Types of mechanics in physics. Mechanics - Mechanics - Topics in physics - Lecture catalog - Physics - in simple terms
- (Greek mechanike, from mechane machine). Part of applied mathematics, the science of force and resistance in machines; the art of applying force to a cause and building machines. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. MECHANICS ... ... Dictionary of foreign words of the Russian language
MECHANICS- (from the Greek mechanike (techne) the science of machines, the art of building machines), the science of mechanical. mother's movement. bodies and the effects that occur between them. Under the mechanical movement is understood as a change over time in the relative position of bodies or ... Physical Encyclopedia
MECHANICS- (from the Greek mechane machine), the science of movement. Until the 17th century, knowledge in this area was almost limited to empirical observations, often erroneous. In the 17th century, the properties of motion began to be mathematically derived for the first time from a few basic principles. Big Medical Encyclopedia
MECHANICS- MECHANICS, mechanics, pl. no, female (Greek mechanike). 1. Department of physics, the doctrine of motion and forces. Theoretical and applied mechanics. 2. Hidden, complex device, background, essence of something (colloquial). Tricky mechanics. "He is, as they say... Explanatory Dictionary of Ushakov
MECHANICS- MECHANICS, a branch of physics that studies the properties of bodies (SUBSTANCES) under the action of forces applied to them. It is divided into solid mechanics and fluid mechanics. Another section, statics, studies the properties of bodies at rest, and DYNAMICS is the movement of bodies. In static... Scientific and technical encyclopedic Dictionary
Mechanics- The science of mechanical motion and mechanical interaction of material bodies. [Collection of recommended terms. Issue 102. Theoretical Mechanics. USSR Academy of Sciences. Committee of Scientific and Technical Terminology. 1984] Topics theoretical ... ... Technical Translator's Handbook
MECHANICS Modern Encyclopedia
MECHANICS- (from the Greek mechanike the art of building machines) the science of the mechanical movement of material bodies (that is, the change in the relative position of bodies or their parts in space over time) and the interactions between them. At the heart of classical mechanics ... ... Big Encyclopedic Dictionary
MECHANICS- MECHANICS, and, wives. 1. The science of movement in space and the forces that cause this movement. Theoretical m. 2. A branch of technology dealing with the application of the doctrine of motion and forces to solving practical problems. Construction m. Applied m. ... ... Explanatory dictionary of Ozhegov
Mechanics- the science of movement. In studying motion, mechanics must also necessarily study the causes that produce and change motions, called forces; forces can also balance each other, and equilibrium can be considered as a special case of motion. ... ... Encyclopedia of Brockhaus and Efron
Mechanics- [from the Greek mechanike (techne) the art of building machines], a branch of physics that studies the mechanical movement of solid, liquid and gaseous material bodies and the interaction between them. In so-called classical mechanics (or simply ... ... Illustrated Encyclopedic Dictionary
Books
- Mechanics , V. A. Aleshkevich , L. G. Dedenko , V. A. Karavaev , The textbook is the first part of the series "University course of general physics", intended for students of physical specialties of universities. 0 its distinguishing feature is ... Category: Mechanics Series: University course of general physics Publisher: FIZMATLIT, Buy for 1181 rubles
- Mechanics, Karl Pichol, V Everyday life we are surrounded not only by a huge number of cars, but also by numerous structures, such as roads, buildings and bridges. In order to design all this, you need ... Category:
Physics is one of the basic sciences of natural science. The study of physics at school begins in the 7th grade and continues until the end of schooling. By this time, schoolchildren should already have formed the proper mathematical apparatus necessary for studying the course of physics.
- The school curriculum in physics consists of several large sections: mechanics, electrodynamics, oscillations and waves, optics, quantum physics, molecular physics and thermal phenomena.
Topics of school physics
In the 7th grade there is a superficial acquaintance and introduction to the course of physics. The main physical concepts, the structure of substances is studied, as well as the pressure force with which various substances act on others. In addition, the laws of Pascal and Archimedes are studied.
In 8th grade various physical phenomena are studied. Initial information is given about the magnetic field and the phenomena in which it occurs. Constant electricity and basic laws of optics. Separately, various aggregate states of matter and the processes that occur during the transition of matter from one state to another are analyzed.
Grade 9 is devoted to the basic laws of motion of bodies and their interaction with each other. Basic concepts are considered mechanical vibrations and waves. The topic of sound and sound waves is analyzed separately. The basics of the theory of electro magnetic field and electromagnetic waves. In addition, there is an acquaintance with the elements of nuclear physics and the structure of the atom and the atomic nucleus is studied.
In 10th grade an in-depth study of mechanics (kinematics and dynamics) and conservation laws begins. The main types of mechanical forces are considered. There is an in-depth study of thermal phenomena, the molecular-kinetic theory and the basic laws of thermodynamics are being studied. The basics of electrodynamics are repeated and systematized: electrostatics, the laws of direct electric current and electric current in various media.
Grade 11 devoted to the study of the magnetic field and the phenomenon of electromagnetic induction. are studied in detail different kinds oscillations and waves: mechanical and electromagnetic. There is a deepening of knowledge from the section of optics. Elements of the theory of relativity and quantum physics are considered.
- Below is a list of grades 7 to 11. Each grade contains physics topics written by our tutors. These materials can be used by both students and their parents, as well as school teachers and tutors.
Kinematics
Newton's second law
Newton's second law: in inertial reference systems, the acceleration of a material point is directly proportional to the vector sum of the forces acting on the material point, and inversely proportional to its mass.
Newton's third law
Newton's third law: in inertial reference frames, any action of one (first) material point on another (second) is accompanied by the influence of the second material point on the first, i.e. it has the nature of interaction; the forces with which material points interact are always equal in absolute value, oppositely directed, act along the straight line connecting these points, are forces of the same nature and are applied to different material points.
Galileo's principle of relativity
Galileo's principle of relativity: no mechanical experiments carried out inside a given inertial system can determine whether this system is at rest or is in uniform and rectilinear motion. In all inertial frames of reference, the laws of mechanics are the same.
- Body weight - the force with which the body presses on the support.
Hooke's Law
Hooke's law: for sufficiently small deformations, the elastic force is proportional to the amount of deformation of the body and is directed in the direction opposite to the deformation.
Pulse
- The momentum of a body (material point) is a vector quantity equal to the product of the mass of the body (material point) and its speed.
- Impulse of the body system(material points) - the vector sum of the impulses of all points.
- The impulse of a force is the product of the force and the time of its action (or the integral over time, if the force changes with time).
- Law of conservation of momentum: In an inertial frame of reference, the momentum of a closed system is conserved.
- Changing the momentum of the system of material points- in the inertial frame of reference, the rate of change of the momentum of the mechanical system is equal to the vector sum of external forces acting on the material points of the system.
Center of mass
The center of mass is an imaginary point C, the position of which characterizes the distribution of the masses of this system.
- The law of motion of the center of mass - in inertial reference frames, the center of mass of the system moves as a material point, in which the mass of the entire system is located and on which a force equal to the geometric sum of all external forces acting on the system acts.
; 
; 
- The center of mass system is a frame of reference that moves translationally in some inertial frame, relative to which the center of mass of the mechanical system is stationary.
work, power, energy
- The work of the force is equal to the product of the modulus of force times the displacement times the cosine of the angle between them.
- Power - the ratio of work to the time for which this work was done.
- Kinetic energy is a value equal to half the product of the body's mass and the square of its speed.
- A value equal to the product of the mass of the body by the height of the body above the Earth's surface is called the potential energy of the body in the field of gravity.
- Conservative forces are forces whose work does not depend on the path traveled by a material point. Depends only from moving.
- Mechanical energy of the system- a value equal to the sum of the kinetic and potential energies of the system.
- In a closed system in which only conservative forces act, mechanical energy is conserved.
- The second cosmic speed is the speed necessary for a material point to leave the Earth's gravitational field and become a satellite of the Sun.
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Great Soviet Encyclopedia - General information When considering the influence of the design of a tank on its main combat properties, first of all, it should be decided: what combat properties it has and what they are. The main combat ... ... Encyclopedia of technology
Crab Nebula Astronomy is the science of the universe that studies the location, movement, structure, origin and ... Wikipedia
The set on which the operation is defined is called. multiplication and satisfying special. conditions (group axioms): in G. there is a single element; for each element of a graph there is an inverse; the operation of multiplication is associative. The concept of G. arose ... ... Physical Encyclopedia
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Mechanics
Kinematic formulas:
Kinematics
mechanical movement
Mechanical movement is called a change in the position of a body (in space) relative to other bodies (over time).
Relativity of motion. Reference system
To describe the mechanical motion of a body (point), you need to know its coordinates at any time. To determine the coordinates, select - reference body and connect with him coordinate system. Often the reference body is the Earth, which is associated with a rectangular Cartesian coordinate system. To determine the position of a point at any point in time, it is also necessary to set the origin of the time reference.
The coordinate system, the body of reference with which it is associated, and the device for measuring time form reference system, relative to which the motion of the body is considered.
Material point
A body whose dimensions can be neglected under given conditions of motion is called material point.
A body can be considered as a material point if its dimensions are small compared to the distance it travels, or compared to the distances from it to other bodies.
Trajectory, path, movement
Trajectory of movement called the line along which the body moves. The length of the trajectory is called the way we have traveled. Way is a scalar physical quantity that can only be positive.
moving is called a vector connecting the start and end points of the trajectory.
The movement of the body, in which all its points are in this moment time move in the same way, is called progressive movement. To describe the translational motion of a body, it is sufficient to select one point and describe its motion.
A movement in which the trajectories of all points of the body are circles with centers on one straight line and all the planes of the circles are perpendicular to this straight line is called rotational movement.
Meter and second
To determine the coordinates of a body, it is necessary to be able to measure the distance on a straight line between two points. Any process of measuring a physical quantity consists in comparing the measured quantity with the unit of measurement of this quantity.
The unit of length in the International System of Units (SI) is meter. A meter is approximately 1/40,000,000 of the earth's meridian. According to the modern idea, a meter is the distance that light travels in the void in 1/299,792,458 of a second.
To measure time, some periodically repeating process is selected. The unit of time in SI is accepted second. A second is equal to 9,192,631,770 periods of radiation of a cesium atom during the transition between two levels of the hyperfine structure of the ground state.
In SI, length and time are taken to be independent of other quantities. Such quantities are called main.
Instant Speed
To quantitatively characterize the process of body movement, the concept of speed of movement is introduced.
instantaneous speed of the translational motion of the body at time t is the ratio of a very small displacement s to a small time interval t during which this displacement occurred:
; 
.
Instantaneous speed is a vector quantity. The instantaneous velocity of movement is always directed tangentially to the trajectory in the direction of body motion.
The unit of speed is 1 m/s. A meter per second is equal to the speed of a point moving in a straight line and uniformly, at which the point moves a distance of 1 m in a time of 1 s.
Acceleration
acceleration is called a vector physical quantity equal to the ratio of a very small change in the velocity vector to a small period of time during which this change occurred, i.e. is a measure of the rate of change of speed:
; 
.
A meter per second per second is such an acceleration at which the speed of a body moving in a straight line and uniformly accelerated changes by 1 m / s in a time of 1 s.
The direction of the acceleration vector coincides with the direction of the velocity change vector ( 
) at very small values of the time interval during which the velocity changes.
If the body moves in a straight line and its speed increases, then the direction of the acceleration vector coincides with the direction of the velocity vector; when the speed decreases, it is opposite to the direction of the speed vector.
When moving along a curvilinear trajectory, the direction of the velocity vector changes in the process of movement, and the acceleration vector can be directed at any angle to the velocity vector.
Uniform, uniformly accelerated rectilinear motion
Moving at a constant speed is called uniform rectilinear motion. In uniform rectilinear motion, the body moves in a straight line and for any equal intervals of time covers the same path.
A movement in which a body makes unequal movements in equal intervals of time is called uneven movement. With such a movement, the speed of the body changes with time.
equivariable is called such a movement in which the speed of the body for any equal time intervals changes by the same amount, i.e. movement with constant acceleration.
uniformly accelerated called uniformly variable motion, in which the magnitude of the speed increases. equally slow- uniformly variable motion, in which the magnitude of the speed decreases.
Addition of speeds
Consider the movement of a body in a moving coordinate system. Let be 
– movement of the body in a moving coordinate system, 
- movement of the moving coordinate system relative to the fixed one, then 
– the movement of the body in a fixed coordinate system is equal to:
.
If the movements and are performed simultaneously, then:
.
In this way
.
We have found that the speed of a body relative to a fixed frame of reference is equal to the sum of the speed of a body in a moving frame of reference and the speed of a moving frame of reference relative to a fixed one. This statement is called the classical law of addition of velocities.
Graphs of dependence of kinematic quantities on time
in uniform and uniformly accelerated motion
With uniform motion:
Velocity graph - straight line y = b;
Acceleration graph - straight line y = 0;
The displacement graph is a straight line y = kx+b.
With uniformly accelerated motion:
if a>0, branches up;
the greater the acceleration, the narrower the branches;
the vertex coincides in time with the moment when the speed of the body is zero;
usually passes through the origin.
Velocity graph - straight line y = kx+b;
Acceleration graph - straight line y = b;
Movement graph - parabola:
Free fall of bodies. Acceleration of gravity
Free fall is the movement of a body when only the force of gravity acts on it.
In free fall, the acceleration of the body is directed vertically downward and is approximately equal to 9.8 m/s 2 . This acceleration is called free fall acceleration and the same for all bodies.
Uniform circular motion
With uniform motion in a circle, the value of the speed is constant, and its direction changes in the process of motion. The instantaneous velocity of a body is always directed tangentially to the trajectory of motion.
Because If the direction of the velocity is constantly changing during uniform motion in a circle, then this motion is always uniformly accelerated.
The time interval for which the body makes a complete revolution when moving in a circle is called the period:
.
Because the circumference s is equal to 2R, the period of revolution for a uniform motion of a body with a speed v along a circle with a radius R is equal to:
.
The reciprocal of the period of revolution is called the frequency of revolution and shows how many revolutions the body makes in a circle per unit time:
.
The angular velocity is the ratio of the angle through which the body has turned to the time of rotation:
.
Angular velocity is numerically equal to the number of revolutions in 2 seconds.
Acceleration with uniform motion of bodies in a circle (centripetal acceleration)
When moving uniformly in a circle, the body moves with centripetal acceleration. Let's define this acceleration.
The acceleration is directed in the same direction as the change in speed, therefore, the acceleration is directed towards the center of the circle. An important assumption: the angle is so small that the length of the chord AB coincides with the length of the arc:
two proportional sides and the angle between them. Consequently:
is the centripetal acceleration module.
Fundamentals of Dynamics
Newton's first law. Inertial reference systems.
Galileo's principle of relativity
Any body remains motionless until other bodies act on it. A body moving at a certain speed continues to move uniformly and in a straight line until other bodies act on it. The Italian scientist Galileo Galilei was the first to come to such conclusions about the laws of motion of bodies.
The phenomenon of maintaining the speed of a body in the absence of external influences is called inertia.
All rest and movement of bodies is relative. The same body can be at rest in one frame of reference and move with acceleration in another. But there are such frames of reference with respect to which translationally moving bodies keep their speed constant if no other bodies act on them. This statement is called Newton's first law (law of inertia).
Reference systems, relative to which the body in the absence of external influences moves in a straight line and uniformly, are called inertial reference systems.
There can be an arbitrarily large number of inertial frames of reference, i.e. any frame of reference that moves uniformly and rectilinearly with respect to the inertial one is also inertial. There are no true (absolute) inertial frames of reference.
Weight
The reason for changing the speed of movement of bodies is always its interaction with other bodies.
When two bodies interact, the speeds of both the first and second bodies always change, i.e. both bodies acquire accelerations. Accelerations of two interacting bodies can be different, they depend on the inertia of the bodies.
inertia- the ability of a body to maintain its state of motion (rest). The greater the inertia of the body, the less acceleration it will acquire when interacting with other bodies, and the closer its movement will be to uniform rectilinear motion by inertia.
Weight- physical quantity characterizing the inertia of the body. The more mass a body has, the less acceleration it receives during interaction.
The SI unit of mass is the kilogram: [m]=1 kg.
Strength
In inertial frames of reference, any change in the speed of a body occurs under the action of other bodies. Strength is a quantitative expression of the action of one body on another.
Strength- a vector physical quantity, the direction of the acceleration of the body, which is caused by this force, is taken as its direction. Force always has a point of application.
In SI, the unit of force is the force that imparts an acceleration of 1 m / s 2 to a body with a mass of 1 kg. This unit is called Newton:
.
Newton's second law
The force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force:
.
Thus, the acceleration of a body is directly proportional to the force acting on the body and inversely proportional to its mass:
.
Addition of forces
With the simultaneous action of several forces on one body, the body moves with an acceleration, which is the vector sum of the accelerations that would arise under the action of each force separately. The forces acting on the body, applied to one point, are added according to the rule of addition of vectors.
The vector sum of all forces acting simultaneously on a body is called resultant force.
The straight line passing through the force vector is called the line of action of the force. If the forces are applied to different points of the body and act not parallel to each other, then the resultant is applied to the point of intersection of the lines of action of the forces. If the forces act parallel to each other, then there is no point of application of the resulting force, and the line of its action is determined by the formula: 
(see picture).
Moment of power. Lever equilibrium condition
The main sign of the interaction of bodies in dynamics is the occurrence of accelerations. However, it is often necessary to know under what conditions a body, which is acted upon by several different forces, is in a state of equilibrium.
There are two types of mechanical movement - translation and rotation.
If the trajectories of movement of all points of the body are the same, then the movement progressive. If the trajectories of all points of the body are arcs of concentric circles (circles with one center - the point of rotation), then the movement is rotational.
Equilibrium of non-rotating bodies: a non-rotating body is in equilibrium if the geometric sum of the forces applied to the body is zero.
Equilibrium of a body with a fixed axis of rotation
If the line of action of the force applied to the body passes through the axis of rotation of the body, then this force is balanced by the elastic force from the side of the axis of rotation.
If the line of action of the force does not cross the axis of rotation, then this force cannot be balanced by the elastic force from the side of the axis of rotation, and the body rotates around the axis.
The rotation of a body around an axis under the action of one force can be stopped by the action of a second force. Experience shows that if two forces separately cause the rotation of the body in opposite directions, then with their simultaneous action the body is in equilibrium if the condition is met:
,
where d 1 and d 2 are the shortest distances from the lines of action of the forces F 1 and F 2. The distance d is called shoulder of strength, and the product of the modulus of force by the arm is moment of force:
.
If a positive sign is assigned to the moments of forces that cause the body to rotate around an axis clockwise, and a negative sign to the moments of forces that cause counterclockwise rotation, then the equilibrium condition for a body with an axis of rotation can be formulated as moment rules: a body with a fixed axis of rotation is in equilibrium if the algebraic sum of the moments of all forces applied to the body about this axis is zero:
The SI unit of torque is a moment of force of 1 N, the line of action of which is at a distance of 1 m from the axis of rotation. This unit is called newton meter.
The general condition for the equilibrium of a body: a body is in equilibrium if the geometric sum of all forces applied to it and the algebraic sum of the moments of these forces about the axis of rotation are equal to zero.
Under this condition, the body is not necessarily at rest. It can move uniformly and rectilinearly or rotate.
Types of balance
Equilibrium is called sustainable, if after small external influences the body returns to its original state of equilibrium. This occurs if, with a slight displacement of the body in any direction from the initial position, the resultant of the forces acting on the body becomes non-zero and is directed towards the equilibrium position.
The balance is called unstable, if with a small displacement of the body from the equilibrium position, the resultant of the forces applied to it is non-zero and is directed from the equilibrium position.
Equilibrium is called indifferent, if, with small displacements of the body from its original position, the resultant of the forces applied to the body remains equal to zero.
Center of gravity
center of gravity called the point through which the resultant of gravity passes at any location of the body.
Newton's third law
Bodies act on each other with forces along one straight line, equal in magnitude and opposite in direction. These forces are of the same physical nature; they are attached to different bodies and therefore do not compensate each other.
Elastic force. Hooke's Law
Elastic force arises as a result of deformation of the body and is directed in the direction opposite to the deformation.
For small deformations compared to the dimensions of the bodies, the elastic force is directly proportional to the magnitude of the absolute deformation of the body. In projection onto the direction of deformation, the elastic force is equal to
,
where x is the absolute strain, k is the stiffness factor.
This law was established experimentally by the English scientist Robert Hooke and is called Hooke's law:
The elastic force arising from the deformation of the body is proportional to the elongation of the body and is directed in the direction opposite to the direction of movement of the particles of the body during deformation.
The coefficient of proportionality in Hooke's law is called the stiffness of the body. It depends on the shape and dimensions of the body and on the material from which it is made (it decreases with increasing length and with decreasing cross-sectional area - see Molecular Physics).
In C, rigidity is expressed as newtons per meter: 
.
The elastic force tends to restore the shape of the body subjected to deformation, and is applied to the body that causes this deformation.
The nature of the elastic force is electromagnetic, because the elastic force arises as a result of the desire of electromagnetic forces acting between the atoms of a substance to return the atoms of the substance to their original position when their mutual position changes as a result of deformation.
Elastic reaction of support, thread, suspension- passive force acting always perpendicular to the surface of the support.
Friction force. Sliding friction coefficient
Friction force occurs when the surfaces of two bodies come into contact and always prevents their mutual movement.
The force arising at the boundary of contact between bodies in the absence of relative motion called static friction force. The static friction force is an elastic force, it is equal in module to the external force directed tangentially to the contact surface of the bodies, and opposite to it in direction.
When one body moves over the surface of another, sliding friction force.
The friction force has an electromagnetic nature, because arises due to the existence of forces of interaction between molecules and atoms of contacting bodies - electromagnetic forces.
The force of sliding friction is directly proportional to the force of normal pressure (or the elastic reaction of the support) and does not depend on the area of the contact surface of the bodies (Coulomb's law):
, where is the coefficient of friction.
The coefficient of friction depends on the surface topography and is always less than unity: “it is easier to move than to tear off”.
gravitational forces. The law of universal gravitation.
The force of gravity
According to Newton's laws, the motion of a body with acceleration is possible only under the action of a force. Because falling bodies move with an acceleration directed downwards, then they are affected by the force of attraction to the Earth. But not only the Earth has the property to act on all bodies by the force of attraction. Isaac Newton suggested that forces of attraction act between all bodies. These forces are called forces gravity or gravitational forces.
Having extended the established laws - the dependence of the force of attraction of bodies to the Earth on the distances between the bodies and on the masses of interacting bodies, obtained as a result of observations - Newton discovered in 1682 law of gravity: All bodies are attracted to each other, the force of universal gravitation is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them:
.
The vectors of forces of universal gravitation are directed along the straight line connecting the bodies. The proportionality factor G is called gravitational constant (universal gravitational constant) and equal to
.
gravity called the force of attraction acting from the Earth on all bodies:
.
Let be 
is the mass of the earth, and 
is the radius of the earth. Consider the dependence of the acceleration of free fall on the height of the rise above the Earth's surface:
Body weight. Weightlessness
Body weight - the force with which a body presses on a support or suspension due to the attraction of this body to the ground. The weight of the body is applied to the support (suspension). The amount of body weight depends on how the body moves with support (suspension).
Body weight, i.e. the force with which the body acts on the support, and the elastic force with which the support acts on the body, in accordance with Newton's third law, are equal in absolute value and opposite in direction.
If the body is at rest on a horizontal support or moves uniformly, only the force of gravity and the elastic force from the side of the support act on it, therefore the weight of the body is equal to the force of gravity (but these forces are applied to different bodies):
.
With accelerated motion, the weight of the body will not be equal to the force of gravity. Consider the motion of a body of mass m under the action of gravity and elasticity with acceleration. According to Newton's 2nd law:
If the acceleration of the body is directed downward, then the weight of the body is less than the force of gravity; if the acceleration of the body is directed upwards, then all bodies are greater than the force of gravity.
The increase in body weight caused by the accelerated movement of the support or suspension is called overload.
If the body is freely falling, then from the formula * it follows that the weight of the body is zero. The disappearance of the weight during the movement of the support with the acceleration of free fall is called weightlessness.
The state of weightlessness is observed in an airplane or spacecraft when they move with the acceleration of free fall, regardless of the speed of their movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravitation acts on the spacecraft. Under the influence of this force, the spacecraft and all the bodies in it move with the same acceleration; therefore, the phenomenon of weightlessness is observed in the ship.
The motion of a body under the influence of gravity. Movement of artificial satellites. first cosmic speed
If the modulus of displacement of the body is much less than the distance to the center of the Earth, then the force of universal gravitation during the movement can be considered constant, and the movement of the body is uniformly accelerated. The simplest case of motion of a body under the action of gravity is free fall with zero initial velocity. In this case, the body moves with the acceleration of free fall towards the center of the Earth. If there is an initial velocity that is not directed vertically, then the body moves along a curvilinear trajectory (parabola, if air resistance is not taken into account).
At a certain initial velocity, a body thrown tangentially to the surface of the Earth, under the action of gravity in the absence of an atmosphere, can move in a circle around the Earth without falling on it and without moving away from it. This speed is called first cosmic speed, and the body moving in this way - artificial earth satellite (AES).
Let's define the first cosmic velocity for the Earth. If a body under the influence of gravity moves around the Earth uniformly in a circle, then the acceleration of free fall is its centripetal acceleration:
.
Hence the first cosmic velocity is
.
The first cosmic velocity for any celestial body is determined in the same way. The free fall acceleration at a distance R from the center of a celestial body can be found using Newton's second law and the law of universal gravitation:
.
Therefore, the first cosmic velocity at a distance R from the center of a celestial body with mass M is
.
To launch a satellite into near-Earth orbit, it must first be taken out of the atmosphere. Therefore, spaceships launch vertically. At an altitude of 200 - 300 km from the Earth's surface, where the atmosphere is rarefied and has almost no effect on the movement of the satellite, the rocket makes a turn and informs the satellite of the first cosmic velocity in the direction perpendicular to the vertical.
Conservation laws in mechanics
body momentum
According to Newton's 2nd law, a change in the speed of a body is possible only as a result of its interaction with other bodies, i.e. under the action of force. Let a force F act on a body of mass m during time t and its speed change from v o to v. Then, based on Newton's 2nd law:
.
Value 
called momentum of force. The impulse of force is a vector physical quantity equal to the product of the force and the time of its action. The direction of the momentum of the force coincides with the direction of the force.
.
– body momentum (momentum) is a vector physical quantity equal to the product of the mass of the body and its speed. The direction of the momentum of the body coincides with the direction of the velocity.
The momentum of the force acting on the body is equal to the change in the momentum of the body.
Law of conservation of momentum
Let us find out how the impulses of two bodies change during their interaction. Let us denote the speeds of bodies with masses m 1 and m 2 before interaction through 
And 
, and after interaction - through 
And 
.
According to Newton's 3rd law, the forces acting on bodies during their interaction are equal in absolute value and opposite in direction; so from can be denoted by F and –F. Then:
Thus, the vector sum of the momenta of two bodies before the interaction is equal to the vector sum of their momenta after the interaction.
Experiments show 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, - in a closed system- the geometric sum of the momenta of the bodies remains constant. The momentum of a closed system of bodies is a constant value - the law of conservation of momentum (p.s.i.).
Jet propulsion
In a jet engine, when fuel is burned, gases are formed that are heated to high temperature, which are ejected from the engine nozzle. The engine and the gases emitted by it interact with each other. Based on the s.s.i. in the absence of external forces, the sum of the momentum vectors of the interacting bodies remains constant. Before the engine started, the momentum of the engine and fuel was equal to zero, therefore, after turning on the engine, the sum of the vectors of the rocket momentum and the momentum of the outflowing gases is equal to zero:
.
This formula is applicable to calculate the speed of an engine, given a small change in its mass as a result of fuel combustion.
A jet engine has a remarkable property: it does not need land, water, or air to move. it moves as a result of interaction with gases formed during the combustion of fuel. Therefore, a jet engine can move in airless outer space.
mechanical work
mechanical work is a scalar physical quantity equal to the product of the force modulus and the displacement modulus of the point of application of the force and the cosine of the angle between the direction of the force and the direction of movement (the scalar product of the force vectors and the point of its displacement):
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Work is measured in Joules. 1 Joule is the work done by a force of 1 N when the point of its application moves 1 m in the direction of the force:
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Work can be positive, negative, zero:
= 0 A = FS > 0;
0 < < 90 A > 0;
= 90 A = 0;
90< < 180 A < 0;
= 180 A = –FS< 0.
A force acting perpendicular to the displacement does no work.
Power
Power is the work done per unit of time.
- average power.
. 1 Watt is the power at which 1 J of work is done in 1 second.
Instant Power:
.
Kinetic energy
Let's establish a connection between the work of a constant force and a change in the speed of a body. Let us consider the case when a constant force acts on the body and the direction of the force coincides with the direction of movement of the body:
. *
A physical quantity equal to half the product of a body's mass and its speed is called kinetic energy bodies:
.
Then from the formula *: 
– kinetic energy theorem: The change in the kinetic energy of the body is equal to the work of all forces acting on the body.
The kinetic energy is always positive, i.e. depends on the choice of reference system.
Conclusion: in physics, the absolute value of energy in general, and kinetic energy in particular, does not make sense. It can only be a difference in energy or a change in energy.
Energy is the ability of a body to do work. Work is a measure of energy change.
Potential energy
Potential energy- this is the energy of interaction of bodies, depends on their mutual arrangement.
The work of gravity (potential energy of the body in the field of gravity)
If the body moves upward, the work done by gravity is negative; down is positive.
The work of gravity does not depend on the trajectory of the body, but depends only on the height difference (on the change in the position of the body above the earth's surface).
The work of gravity in a closed loop is zero.
Forces whose work in a closed loop is zero are called potential (conservative). In mechanics, gravity and elastic force are potential (in electrodynamics - Coulomb force), non-potential - friction force (in electrodynamics - Ampère, Lorentz force).
Potential energy of a body in the field of gravity: 
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The work of a potential force is always equal to the loss of potential energy:
.
Elastic force work (potential energy of an elastically deformed body)
/* If some physical quantity changes linearly, its average value is equal to half the sum of the initial and final values - F y */
Potential energy of an elastically deformed body: 
.
Law of conservation of total mechanical energy
Total mechanical energy- the sum of the kinetic and potential energy of all bodies included in the system:
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According to the kinetic energy theorem, the work of all forces acting on all bodies. If all forces in the system are potential, then the statement is true: . Consequently:
The total mechanical energy of a closed system is a constant value (if only potential forces act in the system).
If there are friction forces in the system, then the following method can be applied: we assign the friction force to an external force and apply the law of change in the total mechanical energy:
.
The work of an external force is equal to the change in the total mechanical energy of the system.
Liquids and gases
Pressure
Pressure is a physical quantity numerically equal to the force of normal pressure acting on a unit area:
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The force of normal pressure always acts perpendicular to the surface.
.
1 Pascal is the pressure that a force of 1 N produces on a surface perpendicular to it, an area of 1 m 2. In practice, off-system units of pressure are also used:
Pascal's law for liquids and gases
The pressure exerted on the fluid is transmitted to it equally in all directions. Pressure does not depend on direction.
hydrostatic pressure is the weight of a column of liquid per unit area:
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The liquid exerts such pressure on the bottom and walls of the vessel at a depth h.
Communicating vessels
The equality of fluid pressures at the same height leads to the fact that in communicating vessels of any shape, the free surfaces of a homogeneous fluid at rest are at the same level (if the influence of capillary forces is negligible).
If liquids with different densities are poured into communicating vessels, then if the pressures are equal, the height of the liquid column with a lower density will be greater than the height of the liquid column with a higher density, because at the same height, the pressure is the same.
The principle of the hydraulic press
The main parts of a hydraulic press are two cylinders with pistons. Under the cylinders there is a slightly compressible liquid, the cylinders are connected by a tube through which the liquid can flow.
Under the action of force F 1 on the piston in a narrow cylinder, some pressure is created. According to Pascal's law, the same pressure is created inside the liquid in the second cylinder, i.e.
.
The hydraulic press gives a gain as many times as the area of its larger piston is larger than the area of the small piston.
The hydraulic press is used in jacks and brake systems.
Atmosphere pressure. Change in atmospheric pressure
with height
Under the influence of gravity, the upper layers of air in the earth's atmosphere press on the underlying layers. This pressure, according to Pascal's law, is transmitted in all directions. Highest value this pressure is called atmospheric, has near the surface of the Earth.
In a mercury barometer, the weight of a column of mercury per unit area (hydrostatic pressure of mercury) is balanced by the weight of a column of atmospheric air per unit area - atmospheric pressure (see figure).
As altitude increases, atmospheric pressure decreases (see graph).
Archimedean force for liquids and gases. Bodies floating conditions
A body immersed in a liquid or gas is subjected to a buoyant force directed vertically upwards and equal to the weight of the liquid (gas) taken in the volume of the immersed body.
The formulation of Archimedes: the body loses in the liquid in weight exactly as much as the weight of the displaced liquid weighs.
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The displacing force is applied in the geometric center of the body (for homogeneous bodies - in the center of gravity).
Two forces act on a body in a liquid or gas under normal terrestrial conditions: gravity and the Archimedean force. If the modulus of gravity is greater than the Archimedean force, then the body sinks.
If the modulus of gravity is equal to the modulus of the Archimedean force, then the body can be in equilibrium at any depth.
If the Archimedean force is greater than the force of gravity, then the body floats. The floating body partially protrudes above the surface of the liquid; the volume of the submerged part of the body is such that the weight of the displaced fluid is equal to the weight of the floating body.
The Archimedean force is greater than the force of gravity if the density of the liquid is greater than the density of the immersed body, and vice versa.
Definition
The founders of classical mechanics are G. Galileo (1564-1642) and I. Newton (1643-1727). The methods of classical mechanics study the motion of any material bodies (except for microparticles) with speeds that are small compared to the speed of light in vacuum. The movement of microparticles is considered in quantum mechanics, and the movement of bodies with speeds close to the speed of light - in relativistic mechanics (special relativity).Mechanics is a part of physics that studies the movement and interaction of material bodies. In this case, mechanical movement is considered as a change over time in the relative position of bodies or their parts in space.
Properties of space and time accepted in classical physics We give definitions to the above definitions.
One-dimensional space - parametric characteristic, in which the position of a point is described by one parameter.
Euclidean space and time means that they themselves are not curved and are described within the framework of Euclidean geometry.
Homogeneity of space means that its properties do not depend on the distance to the observer. The uniformity of time means that it does not expand or contract, but flows evenly. The isotropy of space means that its properties do not depend on direction. Since time is one-dimensional, there is no need to talk about its isotropy. Time in classical mechanics is considered as an "arrow of time", directed from the past to the future. It is irreversible: you cannot go back to the past and “correct” something there.
Space and time are continual (from lat. continuum - continuous, continuous), i.e. they can be broken down into smaller and smaller parts for as long as you like. In other words, there are no “holes” in space and time, inside which they would be absent. Mechanics is divided into Kinematics and Dynamics
In this case, the speed of a material point is considered as the speed of its movement in space or, from a mathematical point of view, as a vector quantity equal to the time derivative of its radius vector:Kinematics studies the movement of bodies as a simple movement in space, introducing into consideration the so-called kinematic characteristics of movement: displacement, speed and acceleration.
The acceleration of a material point is considered as the rate of change of its speed or, from a mathematical point of view, as a vector quantity equal to the time derivative of its speed or the second time derivative of its radius vector:
Dynamics
In this case, the mass of the body is considered as a measure of its inertia, i.e. resistance in relation to the force acting on a given body, seeking to change its state (set in motion or, conversely, stop, or change the speed of movement). Mass can also be considered as a measure of the gravitational properties of a body, i.e. its ability to interact with other bodies that also have mass and are located at some distance from this body. The momentum of a body is considered as a quantitative measure of its movement, defined as the product of the body's mass and its speed:Dynamics studies the motion of bodies in connection with the forces acting on them, using the so-called dynamic characteristics of motion: mass, momentum, force, etc.
Force is considered as a measure of mechanical action on a given material body by other bodies.