies.
Of all the various forms of motion of matter, this type of motion is the simplest.
For example: moving the clock hand on the dial, people are walking, tree branches swaying, butterflies fluttering, an airplane is flying, etc.
Determining the position of the body at any given time is the main task of mechanics.
The movement of a body in which all points move in the same way is called translational.
A material point is a physical body, the dimensions of which in the given conditions of motion can be neglected, assuming that all of its mass is concentrated in one point.
A trajectory is a line that a material point describes as it moves.
The path is the length of the trajectory of the material point.
Displacement is a directed line segment (vector) that connects the initial position of the body with its subsequent position.
A reference system is: a reference body, a coordinate system associated with it, and an instrument for timing.
An important feature of the fur. motion is its relativity.
Relativity of motion is the movement and speed of a body relative to different reference systems are different (for example, a person and a train). The speed of the body relative to the stationary coordinate system is equal to the geometric sum of the speeds of the body relative to the moving system and the speed of the moving coordinate system relative to the stationary one. (V1 is the speed of a person in the train, V0 is the speed of the train, then V \u003d V1 + V0).
The classical law of addition of velocities is formulated as follows: the speed of movement of a material point in relation to the reference frame taken as a stationary one is equal to the vector sum of the velocities of a point in a moving system and the speed of a moving system relative to a stationary one.
The characteristics of mechanical motion are related to each other by the basic kinematic equations.
s \u003d v0t + at2 / 2;
v \u003d v0 + at.
Suppose that the body moves without acceleration (the plane is on the route), its speed does not change for a long time, a \u003d 0, then the kinematic equations will have the form: v \u003d const, s \u003d vt.
Movement in which the speed of the body does not change, that is, the body moves by the same amount for any equal intervals of time is called uniform rectilinear motion.
During the launch, the rocket speed increases rapidly, that is, the acceleration a\u003e 0, a \u003d\u003d const.
In this case, the kinematic equations look like this: v \u003d v0 + at, s \u003d V0t + at2 / 2.
With this movement, the speed and acceleration have the same directions, and the speed changes in the same way for any equal time intervals. This type of movement is called uniformly accelerated.
When braking the car, the speed decreases equally for any equal time intervals, the acceleration is less than zero; since the speed decreases, the equations take the form: v \u003d v0 + at, s \u003d v0t - at2 / 2. This motion is called equally slow.