The concept of a closed physical system. A closed system is a system of bodies for which the resultant of external forces is zero. Closed and open systems
Force is a vector physical quantity. characterizing the interaction of bodies and being a measure of this interaction. The reason for the change in the nature of the movement of the body.
Properties:
Forces add up according to the parallelogram rule
Any force can be decomposed into its components, and repeatedly
Force can be a function of speed and time
Measured in newtons.
29. Potential (conservative) forces. Potential energy.
Canned power - forces, the work of a cat on any closed circuit is 0 (strand force, elastic force, electrostatic force). Unconserved force is the force of friction. Canned force can be defined in the following ways: 1) forces whose work on any closed path is 0; 2) forces whose work does not depend on the path along which the particle moves from one position to another. In the field of canned forces, the concept of energy potential is introduced as a function of coordinates. In Sist where only canned power is active, mechanical energy remains constant. Sweat energy characterizes a hidden reserve of movement, which can then manifest itself in the form of kin energy.
30. Closed and open systems.
Closed systems- syst, the cat is not affected by external forces or their action can be neglected. The concept of a closed system is an idealization, it is applicable to real systems of bodies in cases where the internal forces of interaction between the bodies of the system are much greater than the external forces.
31. Conservation laws in closed systems
In a closed system, 3 conservation laws are fulfilled: the law of momentum conservation p=∑pi=Const, angular momentum L=∑Li=Const, and total energy E=Emex+Einternal=Const. When a system of bodies cannot be considered closed, particular conservation laws are applicable, subject to certain additional conditions
32. Connection of conservation laws with the properties and time of space
The basis of energy conservation is the homogeneity of time - the ambiguity of all moments of time. The conservation of momentum is based on the homogeneity of space - the sameness of the properties of the space of all points. The conservation of angular momentum is based on the isotropy of space - the same properties of space in all directions.
33. The law of conservation of momentum in closed and open systems
The momentum of the closed system of material points remains constant. The momentum remains constant even for an open system if the sum of the external forces is zero. For a closed system, р=mv=const - therefore, the center of mass of a closed system either moves in a straight line and uniformly, or remains stationary
34 .Law of conservation of angular momentum in closed and open systems
The angular momentum of the closed point system remains constant. When the sum of the moments of external forces about some axis is equal to 0, the moment imp syst refers to this axis remains constant.
35. Law of conservation of mechanical and total energy
The total mechanical energy of the source of bodies, on which only conservative forces act, remains constant.
The total mechanical energy of a closed system of bodies, between which only conservative forces act, remains constant .
In a closed system, energy does not disappear, but passes from one form to another. In a closed system where only conserved forces act, the law of conservation of energy is fulfilled. 
The system is called closed
open (E) (A), (R) and (P) flows
Law of conservation of momentum
Law of conservation of momentum is formulated like this:
if the sum of external forces acting on the bodies of the system is equal to zero, then the momentum of the system is conserved.
Bodies can only exchange impulses, while the total value of the impulse does not change. It is only necessary to remember that the vector sum of the impulses is preserved, and not the sum of their modules.
Law of conservation of momentum (Law of conservation of momentum) states that the vector sum of the momenta of all bodies (or particles) of a closed system is a constant value.
In classical mechanics, the law of conservation of momentum is usually derived as a consequence of Newton's laws. 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.
Like any of the fundamental conservation laws, the momentum conservation law describes one of the fundamental symmetries, - homogeneity of space.
When bodies interact, the momentum of one body can be partially or completely transferred to another body. If a system of bodies is not affected by external forces from other bodies, then such a system is called closed.
In a closed system, the vector sum of the impulses of all bodies included in the system remains constant for any interactions of the bodies of this system with each other.
This fundamental law of nature is called the law of conservation of momentum. It is a consequence of Newton's second and third laws.
Consider any two interacting bodies that are part of a closed system.
The forces of interaction between these bodies will be denoted by and According to Newton's third law If these bodies interact during time t, then the impulses of the interaction forces are identical in absolute value and directed in opposite directions: Let's apply Newton's second law to these bodies:
where and are the momenta of the bodies at the initial moment of time, and are the momenta of the bodies at the end of the interaction. From these ratios it follows:
This equality means that as a result of the interaction of two bodies, their total momentum has not changed. Considering now all possible pair interactions of bodies included in a closed system, we can conclude that the internal forces of a closed system cannot change its total momentum, i.e., the vector sum of the momenta of all bodies included in this system.
Fig.1
Under these assumptions, the conservation laws have the form
(1)
(2)
Having made the corresponding transformations in expressions (1) and (2), we obtain
(3)
(4)
where
(5)
Solving equations (3) and (5), we find
(6)
(7)
Let's look at a few examples.
1. When v 2=0 
(8) 
(9)
Let us analyze expressions (8) in (9) for two balls of different masses:
a) m 1 \u003d m 2. If the second ball hung motionless before the impact ( v 2=0) (Fig. 2), then after the impact the first ball will stop ( v 1 "=0), and the second one will move with the same speed and in the same direction as the first ball moved before the impact ( v 2 "=v 1);
Fig.2
b) m 1 >m 2. The first ball continues to move in the same direction as before the impact, but at a slower speed ( v 1 "<v 1). The speed of the second ball after the impact is greater than the speed of the first after the impact ( v 2 ">v 1 ") (Fig. 3);
Fig.3
c) m 1
Fig.4
d) m 2 >>m 1 (for example, collision of a ball with a wall). Equations (8) and (9) imply that v 1 "= -v 1; v 2 "≈ 2m1 v 2 "/m2.
2. When m 1 =m 2 expressions (6) and (7) will look like v 1 "= v 2; v 2 "= v 1; i.e., balls of equal mass, as it were, exchange speeds.
Absolutely inelastic impact- the collision of two bodies, as a result of which the bodies are connected, moving further as a single whole. Absolutely inelastic impact can be demonstrated using plasticine (clay) balls moving towards each other (Fig. 5).
Fig.5
If the masses of the balls are m 1 and m 2 , their velocities before the impact are ν 1 and ν 2 , then using the momentum conservation law
where v is the speed of the balls after the impact. Then 
(15.10)
In the case of balls moving towards each other, they together will continue to move in the direction in which the ball moved with a large momentum. In a particular case, if the masses of the balls are equal (m 1 \u003d m 2), then
Let us determine how the kinetic energy of the balls changes during a central absolutely inelastic impact. Since in the process of collision of balls between them there are forces that depend on their velocities, and not on the deformations themselves, we are dealing with dissipative forces similar to friction forces, so the law of conservation of mechanical energy in this case should not be observed. Due to deformation, there is a decrease in kinetic energy, which is converted into thermal or other forms of energy. This decrease can be determined by the difference in the kinetic energy of the bodies before and after the impact:
Using (10), we get
If the body being struck was initially motionless (ν 2 =0), then
and 
When m 2 >> m 1 (the mass of the motionless body is very large), then ν<<ν 1 и практически вся кинетическая энергия тела переходит при ударе в другие формы энергии. Поэтому, например, для получения значительной деформации наковальня должна быть значительно массивнее молота. Наоборот, при забивании гвоздей в стену масса молота должна быть гораздо большей (m 1 >>m 2), then ν≈ν 1 and almost all the energy is spent on the greatest possible movement of the nail, and not on the permanent deformation of the wall.
A perfectly inelastic impact is an example of mechanical energy loss due to dissipative forces.
Closed and non-closed systems.
In a closed system there is no interaction with the environment. In open - is.
An isolated system (closed system) is a thermodynamic system that does not exchange either matter or energy with the environment. In thermodynamics, it is postulated (as a result of a generalization of experience) that an isolated system gradually comes to a state of thermodynamic equilibrium, from which it cannot spontaneously exit (zero law of thermodynamics).
The system is called closed(isolated 1) if its components do not interact with external entities, and there are no flows of matter, energy and information from or into the system.
An example of a physical closed system hot water and steam in a thermos can serve. In a closed system, the amount of matter and energy remains unchanged. The amount of information can change both in the direction of decrease and increase - this is another feature of information as the initial category of the universe. A closed system is a kind of idealization (model representation), since it is impossible to completely isolate some set of components from external influences.
Constructing the negation of the above definition, we obtain the definition of the system open . It must be allocated a lot of external influences. (E), influencing (i.e. leading to changes) on (A), (R) and (P). Consequently, the openness of a system is always associated with the flow of processes in it. External influences can be carried out in the form of some force actions or in the form of flows substances, energy, or information that can enter or exit a system. An example of an open system is any institution or enterprise that cannot exist without material, energy and information receipts. Obviously, the study of an open system should include the study and description of the influence of external factors on it, and when creating a system, the possibility of the appearance of these factors should be foreseen.
This is a system of bodies that interact only with each other. There are no external forces of interaction.
In the real world, such a system cannot exist, there is no way to remove any external interaction. A closed system of bodies is a physical model, just like a material point is a model. This is a model of a system of bodies that allegedly interact only with each other, external forces are not taken into account, they are neglected.
Law of conservation of momentum
In a closed system of bodies vector the sum of the momenta of the bodies does not change when the bodies interact. If the momentum of one body has increased, then this means that at that moment the momentum of some other body (or several bodies) has decreased by exactly the same amount.
Let's consider such an example. Girl and boy are skating. A closed system of bodies - a girl and a boy (we neglect friction and other external forces). The girl stands still, her momentum is zero, since the speed is zero (see the body momentum formula). After the boy, moving at some speed, collides with the girl, she will also begin to move. Now her body has momentum. The numerical value of the momentum of the girl is exactly the same as the momentum of the boy decreased after the collision.
One body of mass 20kg moves with a speed of , the second body of mass of 4kg moves in the same direction with a speed of . What is the momentum of each body. What is the momentum of the system?
Impulse of the body system is the vector sum of the impulses of all bodies in the system. In our example, this is the sum of two vectors (since two bodies are considered) that are directed in the same direction, therefore
When calculating the flight speed, based on experimental data, the law of conservation of angular momentum during an inelastic impact and the law of conservation of total mechanical energy after its completion are used.
2. Speed. Physical meaning. Average and instantaneous speed of a translational quantity. Units of measurement
Speed is a physical quantity that characterizes the movement of a body in space. Physical meaning - Change of coordinates per unit of time.
The average speed of movement characterizes the speed of change of the path in time. Instantaneous speed (commonly used term speed) characterizes the rate of change of the radius-vector of a material point in time. Units: Kilometer per hour, Meter per second
3. mechanical system
A mechanical system is a set of material points interacting with each other and with external bodies, the movement of which is subject to the laws of classical mechanics.
4.Body momentum.Unit
The momentum of a body is a physical vector quantity equal to the product of the body's mass and its speed. Measured kg*m/s
5. Total momentum of a mechanical system
the law of conservation of momentum in a closed system, which is formulated as follows: the total momentum of a closed system of bodies remains constant for any interactions of the bodies of this system with each other.
6.closed mechanical system
We call a closed mechanical system of points such a system in which the movement of particles is due only to interaction forces, or internal forces
7. The law of conservation of momentum of a closed mechanical system in general terms and its application for this work
p=p 1 +p 2 = const.
The formula expresses law of conservation of momentum in a closed system, which is formulated as follows: the total momentum of a closed system of bodies remains constant for any interactions of the bodies of this system with each other. In other words, internal forces cannot change the total momentum of the system either in absolute value or in direction.
8. concept of energy. kinetic energy of the body. units of measurement
Energy is a general quantitative measure of the movement and interaction of all types of matter. Kinetic energy is a value equal to half the product of the mass of the body and the square of its speed. =J
9. potential energy of a body raised above the earth's surface. potential energy of a compressed spring
Potential energy - interaction energy of bodies or body parts
The value mgh is the potential energy of a body raised to a height h above the zero level.
is the potential energy of the compressed spring
10. law of conservation of mechanical energy. conditions for its implementation. application of this law to this work
If forces, friction and resistance forces do not act in a closed system, then the sum of the kinetic and potential energies of all bodies of the system remains constant.
11.elastic and inelastic shocks
- absolutely elastic, at which the total mechanical energy is conserved, that is, the internal energy of the particles does not change. There are no deformations in the interacting bodies.
Absolutely inelastic, in which the particles "stick together", moving further as a whole or at rest. Kinetic energy is partially or completely converted into internal energy.
12 derivation of the calculation formula
When a bullet collides with a pendulum, the law of conservation of momentum is valid
where m- weight of the bullet M is the mass of the pendulum, v- bullet speed V is the speed of the pendulum immediately after the impact.
mechanical system material points or bodies is such a set of them in which the position or movement of each point (or body) depends on the position and movement of all the others.
We will also consider a material absolutely rigid body as a system of material points that form this body and are interconnected so that the distances between them do not change, they remain constant all the time.
A classic example of a mechanical system is the solar system, in which all bodies are connected by forces of mutual attraction. Another example of a mechanical system is any machine or mechanism in which all bodies are connected by hinges, rods, cables, belts, etc. (i.e. different geometric relationships). In this case, the forces of mutual pressure or tension act on the bodies of the system, transmitted through the connections.
A set of bodies between which there are no interaction forces (for example, a group of aircraft flying in the air) does not form a mechanical system.
The forces acting on the points or bodies of the system can be divided into external and internal.
External called the forces acting on the points of the system from points or bodies that are not part of this system.
Internal called the forces acting on the points of the system from other points or bodies of the same system. We will denote the external forces with the symbol - , and internal - .
Both external and internal forces can be in turn or active, or bond reactions.
Bond reactions or simply - reactions, these are forces that limit the movement of system points (their coordinates, speed, etc.). In statics, these were forces replacing bonds.
Active or given forces All forces except reactions are called.
The division of forces into external and internal is conditional and depends on the motion of which system of bodies we are considering. For example, if we consider the movement of the entire solar system as a whole, then the force of attraction of the Earth to the Sun will be internal; while studying the motion of the Earth in its orbit around the Sun, the same force will be considered as external.
Internal forces have the following properties:
1. The geometric sum (principal vector) of all internal forces of the system is equal to zero.
According to the third law of dynamics, any two points of the system act on each other with equal in magnitude and oppositely directed forces and , the sum of which is equal to zero.
2.The sum of the moments (principal moment) of all internal forces of the system about any center or axis is equal to zero. If we take an arbitrary center O, then . A similar result will be obtained when calculating the moments about the axis. Therefore, for the whole system it will be:
It does not follow from the proven properties, however, that the internal forces are mutually balanced and do not affect the motion of the system, since these forces are applied to different material points or bodies and can cause mutual displacements of these points or bodies. The internal forces will be balanced when the system under consideration is an absolutely rigid body.
closed system is a system that is not acted upon by external forces.
An example of a physical closed system is hot water and steam in a thermos. In a closed system, the amount of matter and energy remains unchanged. A closed system is a kind of idealization (model representation), since it is impossible to completely isolate some set of components from external influences.
19. Law of conservation of momentum.
Law of conservation of momentum: The vector sum of the momenta of two bodies before the interaction is equal to the vector sum of their momenta after the interaction.
We denote the masses of two bodies and and the speeds before the interaction, and after the interaction (collision)
According to Newton's third law, the forces acting on bodies during their interaction are equal in absolute value and opposite in direction; so they can be labeled
For changes in the impulses of bodies during their interaction, based on the Impulse of force, it can be written as follows
For the first body:
For the second body:
And then we get that the law of conservation of momentum looks like this:
Experimental studies of the interactions of various bodies - from planets and stars to atoms and elementary particles - have shown that in any system of bodies interacting with each other, in the absence of the action of forces from other bodies that are not included in the system, or are equal to zero, the sum of the momenta of the bodies remains unchanged.
A necessary condition for applicability law of conservation of momentum to the system of interacting bodies is the use of an inertial frame of reference.
Interaction time of bodies
Momentum 1 body before interaction
Momentum of 2 bodies before interaction
Momentum 1 of the body after interaction
Momentum 2 body after interaction