Application of kinematics laws in practice Presentation. Kinematics Basic concepts Presentation is prepared by the teacher of GOUPO MO. B) mechanical movement is a physical value

Brief historical reference Ø Ø Ø Kinematics development as science began in ancient world and is associated with such a name as Galilee, which introduces the concept of acceleration. Kinematics development in the XVIII century. It is associated with the works of Euler, which laid the foundation of the kinematics of the solid and creating analytical methods to solve the problems of mechanics. The deeper studies of the geometric properties of the body movement were caused by the development of technology at the beginning of the XIX century. And, in particular, the rapid development of mechanical engineering. Large studies in the field of kinematics of mechanisms and machines belong to both Russian scientists: the founder of the Russian school of the theory of machines and mechanisms of P. L. Chebyshev (1821 -1894), L. V. Assura (1878 -1920), N. I. Merzalov (1866 - 1948), L. P. Kotelnikov (1865 -1944) and other scientists.

The basic concepts of kinematics: kinematics (from Greek. Κινειν - to move) - the section of mechanics in which the movement of bodies is considered without clarifying the reasons for this movement. The main task of kinematics: knowing the law of the movement of this body, to determine all the kinematic values \u200b\u200bcharacterizing both the movement of the body as a whole and the movement of each of its points separately.

Kinematics is a description of the movement of bodies with mathematical answers to the questions: 1. Where? 2. When? 3. How? For answers to the questions, the following concepts are needed:

Mechanical movement of the body (point) is a change in its position in space relative to other bodies over time.

The material point body can be considered a material point if: 1. Discipers passable by the body, significantly larger than the sizes of this body; 2. The body moves progressively, i.e. all of its points move the same at any time.

The material point is the body, the sizes and the form of which in the conditions of the problem under consideration can be neglected; The trajectory is a conditional line of body movement in space; The path is the length of the trajectory; Move - directional segment

Ways to set the movement of the point Ø natural with this method asks: the point of point and the law of the movement along this trajectory Ø The coordinate position of the point relative to a certain reference system is given by its coordinates of the point of movement of the point in the rectangular coordinates x \u003d f 1 (t), y \u003d f 2 (t ), z \u003d f 3 (t)

Speed: A vector value characterizes the speed of movement, shows how the movement of the body makes a move of time, in which the body for any equal intervals make the same movement. Call straight uniform. The speed of uniform motion - [m / s] Movement, in which in equal intervals of the body makes unequal movements, are called uneven the speed of uneven movement: the speed direction at: Ø straight movement - invariably Ø curvilinear movement - by tangential to the trajectory at a given point or variables.

Acceleration The value characterizing the change in speed with uneven movement of the body. The average acceleration of the uneven movement in the interval from T to T + ΔT is the vector value equal to the ratio of the rate of speed ΔV to the time interval Δt: with a free drop near the ground surface, where

An acceleration vector component, directed along the tangent to the trajectory at a given point, is called a tangential (tangent) acceleration. Tangential acceleration characterizes the change in the velocity vector. The vector Aτ is directed towards the movement of the point in an increase in its speed (Figure - a) and in the opposite direction - with diminishing speed (Figure - b). A B.

The tangential component of the acceleration of Aτ is equal to the first time derivative from the speed module, thereby determining the speed of changing the speed of the module: the second component of the acceleration, equal: is called the normal component of the acceleration and is directed by normal to the trajectory to the center of its curvature (therefore, it is also called the centripetal acceleration ). Complete acceleration is the geometric sum of the tangential and normal components.

Description of the presentation on individual slides:

1 Slide

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The subject of the lesson: the basic concepts and equations of kinematics. The purpose of the lesson: repeat the basic concepts of kinematics - the trajectory, acceleration, speed passed path and movement.

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Plan what studies mechanics? Its main task. Kinematics. Basic concepts: reference body, coordinate system, reference system The law of independence of the movements The material point and absolutely solid is the progressive and rotational movement trajectory, path, movement speed acceleration Classification of mechanical movements. Basic equations. Graphics movements.

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What does the mechanic study? Its main task. The section of physics - mechanics is engaged in the study of the mechanical movement of tel. Mechanical movement is called a change in the position of the body (in space) relative to other bodies over time. The main task of mechanics is to determine the position of the body at any time.

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Kinematics. Basic concepts: Mechanics consists of two main sections: kinematics and speakers. The section that does not consider the causes of the mechanical movement and describes only its geometrical properties is called kinematics. Kinematics uses such concepts as a trajectory, path and movement, speed and acceleration.

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The relativity of movement. Reference system. To describe the mechanical movement of the body (point), you need to know its coordinates at any time. To determine the coordinates, select the reference body and associate the coordinate system with it. Often the body of reference is the land with which the rectangular decartian coordinate system is associated. To determine the position of the point at any time you also need to set the start of the time. Coordinate system, the reference body with which it is connected, and the device for measuring time is formed by the reference system relative to which the body movement is considered.

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The movement of real bodies is usually complex. Therefore, to simplify the consideration of movements enjoy the law of independence of movements: any complex movement can be represented as an amount of independent simple movements. The simplest movements include progressive and rotational. Physics are widely used by models that allow from all the variety of physical properties to choose the main thing that determines this physical phenomenon. One of the first models of real bodies is a material point and an absolutely solid body. Law of independence movements

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The body, the sizes of which in these conditions of movement can be neglected, called a material point. The body can be viewed as a material point if its dimensions are small compared to the distance it passes, or compared with distances from it to other bodies. An absolutely solid body is called the body, the distance between any two points of which remains constant when its movement. These models make it possible to exclude deformation of the bodies when driving. Material point and absolutely solid body.

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Progressive and rotational movement. There is a progressive movement, in which the segment connecting any two solid points is moved by movement in parallel to itself. It follows from this that all points of the body in progressive movement move the same, i.e. With the same speeds and accelerations. The rotational is called a movement, in which all points of absolutely solid body move around the circles, the centers of which lie on one straight line, called the axis of rotation, and these circles lie in the planes perpendicular to the axis of rotation. Using the law of independence of movements, the complex movement of the solid body can be considered as the sum of the progressive and rotational movements.

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Progressive movement Choose a correct statement about the translational movement: translational movement is the movement of the body, in which the straight line connecting two any points belonging to this body moves, remaining parallel to itself. In prigly movement, all the points of the solid are moving the same, describe the same trajectories and at each moment of time have the same speeds and acceleration. Parachutic movement is an example of translational movement. The moon around the earth is moving progressively.

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The trajectory, the path, moving the trajectory of movement is called the line along which the body moves. The length of the trajectory is called traveled. The path is a scalar physical value, the sum of the lengths of the trajectory segments can only be positive. The movement is called a vector connecting the initial and endpoint of the trajectory. Examples:  The path traveled -  vector of movement - S A and B - the initial and final point of the path with curvilinear movement of the body. S Fig. 1 s Fig. 2 ACDENB - Trajectory Travel Vector - S

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An example of the movement vector movement - there is a difference between the final and initial position and is indicated:

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Speed \u200b\u200bThe nature of the body movement is determined by its speed. If the speed is constant, the movement is called uniform and the movement equation is as follows: [m / C2] The speed module is: if the speed increases to the same value for the same periods of time, then the movement is called equivalent. If the speed decreases to the same value for the same time intervals, the movement is called equible. Such types of movements are called equalized movement.

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The average and instantaneous speed of the speed of changing the position of the material point in space over time is characterized by medium and instantaneous speeds. The average speed is a vector value equal to the ratio of movement to a period of time, for which this movement happened: Vc \u003d S / T. Instant speed is called the limit of the displacement ratio s to the time interval t, for which this movement occurred, with the desire t to zero: VMGH \u003d Limt -\u003e 0 s / t.

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Addition of speeds Consider the movement of the body in the movable coordinate system. Let S1 be the movement of the body in the movable coordinate system, S2 moving the movable coordinate system relatively fixed, then S - the movement of the body in the fixed coordinate system is: if the movement S1 and S2 are performed simultaneously, then: thus, the body speed is relative to the fixed system The reference is equal to the amount of body velocity in the movable reference system and the speed of the movable reference system relatively fixed. This statement is called the classical law of addition of speeds.

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Acceleration The value of the speed change per unit of time is acceleration: during the movement, the speed may change, the absence of a change in speed leads to a lack of acceleration. The fixed body or the body driving with a constant speed has zero acceleration. Acceleration determines how the speed has increased with an equilibrium movement, and how much decreased with an equilibrium movement in 1 second.

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For example: the cyclist moves with acceleration A \u003d 5M / C2, then through every second its speed will take values:

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Average and instantaneous acceleration The value that characterizes the speed of changing the speed is called acceleration. The average acceleration is the value equal to the ratio of the speed change by the period of time, for which this change occurred: ASR \u003d V / T. If V1 and V2 are instantaneous speeds at times T1 and T2, then v \u003d V2-V1, t \u003d T2-T1. Instant acceleration - the acceleration of the body at the moment. This is a physical value equal to the limit of the ratio of a speed change by a period of time, for which this change occurred, when the time interval is designed to zero: AMGN \u003d LIM T -\u003e 0 V / T.

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Basic equations.

Mechanics

The basic concepts of kinematics

Subject: space, time, movement, speed. The main task of mechanics.

Mechanics (from Greek. Art of the Machine Machine)

Section of physics on the movement of material objects and interaction between them .

Mechanics

Kinematics (traffic)

Dynamics (force)

the section of mechanics in which the movement of bodies is considered without clarifying the reasons for this movement.

the mechanics section in which the causes of mechanical movement are studied.

The basic concepts of kinematics

1. Space and time

The world around us is material

There is objectively and actually. Regardless of our consciousness and outside it.

It is capable of acting to our senses and cause certain sensations.

Space and time (Event Development Time)

Time property: one-dimensional, continuity

Unit of Time - Second

The difference of values \u200b\u200bof any values \u200b\u200bdenote Δ (delta), for example: Δt - time interval.

The main spatial characteristic is the distance

Properties of applications:

- Continuity

- Three-dimensionality

- Childness

Measure distance - meter

There are three levels of the world of the world:

Megamir (world of galaxies)

Macromir (from the sands to the planets of the solar system)

Microworld (molecules, atoms, elementar particles)

2. Reference system

Body reference - The body relative to which the movement of other bodies is considered.

Reference system - A combination of the coordinate system, the reference body with which it is connected, and the device for measuring time.

Coordinate systems

One-dimensional - coordinate straight

Two-dimensional - coordinate plane

Spatial system

Coordinates (three-dimensional)

3. Mechanical movement (MD)

Mechanical movement body (points) is called a change in its position in space relative to other bodies over time.

4. Material point

Material point - The body, sizes and the form of which in the conditions of the problem under consideration can be neglected. The body can be considered a material point if: 1. Distances passable by the body, much larger than the sizes of this body; 2. The body moves progressively, i.e. All of its points are moving equally at any time.

5. The main task of mechanics

Determination of the position of the particle in the selected reference system at any time

6. Trajectory, travel path.

Trajectory - imaginary line for which the body moves

Way ( S) - Length of the trajectory. Move - Vector connecting the initial and endpoint of the trajectory.

7. Speed

Speed - Physical vector magnitude that characterizes the direction and speed of movement. Shows what movement made body per unit time:

Instant speed - body speed at the moment of time or at this point of the trajectory. Equal to the ratio of small movement to a small period of time, for which this movement is made:

average speed - The physical value equal to the ratio of all the time passed to all time:

Solving tasks

Task 1. . When you can, when you can not take for the material point: scissors, car, rocket?

Task 2. Walking young man went 3 km north, where he met his girlfriend. After the meeting, they sat on the bus and drove 4 km in the eastern direction. Determine the path and travel performed by a young man

Task 3. What amount measures the counter in the car: the path traveled or the length of movement?

Task 4. When we say that the change of the day and night on Earth is explained by the rotation of the earth around its axis, then we mean the system of commercially related to ... a) planets; b) the sun; c) earth; d) any body.

Level 1.

1) P. on the given trajectory of the body movement (see crisis) Find (graphically)

2) Dictation "Write- Do not believe" (+ or -):

A) mechanics - part of physics studying mechanical phenomena;

B) mechanical movement is a physical quantity;

C) the movement of the groove ball - a mechanical phenomenon;

D) the center of the wheel of the bicycle (when driving along the horizontal road) performs translational movement;

E) when falling at some height, the ball performs translational movement.

Level 2:

A) the ruler can be taken for the material point if it makes the rotational movement on the table;

B) the trajectory of the end of the clock arrow - a circle;

C) Earth when moving it in orbit can be taken for the material point.

3 level

3) the distance between points A and B is direct 6 km. The man passes this distance there and back in 2 hours. What is the path and movement of a person for 2h and 1h?

4) The cyclist moves around the circumference with a radius of 100 m makes 1 turnover in 2 minutes. Determine the path and movement of the cyclist for 1 min and 2 minutes.

"Movement of Tel" - the basic concepts of kinematics. And more than 5 minutes on the chart there is no such interim. Which body is moving with the highest speed? Intensive preparation rate for a single state exam. - M.: Iris press, 2007. The relativity of movement. The path l The length of the trajectory passed by the body for some time t.

"Uniform and uneven movement" - features of this movement. Move (traveled path) time speed. Features of uneven movement. Uniform movement. Body speed with uniform motion can be determined by the formula. Apple Level. Body speed with uneven motion can be determined by the formula. Uneven movement.

"The concept of kinematics" - vector quantities. The value gives the number of revolutions per unit of time. Vector a. Vector angular velocity. Unit vector. The vector connecting the initial point (1) of movement with the final (2). Vector addition speed. In textbooks, the vectors are denoted by greasy letters. Choose a rectangular coordinate system.

"Studying the body's movement around the circumference" - the movement of bodies around the circumference. Perform a test. Dynamics of the movement of bodies around the circumference. Decide the task. P.N.nesterov. Decide independently. Check the answers. A basic level of. Algorithm for solving problems. Body weight. Studying the method of solving problems.

"The movement of the body around the circumference" - with what linear speed, the wolf threw the hat. Period in the event of a uniform circular motion. A minute clock arrow 3 times longer than the second one. Acceleration is directly proportional to the speed of movement. Which minimal speed must move the attraction aircraft. Angular movement. Angular velocity.

"Kinematics Points" - acceleration of Coriolis. Theorem Euler. Solid kinematics. General case of composite body movement. Flat-parallel solid movement. Complex traffic point. Corner speed and angular acceleration. Causes of the acceleration of Coriolis. Transformation of rotations. Complex movement of solid.