Love

A vector connecting the initial position. A displacement is a vector connecting the start and end points of the trajectory. Basic concepts of kinematics

Weight is a property of a body that characterizes its inertia. With the same impact from the surrounding bodies, one body can quickly change its speed, and the other, under the same conditions, much more slowly. It is customary to say that the second of these two bodies has more inertia, or, in other words, the second body has more mass.

If two bodies interact with each other, then as a result, the speed of both bodies changes, i.e., in the process of interaction, both bodies acquire accelerations. The ratio of the accelerations of two given bodies is constant under any impact. It is accepted in physics that the masses of interacting bodies are inversely proportional to the accelerations acquired by the bodies as a result of their interaction.

Strength is a quantitative measure of the interaction of bodies. Force is the cause of a change in the speed of a body. In Newtonian mechanics, forces can have a different physical nature: friction force, gravity force, elastic force, etc. The force is vector quantity. The vector sum of all forces acting on a body is called resultant force.

To measure forces, you need to install strength standard And comparison method other forces with this standard.

As a force standard, you can take a spring stretched to some given length. Force module F 0 , with which this spring, under a fixed tension, acts on a body attached to its end, is called 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 absolute value F = F 0 (Fig. 1.7.3).

If the measured force F is greater (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 . 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 tells a body weighing 1 kg an acceleration of 1 m / s 2

In practice, there is no need to compare all measured forces with the standard. To measure 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). First law: "Every body continues to be held in its state of rest or uniform and rectilinear motion, until and insofar as it is forced by applied forces to change this state." The second law: "The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts." The third law: “There is always an equal and opposite reaction to an action, 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 affected by forces from other bodies, is at rest or uniform rectilinear motion (the concept of speed here applies to the center of mass of the body in the case of non-translational motion). In other words, bodies are characterized by inertia (from Latin inertia - “inactivity”, “inertia”), that is, the phenomenon of maintaining speed if external influences on them are compensated. Frames of reference in which the law of inertia is fulfilled are called inertial frames of reference (ISR). The law of inertia was first formulated by Galileo Galilei, who, after many experiments, concluded that no external cause is needed for a free body to move at a constant speed. Prior to this, a different point of view (dating back to Aristotle) was generally accepted: a free body is at rest, and in order to move at a constant speed, a constant force must be applied. Subsequently, Newton formulated the law of inertia as the first of his three famous laws. Galileo's principle of relativity: in all inertial frames of reference, 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 (conditionally “at rest”), all processes proceed in exactly the same way as in a frame at rest. It should be noted that the concept of an inertial frame of reference is an abstract model (some ideal object considered instead of a real object. An absolutely rigid body or a weightless thread serve as examples of an abstract model), real frames of reference are always associated with some object and the correspondence of the actually observed movement of bodies in such systems with the results of the calculations will be incomplete. 1.2 Law of motion - a mathematical formulation of how a body moves or how a movement of a more general form occurs. In the classical mechanics of a material point, the law of motion is 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 task, either from the differential laws of mechanics or from integral ones. Law of energy conservation - the basic law of nature, which consists in the fact 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 in total with thermal energy. Since the law of conservation of energy does not refer to specific quantities and phenomena, but reflects a general pattern that is applicable everywhere and always, 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 conserved 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+Ep1=Ek2+Ep2 The law of conservation of energy is an integral law. This means that it is made up 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 it's not. In fact, in every project of a perpetual motion machine, one of the differential laws is triggered and it is he who makes the engine inoperable. 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. Law of conservation of momentum (Law of conservation of momentum 2nd Newton's law) asserts 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, 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 law of conservation of momentum is usually derived as a consequence of Newton's laws. However, this conservation law is also true in cases where Newtonian mechanics is inapplicable (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 are the forces related? Newton's third law states that the action force is equal in magnitude and opposite in direction to the reaction force. We 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 frames of reference. If we honestly write down the equation of motion of a body in a non-inertial frame of reference, then it will differ in appearance from Newton's second law. However, often, to simplify the consideration, some fictitious "inertia force" is introduced, and then these equations of motion are rewritten in a form very similar to Newton's second law. Mathematically, everything here is correct (correct), 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. We emphasize once again: “inertial force” 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 in space (strain rate) for fluid bodies (liquids and gases): where the value η is called the coefficient of internal friction or the dynamic coefficient of viscosity (CGS unit is poise). The kinematic coefficient of viscosity is the value μ = η / ρ (the CGS unit is Stokes, ρ is the density of the medium). Newton's law can be obtained analytically by methods 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 thermal motion of molecules, λ is the mean free path.

The projection is considered positive if (a x > 0) from the projection of the beginning of the vector to the projection of its end, you need to go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x 0) from the projection of the beginning of the vector to the projection of its end must go in the direction of the axis. Otherwise, the projection of the vector (a x
Do we pay for the journey or transportation when traveling in a taxi? The ball fell from a height of 3 m, bounced off the floor and was caught at a height of 1 m. Find the path and move the ball. The cyclist moves in a circle with a radius of 30 m. What is the path and displacement of the cyclist for half a turn? For a full turn?

§ § 2.3 answer the questions at the end of the paragraph. Ex. 3, p.15 the trajectory ABSD of the movement of a point from A to D is shown. Find the coordinates of the points of the beginning and end of the movement, the distance traveled, the displacement, the projection of the displacement on the coordinate axes. Solve the problem (optional): The boat went to the northeast for 2 km, and then to the north for another 1 km. Find the displacement (S) and its modulus (S) by geometric construction.

Definition 1

body trajectory- this is a line that was described by a material point when moving from one point to another over time.

There are several types of motions and trajectories of a rigid body:

progressive;
rotational, that is, movement in a circle;
flat, that is, moving along a plane;
spherical, characterizing the movement on the surface of the sphere;
free, in other words, arbitrary.

Picture 1 . Determination of a point using coordinates x = x (t) , y = y (t) , z = z (t) and radius vector r → (t) , r 0 → is the radius vector of the point at the initial time

The position of a material point in space at any time can be set using the law of motion, defined in a coordinate way, through the dependence of coordinates on time x = x(t) , y = y(t) , z = z(t) or from the time of the radius vector r → = r → (t) drawn from the origin to the given point. This is shown in Figure 1.

Definition 2

S → = ∆ r 12 → = r 2 → - r 1 → is a directed straight line segment connecting the initial point with the end point of the body trajectory. The value of the path traveled l is equal to the length of the trajectory traveled by the body in a certain period of time t.

Figure 2. Distance traveled l and the displacement vector s → during the curvilinear motion of the body, a and b are the starting and ending points of the path, accepted in physics

Definition 3

Figure 2 shows that when the body moves along a curvilinear trajectory, the module of the displacement vector is always less than the distance traveled.

The path is a scalar value. Considered a number.

The sum of two consecutive movements from point 1 to point 2 and from current 2 to point 3 is the movement from point 1 to point 3, as shown in figure 3.

Picture 3 . The sum of two consecutive movements ∆ r → 13 = ∆ r → 12 + ∆ r → 23 = r → 2 - r → 1 + r → 3 - r → 2 = r → 3 - r → 1

When the radius vector of a material point at a certain time t is r → (t), at the moment t + ∆ t is r → (t + ∆ t) , then its displacement ∆ r → in time ∆ t is equal to ∆ r → = r → (t + ∆t) - r → (t) .

The displacement ∆ r → is considered to be a function of time t: ∆ r → = ∆ r → (t) .

Example 1

By condition, a moving aircraft is given, shown in Figure 4. Determine the type of trajectory of the point M.

Picture 4

Solution

It is necessary to consider the reference system I, called "Aircraft" with the trajectory of the point M in the form of a circle.

Reference system II "Earth" will be set with the trajectory of the existing point M in a spiral.

Example 2

Given a material point that moves from A to B. The value of the radius of the circle R = 1 m. Find S , ∆ r → .

Solution

While moving from A to B, the point travels a path that is equal to half the circle written by the formula:

Substitute the numerical values and get:

S \u003d 3.14 1 m \u003d 3.14 m.

The displacement ∆ r → in physics is considered to be a vector connecting the initial position of the material point with the final one, that is, A with B.

Substituting the numerical values, we calculate:

∆ r → = 2 R = 2 1 = 2 m.

Answer: S = 3, 14 m; ∆r → = 2 m.

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Question 1. Radius vector. Displacement vector.

- radius vector is the vector drawn from the origin ABOUT to the considered point M.

- moving(or changing the radius vector) is the vector connecting the start and end of the path.

radius vector in rectangular Cartesian coordinates:

Where - call point coordinates.

Question 2. The speed of movement. Average and instantaneous speeds.

Travel speed(vector) - shows how the displacement changes per unit of time.

Medium: Instant:

The instantaneous velocity is always directed tangentially to the trajectory,

and the middle one coincides with the displacement vector.

Projection: Module:

Question 3. Path. Its connection with the speed module.

S– way is the length of the trajectory (scalar value, > 0).

S is the area of the figure bounded by the curve v(t) and the straight lines t 1 and t 2 .

Question 4. Acceleration. Acceleration module.

Acceleration - in meaning - shows how the speed changes per unit of time.

Projection: Module: Mean:

Question 5. Uneven movement of a point along a curved path.

If the point moves along a curved path, then it is advisable to decompose the acceleration into components, one of which is tangentially directed 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 direction, - in magnitude.

Where r - radius of curvature.

A point moving along a curved path always has normal acceleration, and tangential acceleration 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 equally 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 a cinematography. 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. ROTATION KINEMATICS.

Question 1. Kinematic characteristics of rotational motion.

angular displacement- 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 uniform deceleration (-) of rotational motion.

(4, 5, 6) Topic 4. KINEMATICS ATT.

Question 1. Definition of ATT. Translational and rotational movements of ATT.

ATT A body whose deformations can be neglected under the conditions of a given problem is called.

All ATT movements can be decomposed into translational and rotational, relative to some instantaneous axis. Progressive movement - this is a movement in which a straight line drawn through any two points of the body moves parallel to itself. In translational motion, all points of the body make the same movement. rotational movement- this is a movement in which all points of the body move along circles, the centers of which lie on the same straight line, called the axis of rotation.

As a kinematic equation for the rotational motion of the ATT, 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 some point of the body (if the axis is fixed). That is, fundamentally, the kinematic equations of motion for a point and ATT do not differ.

Topic 5. NEWTON'S LAWS.

Topic 6. LAW OF CONSERVATION OF MOMENTUM.

Topic 7. WORK. POWER. ENERGY.

Question 7. Conservation laws as applied to an absolutely elastic impact of two balls.

Absolutely elastic impact is the impact at which the kinetic energy of the entire system is conserved.

Topic 10. FORCE FIELDS

Question 3. Reducing the length.

l 0 is the length of the rod in the system relative 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¢). because and find a connection between l And l 0: .

Thus, it follows from SRT that the dimensions of moving bodies should decrease in the direction of their movement, 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 but cro from the scopic point of view, it is a gas for which the gas laws are satisfied ( pV = const, p/T = const, V/T = const). FROM m And cro From the scopic point of view, it is a gas for which one can neglect: 1) the interaction of molecules with each other and 2) the own volume of gas molecules compared to the volume of the vessel in which the gas is located.

The equation that relates the state parameters to each other is called equation of state gas. One of the simplest equations of state is

( ; ; ) the Mendeleev-Clapeyron equation.

(n- concentration, k- Boltzmann constant) - the ideal gas equation of state in a different form.

Topic 15. BASIC CONCEPTS OF THERMODYNAMICS

Question 1. Basic concepts. Reversible and irreversible processes.

Reversible process - it is such a process of transition of the system from the state BUT into a state IN, at which the reverse transition from IN to BUT through the same intermediate states and at the same time no changes occur in the surrounding bodies. The system is called isolated if it does not exchange energy with the environment. On the graph, states are indicated by dots, and processes by lines.

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. Quantities whose values in a given state depend on previous processes are called process functions - it's warmth Q and work A, their change is often denoted as dQ, dA or . ( d- Greek letter - delta)

Work And heat- these are two forms of energy transfer from one body to another. When work is performed, 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 movement of molecules.

TO internal energy include: 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 the 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 the nucleus in an atom , 5) the energy of interaction of protons and neutrons inside the nucleus of an atom. 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 energy of interaction of nucleons in the nucleus is ~ 10 MeV. Therefore, these interactions are considered separately.

Internal energy of an ideal gas is the kinetic energy of the thermal motion of its molecules. It depends only on the temperature of the gas. Its change has the same expression for all processes in ideal gases and depends only on the initial and final temperatures of the gas. is the internal energy of an ideal gas.

Topic 16.

Question 1. Entropy

The second law of thermodynamics, like the first law, 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 ntropium - S- one of the most important thermodynamic functions that characterizes the state or possible changes in the state of matter - this is a multifaceted concept.

1)Entropy is a state function. The introduction of such quantities is valuable in that the change in the state function is the same for any processes, so a complex real process can be replaced by "fictional" simple processes. For example, the real process of the transition of the system from state A to state B (see Fig.) can be replaced by two processes: isochoric A®C and isobaric C®B.

Entropy is defined as follows.

For reversible processes in ideal gases, one can obtain formulas for calculating the entropy in various processes. Express dQ from the I beginning and substitute into the expression for dS .

general expression for entropy change in reversible processes.

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 law of thermodynamics for a reversible isothermal process, taking into account that dQ=T×dS and express the work dA
the thermodynamic function is called the free energy the quantity is called the bound energy
From the formulas, we can conclude that not all of the internal energy of the system can be converted into 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 the disorder of a system

Let us introduce the concept of thermodynamic probability. Let us have a box divided into n compartments. Moves freely in all compartments in the box N molecules. In the first compartment will be N 1 molecules, in the second compartment N 2 molecules...

in n-th compartment - N n molecules. Number of ways w that can be distributed N molecules according to n states (compartments) is called thermodynamic probability. In other words, thermodynamic probability shows how many micro distributions, you can get this macro distribution It is calculated by the formula:

For 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=3(three molecules) and n=3(three compartments), the molecules are considered distinguishable.

In the first case, macrodistribution is a uniform distribution of molecules in compartments; it can be carried out by 6 microdistributions. The probability of such a distribution is the highest. An even distribution can be called "disorder" (by analogy with scattered things in a room). In the latter case, when the molecules are collected in only one compartment, the probability is the smallest. Simply put, we know from everyday observations that the air molecules are more or less evenly distributed in a room, and it is almost completely unbelievable that all the molecules would gather 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 a system.

Question 6. Now we can formulate the II law of thermodynamics.

1) For any processes occurring in a thermally insulated system, the entropy of the system cannot decrease:

The sign "=" refers to reversible processes, the sign ">" - to irreversible (real) processes. In non-closed 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 should have the same energy. Hence the conclusion was made about the tendency of our Universe to heat death. "The entropy of the world tends to a maximum" (Clausius). Since the laws of thermodynamics are derived on the basis of 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 thermal reservoir ”(Thomson, Planck)

There must also be a body to which it “will have to” give up part of the heat. Simply taking heat away from some body and converting it into work is impossible 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 in order to D.S. = 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 a process in which the system, after going through a series of states, returns to its original state. If the process is carried out clockwise, it is called direct, counterclock-wise - reverse. Because internal energy is a state function, then in a circular process

A device that expends heat and produces work is called thermal machine. All heat engines operate in a direct cycle consisting of various processes. A device that works in reverse is called refrigeration machine. Work is expended in the refrigeration machine, and as a result, heat is taken away from the cold body, i.e. there is additional cooling of this body.

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 coefficient of performance (COP) of heat engines.

1-2 isothermal expansion		the heat supplied is used to work the gas
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 adiabatic equations)	total work per cycle; full on chart BUT equal to the area covered by the curve 1-2-3-4-1

Thus, per cycle, the gas was reported Q1 heat transferred to the refrigerator Q2 warmth and work received BUT.

It follows from the resulting expression that: 1) the efficiency is always less than unity,

2) The efficiency does not depend on the type of working fluid, but only on the temperature of the heater and refrigerator, 3) in order to increase the efficiency, it is necessary to increase the temperature of the heater and reduce the temperature of the refrigerator. In modern engines, combustible mixtures are used as a heater - gasoline, kerosene, diesel fuel, etc., having certain combustion temperatures. The refrigerator is most often the environment. Consequently, it is possible to really increase the efficiency only by reducing friction in various parts 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 its positive charge are concentrated in the nuclei, their dimensions are about 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 decreases sharply outside it. When two molecules interact, both attractive 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 F from distance r between molecules, which is also 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 predominate. At distances equal to several molecular diameters, attractive forces act. Distance r o between the centers of two molecules, on which F=0, is the position of balance. Since force is related to potential energy F=-dE sweat /dr, then integration will give the dependence of the potential energy on r(potential curve) . The equilibrium position corresponds to the minimum potential energy - Umin. For different molecules, the shape of the potential curve is similar, but the numerical values r o And Umin are different and determined by the nature of these molecules.

In addition to potential, the molecule also has kinetic energy. Each type of molecule has its own minimum potential energy, and the kinetic energy depends on the temperature of the substance ( Ye kin~ kT). Depending on the ratio between these energies, a given substance can be in a particular state of aggregation. For example, water can be in a solid state (ice), liquid and vapor.

For inert gases Umin small, so they go into a liquid state at very low temperatures. Metals are large Umin therefore, they are in a solid state up to the melting point - it can be hundreds and thousands of degrees.

Question 3.

Wetting leads to the fact that on the walls of the vessel the liquid, as it were, "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, an additional (compared to atmospheric) pressure is created Dr directed towards the center of curvature of the liquid surface.

Additional pressure near a curved liquid surface D p leads to the rise (when wetted) or lowering (when not wetted) of the liquid in the capillaries.

At equilibrium, the additional pressure is equal to the hydrostatic pressure of the liquid column. From the Laplace formula for a circular capillary D p = 2s /R, hydrostatic pressure R = r g h. Equating Dr = R, find h.

It can be seen from the formula that the smaller the radius of the capillary, 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 the 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 extracted oil turns out to be non-wetting in relation to the rock, then it will clog the tubules, and it will be very difficult to extract it. By adding certain substances to a liquid, even in a very small amount, its surface tension can be significantly changed. Such substances are called surfactants. radius vector in rectangular Cartesian coordinates:

Where - call point coordinates.