Determination of the coordinates of a moving body. Determination of the coordinates of the moving body Definition of the coordinates of a moving body Development of a lesson

When we talk about moving, it is important to remember that move Depends on the reference system in which movement is considered. Pay attention to the drawing.

Fig. 4. Determination of body movement module

The body moves in the Xoy plane. Point A is the initial position of the body. Its coordinates A (x 1; in 1). The body moves to the point in (x 2; in 2). The vector is the movement of the body:

Lesson 3. Definition of coordinates of a moving body

Yerutkin Evgeny Sergeevich

The subject of the lesson is "determining the coordinates of the moving body." We have already discussed the characteristics of the movement: the path passed, speed and movement. The main characteristic of the movement is the location of the tel. To characterize it, it is necessary to use the concept of "moving", it is it that makes it possible to determine the location of the body at any time, precisely this is the main task of mechanics.

.

Fig. 1. Path as the sum of many rectilinear movements

Trajectory as the amount of movements

In fig. 1 shows the trajectory of the body movement from the point A to the point in in the form of a curve line, which we can imagine as a set of small displacements. Move - This is a vector, consequently, the whole path we can imagine as a set of sums of very small movements along the curve. Each of small movements is a straight line, all together they will constitute the entire trajectory. Note: - It is moving that determines the body position. Any movement we must consider in a specific reference system.

Coordinates of the body

The drawing must be combined with the reference system of the body. The easiest of the methods under consideration is the movement in a straight line, along one axis. To characterize the movements, we will use the method associated with the reference system - with one line; straight movement.

Fig. 2. One-dimensional movement

In fig. 2 shows the axis oh and the case of one-dimensional movement, i.e. The body moves along straight, along one axis. In this case, the body moved from point A to a point in, moving was the vector AB. To determine the coordinates of the point and we must do the following: omit perpendicular to the axis, the coordinate of the point A on this axis will be denoted by x 1, and by lowering the perpendicular from the point B, we obtain the coordinate of the end point - x 2. After doing this, you can talk about the projection of the vector on the axis oh. When solving tasks, we will need a projection of the vector, a scalar value.

Vector projection on the axis

In the first case, the vector is directed along the axis oh, coincides in the direction, so the projection will be with a plus sign.

Fig. 3. Projection of movement

with a minus sign

An example of a negative projection

In fig. 3 shows another possible situation. The vector AB in this case is directed against the selected axis. In this case, the projection of the vector on the axis will have a negative value. When calculating the projection, the symbol of the vector S is necessarily set, and at the bottom - the index x: s x.

Path and movement with rectilinear motion

Straight movement is a simple mode of movement. In this case, we can say that the vector projection module is and will be traveled. It should be noted that in this case the length of the vector module is equal to the path traveled.

Fig. 4. The traveled path coincides

with the projection of movement

Examples of various mutual orientation of the axis and movement

To finally deal with the question of the project's projection on the axis and with coordinates, consider several examples:

Fig. 5. Example 1.

Example 1. Module of movement equals projection of movement and is defined as x 2 - x 1, i.e. From the final coordinate, we submit the initial one.

Fig. 6. Example 2.

Example 2. The second drawing under the letter B. is very curious if the body moves perpendicularly selected axis, the body coordinate on this axis does not change, and in this case the movement module along this axis is 0.

Figure 7. Example 3

Example 3. If the body moves at an angle to the axis OH, then, determining the projection of the vector on the axis oh, it can be seen that the projection in its value will be less than the module of the vector S. by subtracting x 2 - x 1, determine the scalar value of the projection.

Solving the task of determining the path and movement

Consider the task. Determine the location of the engine boat. The boat moved away from the pier and passed along the coast straight and evenly first 5 km, and then in the opposite direction for another 3 km. It is necessary to determine the traveled path and module of the movement vector.

Topic: Laws of interaction and movement

Lesson 4. Move with rectilinear uniform motion

Yerutkin Evgeny Sergeevich

Uniform straight movement

To begin with, let's remember the definition uniform motion. Definition: Uniform movement is called such a movement in which the body passes the same distances in any equal intervals.

It should be noted that uniform can not only be straightforward, but also curvilinear movement. Now we will look at one particular case - the movement along the straight. So, uniform rectilinear movement (RPD) is a movement in which the body moves along the line and in any equal periods of time makes the same movement.

Speed

An important characteristic of this movement - speed. From the 7th grade you know that speed is a physical value that characterizes the speed of movement. With a uniform rectilinear movement, the speed is permanent. The speed is the vector, indicated, the unit measurement unit is m / s.

Fig. 1. Speed \u200b\u200bProjection Sign

depending on its direction

Pay attention to fig. 1. If the speed vector is directed towards the axis direction, then the speed projection will be. If the speed is directed against the selected axis, the projection of this vector will be negative.

Determination of speed, path and movement

We turn to the formula for calculation of speed. The rate is defined as the ratio of movement by the time during which this movement occurred :.

We draw your attention to the fact that with a straight line movement of the length of the movement vector is equal to the path passed by this body. Therefore, we can say that the movement module is equal to the path traveled. Most often, you met this formula in grade 7 and in mathematics. It is recorded simply: S \u003d V * T. But it is important to understand that this is only a special case.

Motion equation

If you remember that the projection of the vector is defined as the difference in the final coordinate and the initial coordinate, i.e. S x \u003d x 2 - x 1, then you can get the law of movement with a straightforward uniform movement.

Speed \u200b\u200bgraph

Please note that the speed projection can be both negative and positive, so it is placed in a plus or minus, depending on the direction of speed relative to the selected axis.

Fig. 2. Chart of the velocity projection rate for RPD

The graph of the projection of the speed of the time presented above, the immediate characteristic of the uniform movement. Along the horizontal axis, the time is postponed, the vertical axis is the speed. If the speed projection schedule is located above the abscissa axis, then this means that the body will move along the axis oh, in the positive direction. In the opposite case, the direction of movement does not coincide with the direction of the axis.

Geometric interpretation of the journey

Fig. 3. Geometric meaning of speed schedule

Topic: Laws of interaction and movement

Lesson 5. Straighty equilibrium movement. Acceleration

Yerutkin Evgeny Sergeevich

The subject of the lesson "uneven rectilinear movement, straight equivalent movement". To describe such a movement, we introduce an important amount - acceleration. Recall that in previous classes we discussed the question of a straight uniform movement, i.e. Such movement when the speed remains permanent.

Uneven movement

And if the speed changes, what then? In this case, they suggest that the movement is uneven.

Instant speed

For the characteristics of the uneven movement, a new physical value is introduced - instant speed.

Definition: Instant speed is the body speed at the moment or at this point of the trajectory.

The device that shows instantaneous speed is on any moving agent: in the car, train, etc. This is a device called a speedometer (from English - Speed \u200b\u200b(Speed)). We draw your attention to the fact that the instantaneous rate is defined as the ratio of movement by the time during which this movement occurred. But after all, this definition is no different from the previously given speed of the RPD. For a more accurate definition, it should be noted that the period of time and the corresponding movement is taken very small, seeking to zero. Then the speed does not have time to change strongly, and we can use the formula that was introduced earlier :.

Pay attention to fig. 1. x 0 and x 1 is the coordinates of the movement vector. If this vector is very small, then the speed change will happen quickly. This change in this case we characterize the change in instantaneous speed.

Fig. 1. To the question of determining instantaneous speed

Acceleration

In this way, uneven movement It makes sense to characterize a change in speed from point to point, how quickly it happens. This speed change is characterized by the value called acceleration. The acceleration is indicated, this is a vector magnitude.

Definition: Acceleration is defined as the ratio of the change in the speed to the time during which this change occurred.

Acceleration is measured by m / s 2.

In essence, speed change speed is acceleration. The value of the projection of acceleration, since this vector may be negative and positive.

It is important to note that where the change in speed is directed, acceleration will be sent there. This particular importance acquires with a curvilinear movement when the value changes.

Topic: Laws of interaction and movement

Lesson 6. Speed \u200b\u200bof straight equal to the movement. Speed \u200b\u200bgraph

Yerutkin Evgeny Sergeevich

Acceleration

Recall what acceleration is. Acceleration - This is a physical value that characterizes the change in the speed for a certain period of time. .

that is, the acceleration is the value that is determined by the change in speed during which this change occurred.

Speed \u200b\u200bequation

Taking advantage of the acceleration equation, it is convenient to record a formula for calculating the instantaneous speed of any interval and for any point in time:

This equation makes it possible to determine the speed at any time of the body movement. When working with the law, the speed change of time must be taken into account the direction of speed relative to the selected CO.

Speed \u200b\u200bgraph

Speed \u200b\u200bgraph(speed projections) is the law of changing the speed (speed projection) on time for an equilibrium straight line, presented graphically.

Fig. 1. Graphs of the dependence of the projection of the speed of time for an equilibrium straight movement

Let's analyze various graphs.

First. Speed \u200b\u200bprojection equation :. Speed \u200b\u200band time increase, note that on the graph in the place where one of the axes is time, and the other is the speed, there will be a straight line. This line begins from the point that characterizes the initial speed.

The second is a dependence in the negative value of the projection of acceleration, when the movement is slow, that is, the speed of the module is first reduced. In this case, the equation looks like :.

The graph begins at the point continues to the point, the intersection of the time axis. At this point, the body speed becomes zero. This means that the body stopped.

If you carefully look at the speed equation, then remember that there was a similar function in mathematics. This equation is direct, which is confirmed by the schedules considered by us.

Some special cases

To finally deal with the speed schedule, consider a special case. In the first graph, the dependence of the speed of time is related to the fact that the initial speed, equal to zero, the projection of acceleration is greater than zero.

Record this equation. Well, the very type of graph is quite simple (schedule 1):

Fig. 2. Various cases of equivalent movement

Two more cases equal asked movement Presented in the following two charts. The second case is a situation where first the body was moving with a negative projection of acceleration, and then began to accelerate in the positive direction of the axis oh.

The third case is a situation where the acceleration projection is less than zero and the body is continuously moving in the direction opposite to the positive direction of the axis oh. In this case, the speed module is constantly increasing, the body is accelerated.

This video tutorial will help users get an idea of \u200b\u200bthe topic "Move with rectilinear equivalent movement". During this classes, students will be able to expand their knowledge of straight equivalent movement. The teacher will tell how to correctly determine the movement, coordinates and speed with such a movement.

Topic: Laws of interaction and movement

Lesson 7. Movement with rectilinear equative movement

Yerutkin Evgeny Sergeevich

In previous lessons, we discussed how to determine the traveled path with a uniform rectilinear movement. It is time to learn how to determine the coordinate of the body, traveled path and move when. This can be done if we consider a straight line equivalent movement as a set of a large number of very small uniform body movements.

Experience Galilea

The first to solve the problem of the location of the body at a certain point in time at an accelerated movement Italian scientist Galileo Galilee. He spent his experiments with an inclined plane. In the groove, he launched a ball, a muscutal bullet, and then determined the acceleration of this body. How did he do it? He knew the length of the inclined plane, and the time was determined by the beat of his heart or the pulse.

Definition of movement by speed schedule

Consider a chart of speed dependency equal asked straight line from time. This dependence is known to you, it represents a straight line: V \u003d V 0 + AT

Fig.1. Definition of movement

with an equilibrium straight movement

Speed \u200b\u200bgraph is divided into small rectangular sections. Each site will correspond to a certain constant speed. It is necessary to determine the path traveled during the first time interval. We write the formula :.

Now we consider the total area of \u200b\u200ball the figures we have. And the amount of the area with a uniform movement is a complete path passed.

Please note that the point to the point will change the speed, thereby getting the way passed by the body with rectilinear equative movement.

Note that with rectilinear equilibrium movement of the body, when the speed and acceleration are directed in one direction, the movement module is equal to the path traveled, so when we determine the movement module - determine distance traveled. In this case, we can say that the movement module will be equal to the area of \u200b\u200bthe figure, limited by speed and time graph.

We use mathematical formulas to calculate the area of \u200b\u200bthe specified figure.

The area of \u200b\u200bthe figure, (numerically equal to the distance traveled), is equal to half the bases multiplied by height. Note that in the figure is one of the bases is the initial speed. And the second base of the trapezium will be the final speed indicated by the letter multiplied by. This means that the height of the trapezium is a period of time for which the movement occurred.

The final rate discussed at the previous lesson, we can record as the sum of the initial speed and the contribution due to the presence of constant acceleration in the body. It turns out an expression:

If you open brackets, it becomes doubled. We can record the following expression:

If separately burn each of these expressions, the result will be the following:

This equation was first obtained thanks to the experiments of Galileo Galileo. Therefore, we can assume that it was this scientist for the first time gave the opportunity to determine the location of the body at any time. This is the solution to the main task of mechanics.

Definition of body coordinates

Now let's remember that the path passed equal to in our case module movement, expressed by the difference:

If in the Galilean equation to substitute the expression for S, we will write the law to which the body moves with a straight equative movement:

It should be remembered that the speed, its projection and acceleration may be negative.

The next stage of the consideration of the movement will be the study of movement on the curvilinear trajectory.

Topic: Laws of interaction and movement

Lesson 8. Moving the body with straight equative movement without initial speed

Yerutkin Evgeny Sergeevich

Straight equivalent movement

Consider some features of body movement when straight equative movement without initial speed. The equation, which describes this movement, was derived by Galileem in the XVI century. It must be remembered that with a straightforward uniform or uneven movement, the movement module coincides with its own value. The formula is as follows:

S \u003d V O T + AT 2/2,

where and is an acceleration.

Case of uniform movement

The first, the easiest case is the situation when the acceleration is zero. This means that the equation above will turn into the equation: S \u003d V 0 T. This equation makes it possible to find distance traveled Uniform movement. S, in this case, is a vector module. It can be determined as the difference in coordinates: the final coordinate x minus the initial coordinate x 0. If we substitute this expression in the formula, the dependence of the coordinates from time to time.

Movement case without initial speed

Consider the second situation. At v 0 \u003d 0, the initial speed is 0, it means that the movement begins from the state of rest. The body rested, then begins to acquire and increase the speed. Movement from the rest of the rest will be recorded without the initial speed: S \u003d AT 2/2. If s - module of movement(or traveled) designate as the difference in the initial and final coordinate (from the final coordinate, we submit the initial one), then the equation of motion, which makes it possible to determine the body coordinate for any point in time: x \u003d x 0 + AT 2/2.

The projection of the acceleration can be both negative and positive, so you can talk about the coordinate of the body, which can both increase and decrease.

Proportionality of the Square of Time

Important patterns of equations without initial speed, i.e. When the body begins his movement from resting:

S X - the path passed, it is proportional to T 2, i.e. Square time. If we consider equal intervals of time - T 1, 2T 1, 3T 1, then the following ratios can be seen:

S 1 ~ 1 S 1 \u003d A / 2 * T 1 2

S 2 ~ 4 S 2 \u003d A / 2 * (2T 1) 2

S 3 ~ 9 S 3 \u003d A / 2 * (3T 1) 2

If you continue, the pattern will continue.

Traveling for sequential time intervals

You can do the following conclusion: The distances have passed in proportion to the square increase in the time intervals. If there was one time interval, for example, 1 s, then the path passed will be proportional to 1 2. If the second segment 2 s, then the distance passed will be in proportion to 2 2, i.e. \u003d 4.

If a certain interval is chosen per unit of time, then the full distances covered by the body over the subsequent equal intervals will relate to the squares of integers.

In other words, moving performed by the body for each subsequent second will be treated as odd numbers:

S 1: S 2: S 3: ...: S n \u003d 1: 3: 5: ...: (2N-1)

Fig. 1. Movement

each second includes as odd numbers

Considered patterns on the example of the task

The investigated two very important conclusions are characterized only by rectilinear equilibrium movement without initial speed.

Task: The car begins to move from the stop, i.e. From the state of rest, and for 4 from its movement passes 7 m. Determine the acceleration of the body and instantaneous speed after 6 seconds after the start of movement.

Fig. 2. Solution of the task

Solution: The car begins to move from resting state, therefore, the path that the car passes is calculated by the formula: S \u003d AT 2/2. Instant speed is defined as V \u003d AT. S 4 \u003d 7 m, the distance that the car passed in 4 from his movement. It can be expressed as the difference in the full path traveled by the body for 4 s, and the path traveled by the body for 3 s. Using this, we obtain acceleration a \u003d 2 m / s 2, i.e. Accelerated, straightforward movement. To determine instantaneous speed, i.e. Speed \u200b\u200bat the end of 6 s, should be accelerated to multiply at the time, i.e. On 6 s, during which the body that continued to move. We obtain the speed V (6c) \u003d 12 m / s.

Answer: The acceleration module is 2 m / s 2; Instant speed at the end of 6 s is 12 m / s.

Topic: Laws of interaction and movement

Lesson 9: Laboratory work №1 "Study of an equilibrium movement

without initial speed

Yerutkin Evgeny Sergeevich

purpose of work

The purpose of the laboratory work is to determine the acceleration of the body movement, as well as it instant speed At the end of the movement.

For the first time, this laboratory work carried out Galileo Galilee. It is thanks to this work, Galileo managed to establish an experienced acceleration of free fall.

Our task is to consider and disassemble how to determine acceleration When the body is moving along an inclined horror.

Equipment

Equipment: a tripod with a clutch and a paw, in the foot is reinforced by inclined flavor; In the gland is the focus in the form of a metal cylinder. The moving body is a ball. Time meter is a metronome, if you run it, it will take time. The measuring tape will be needed to measure the distance.

Fig. 1. Tripod with clutch and paw, chute and ball

Fig. 2. Metronome, cylindrical emphasis

Table measurements

We will make a table consisting of five columns, each of which must be fill.

The first column is the number of metronoma strikes, which we are used as a time counter. S - The next column is the distance that the body passes, the ball rolling along the inclined horror. Next - traffic time. The fourth column is the calculated acceleration of the movement. In the last column - instantaneous speed at the end of the ball movement.

Necessary formulas

To obtain the result, use the formulas: S \u003d AT 2/2.

It is easy to obtain that the acceleration will be equal to the ratio of the double distance divided by the square of the time: a \u003d 2s / t 2.

Instant speed Determined as a product of acceleration at the time of movement, i.e. The time interval from the beginning of the move to the moment the ball will face the cylinder: V \u003d AT.

Experiment

Let us turn to the experiment itself. It should be adjusted for its execution metronome So that it takes one minute 120 shots. Then between two strokes of the metronome there will be a period of time equal to 0.5 s (half amecond). We launch the metronome and follow how it counts the time.

Next, with the help of a measuring tape, we determine the distance between the cylinder, which is emphasis, and the initial point of movement. It is 1.5 m. The distance is chosen so that the body rolls down on the alard has laid at least 4 metronome shots.

Fig. 3. Stopping experience

Experience: a ball that put at the beginning of the movement and let go with one of the shots, gives the result - 4 shock.

Filling table

The results are written to the table and go to the calculations.

In the first column made a digit 3. But there were 4 metronome blows?! The first blow corresponds to the zero mark, i.e. We begin the countdown of time, so the time of movement of the ball is the gaps between the blows, and there are only three of them.

Length path traveled. The length of the inclined plane is 1.5 m. Substituting these values \u200b\u200bto the equation, we obtain an acceleration of approximately 1.33 m / s 2. Please note that it is an approximate calculation, up to the second semicolon.

Instant speed at the moment of impact is approximately 1.995 m / s.

So, we found out how to determine the acceleration of the moving body. We draw your attention to the fact that in their experiments, Galileo Galilee performed the acceleration, changing the angle of inclination of the plane. We offer you to independently analyze the sources of errors when performing this work and draw conclusions.

Topic: Laws of interaction and movement

Lesson 10. Solving tasks to determine the acceleration, instantaneous speed and movement with an equilibrium straightforward movement

Yerutkin Evgeny Sergeevich

The occupation is devoted to solving problems on determining the acceleration, instantaneous speed and movement of the driving body.

The task of determining the path and movement

Task 1 is devoted to the study of the path and movement.

Condition: The body moves around the circumference, passing it half. It is necessary to determine the attitude of the path traveled to the movement module.

Please note: the condition of the task is given, but there is not a single number. Such tasks will be found in the course of physics quite often.

Fig. 1. Path and movement of the body

We introduce notation. The radius of the circle along which the body moves is equal to R. When solving the problem, it is convenient to make a picture on which the circle and an arbitrary point from which the body moves, and denotes a; The body moves to the point in, and S is half the circumference, S is moveconnecting the starting point of movement with the final.

Despite the fact that there is no number in the task, however, in response, we obtain a completely specific number (1.57).

Task on speed schedule

Task 2 will be devoted to speed schedules.

Condition: Two trains move towards each other along the parallel paths, the speed of the first train is 60 km / h, the speed of the second is 40 km / h. Below are 4 graphics, and you need to choose those on which the schedules of the projection of the speed of these trains are correctly depicted.

Fig. 2. To task condition 2

Fig. 3. Graphs

task 2.

Speed \u200b\u200baxis - vertical (km / h), and the time axis is horizontal (time in h).

On the 1st chart, there are two parallel straight lines, these are modules of the velocity of the body of the body - 60 km / h and 40 km / h. If you look at the bottom schedule, at number 2, you will see the same thing only in the negative area: -60 and -40. On two other charts 60 from above and -40 below. On the 4th chart 40 at the top, and -60 below. What can be said about these charts? According to the problem of the problem, two trains go towards each other, along the parallel paths, so if we choose the axis associated with the direction of the speed of one of the trains, the projection of the velocity of one body will be positive, and the projection of the speed of another negative (since the speed itself is directed against the selected axis) . Therefore, neither the first schedule nor the second to answer the answer. When projection speed It has the same sign, you need to say that two trains move in one direction. If we choose a reference system associated with 1 train, then the value of 60 km / h will be positive, and the value of -40 km / h is negative, the train goes towards. Or, on the contrary, if we associate the report system with the second train, then one of them is a speed projection of 40 km / h, and the other -60 km / h, negative. Thus, both graphics are suitable (3 and 4).

Answer: 3 and 4 graphics.

The task of determining speed with an equilized movement

Condition: The car moves at a speed of 36 km / h, and for 10 s inhibits with an acceleration of 0.5 m / s 2. It is necessary to determine its speed at the end of the braking

In this case, it is more convenient to choose the axis oh and send the initial speed along this axis, i.e. The vector of the initial speed will be directed to the same side as the axis. Acceleration will be directed in the opposite direction, because the car slows down its movement. The projection of acceleration on the axis oh will be with a minus sign. To find the instantaneous, ultimate speed, we use the equation of speed projection. We write the following: V x \u003d v 0x - AT. Substituting the values, we obtain the final speed of 5 m / s. So, after 10 s after braking, the speed will be 5 m / s. Answer: V x \u003d 5 m / s.

The task of determining speeding acceleration

The graph shows 4 dependences of the speed of time, and it is necessary to determine which of these bodies is the maximum, and how minimal acceleration.

Fig. 4. To task condition 4

To solve, it is necessary to consider all 4 graphics alternately.

To compare accelerations, you need to determine their values. For each body, the acceleration will be determined as the ratio of the speed change by the time during which this change occurred. Below the calculations of acceleration for all four tel:

As we see, the second body has a minimum acceleration module, and the third body is maximum.

Answer: | A 3 | - Max, | A 2 | - min.

Lesson 11. Solving problems on the topic "Straight uniform and uneven movement"

Yerutkin Evgeny Sergeevich

Let's consider two tasks, and the decision of one of them is in two versions.

The task of determining the path has passed with an equalized movement

Condition: A plane flying at a speed of 900 km / h makes landing. Time until the aircraft stops 25 s. It is necessary to determine the length of the take-off strip.

Fig. 1. To task condition 1

The main task of mechanics is solved in kinematics:
According to the well-known initial conditions and nature of the movement, the position of the body is determined at any time.

Algorithm for solving problems of kinematics

1. Select a convenient coordinate system.
2. Schematically show the bodies or material points.
3. Show vectors, initial coordinates, vectors projection.
4. Record the main equations (in vector form or in projections).
5. Find the projection of all known values \u200b\u200band substitute in the equation.
6. Solve equations

Rules of addition vectors

When solving problems on mechanics, the ability to work with vector values \u200b\u200bis required.
How, for example, to determine the resulting force if several forces actually act on the body?
How, for example, to determine the direction of movement of the swimmer, whipping the river, if it demolines the flow?
To do this, one of the rules for the addition of vectors will be useful:

Kinematics - Class! Naya Physics

Did you know?

Floods on Mars

For a long time, the canals on Mars considered artificial structures built by the inhabitants of Mars. Over the mystery of the origin of the channels, scientists break their heads today.

According to one of the hypotheses, Martian channels are the result of floods that took place on the planet millions of years ago.

Martian Channels, judging by the photos, very different - from small, size with the middle ground, to huge, hundreds of meters and a width of up to two kilometers.

According to scientists, under the surface of Mars once there were huge deposits of ice. Falls of meteorites or processes inside the planet caused his stormy melting. Water streams splashed to the surface, formed channels. Then in the cold sparse atmosphere of Mars Ice evaporated and partially returned to the planet in the form of snow.

https://accounts.google.com.

Signatures for slides:

Physics laws of interaction and movement of tel. Mechanical oscillations and waves. The sound of the um field. The structure of the atom and the atomic nucleus.

Topic 1 "The laws of interaction and movement of the tel" lesson 1. The material point. Reference system. Moving Yulia Rinatna Zalyaliyeva, teacher of physics and mathematics MBOU SOSH No. 8. 2.09.2015

Movement is an integral material of matter movement

Mechanical movement - change of body position in space relative to other bodies over time. Mechanical movement

Distance traveled; Speed; Trajectory; Moving; Body coordinates. Motion characteristics:

Speed \u200b\u200bis a value that characterizes the speed of the movement υ (m / s)

Body coordinate - body position in space at any time of the body coordinate

with a delicate table r Rafic and nylitic (formula) Method descriptions

The verbal description leaving from point A, the train 2 hours drove at a speed of 100 km / h, then the hour stood, and at point B arrived in 3 hours, all this time moving at a constant speed of 50 km / h.

Table Description Graphic Description

Analytical description

Motion descriptions

The material point is the body, the sizes of which can be neglected in the conditions of this task the material point

For example, for the material point, the land is very often considered if they explore her movement around the sun.

Is it possible to consider the material points of the body described in the following situations? 1. Rain the path of the Earth in orbit around the sun. 3. For the determination of the ball volume, it is lowered in the menzurka. 4. For measuring the mass of lemon, it is put on the scales. 5. Your examples

To determine the position of the body (material point) in space, you must: set the reference body; Select the coordinate system; Have a device for time counting (clock)

What is the reference body? The body of the reference is a body relative to which the position of other (moving) bodies is determined.

Coordinate system

Reference system:

Repeat What is a mechanical movement? What is the material point? In what cases can the body be considered a material point? What movement is called translational? What is the reference system?

§ 1-2, questions after paragraph UPR. 1 (2,4), UPR.2 (1) Know all definitions (!) Homework:

1 point number Movement type Definition Examples 1 Transfer 2 straight line 3 rotational 4 curvilinear 5 uniform 6 non-uniform

The trajectory is a line, along which the body moves the path passed is the length of the trajectory movement - a vector connecting the initial position of the body with its subsequent position S (M) S (m)

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Theme lesson. Determination of the coordinates of the moving body lesson 2

Scalar and vector variables path travel path

The trajectory is a line, along which the body moves the path passed is the length of the trajectory movement - a vector connecting the initial position of the body with its subsequent position S (M) S (m)

Determination of the traveled path and movement

Task1. The car moved from the point with the coordinate x 0 \u003d 200 m to the point with the coordinate x \u003d -200 m. Determine the projection of the car movement. Danched: x 0 \u003d 200 m x \u003d -200 m s -? Solution of calculation s x \u003d -200 m-200 m \u003d -400 m Answer: S x \u003d -400 m

Determine the schedule traveled path and module for moving the material point. S \u003d AB + Sun + C d \u003d 8 m + 4 m + 8 m \u003d 20 m | s | \u003d A d \u003d 4 m

Collection of tasks in physics A.P. Rymkevich 2, 9 №11 № 17

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Forces in dynamics 11/19/15

Gravity

Gravity

Power reaction support

The force of elasticity is the force arising during body deformation, which seeks to restore the previous sizes and shape of the body

The law of the bitch f \u003d - kx k is the stiffness coefficient (N / M) depends on the material of the spring and the geometric dimensions x - the elongation of the body (M) x \u003d ℓ 2 - ℓ 1

Comparison forces force gravity strength elasticity body weight nature forces direction point application depends on the formula

The friction force is the power of resistance to relative movement of contacting surfaces of tel. The friction coefficient μ is the value of dimensionless. μ.

Homework Table Preparation for laboratory work Notebook for laboratory work

Preparation for laboratory work

Determination of the coefficient of friction

***The task. The load rolls off the inclined plane. Picture all the forces acting on the body.

Comparison of Force Force Highness Power Elasticity Body Weight The nature of the forces Gravitational electro-magnetic electro-magnetic direction to the center of the earth against deformation Different point of the application Mass Center Center The center of mass of the body of the support or suspension depends on body weight and height above the surface of the rigidity coefficient of spring and body weight deformity , acceleration, external environment Formula F \u003d Mg f \u003d - kx p \u003d m (g ± a)

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

01/13/16 oscillatory movement.

What is called mechanical oscillations? What types of oscillations are you known?

Free is fluctuations that occur under the influence of the inner forces after the system was removed from the state of equilibrium. Forced, these are oscillations occurring under the action of external forces. Mechanical oscillations are movements that are exactly or approximately repeated at equal intervals.

List the values \u200b\u200bcharacterizing oscillations

A amplitude is the module of the greatest value of the changing value. A [a] \u003d m amplitude of oscillations

The period is the time for which one oscillation is performed. [T] \u003d C T T \u003d N x, m T, C 5 2 4 6 8 10 12 t t

Frequency is the number of oscillations performed for 1 s. V \u003d n T [v] \u003d Hz Unit of measurement is named so in honor of the German physics of Herry Hertz 1Hz is one oscillation per second. About this frequency beats the human heart V \u003d 1 T

D / s §24-26 (know definitions)

P.105 No. 1-4 Preparation for testing

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Uniform movement around the circumference. § 18-19, UPR 18 (1)

Mechanical movement straightforward (trajectory - straight) curvilinear (trajectory - curve) And about in about and in motion

N s table (top view) magnet inclined gutter ball gathered

Any curve can always be represented as a set of arc circles of various radii. With curved motion, change: 1) coordinates 2) Direction Movement 3) Direction and module of speed and acceleration The curvilinear movement is always a movement with acceleration, even if the module does not change the speed.

Instant body velocity at any point of the trajectory is directed towards the trajectory at this point. O and B.

Uniform movement around the circle is a movement around the circumference with a constant speed by module. A O R R is the radius of the circle - the initial velocity in - the final speed with a uniform movement around the circumference of its acceleration in all points of the circle rushed to the center - the centripetal acceleration. - Centripetal acceleration anywhere in the trajectory:

We will find the acceleration module A in M \u200b\u200bn Consider ΔAs and ΔA Mn Δ AOs - isceived, because OA \u003d V \u003d R Δ amn is a chaired, because Slide 9.

According to II Z.N. Strength, under the action of which the body moves around the circumference with a constant speed at each point, directed along the radius to the center of the circle - the power of the centripetal. Centripetal force

Preview:

To enjoy previewing presentations, create yourself an account (account) Google and log in to it: https://accounts.google.com

Signatures for slides:

Municipal educational institution Domodedovskaya Secondary school № 2 Physics - 9th grade Teacher Physics: Shekunova Natalia Vladimirovna

Lesson theme: Pulse. The law of preserving the impulse.

The body pulse is called a vector magnitude equal to the product of body weight at its speed:

Pulse P - vector magnitude. It always coincides towards the body velocity vector. Any body that moves, has an impulse.

The concept of impulse

The bodies system is called closed if the interacting bodies do not interact with other bodies.

In a closed system, the vector sum of pulses of all bodies that are in the system remains constant for any interactions of the body of this system among themselves. The law of preserving the impulse.

Pulse manifestation

When the firefighters use Brands-Point, they always keep it together or even threesome. So it is necessary to do to counteract the pulse of the beating jet.

The law of preserving the impulse on the example of the collision of the balls.

Law of preserving impulse

Give the answer: What is called body pulse? Record the body pulse formula. What is the unit for measuring body pulse in si? What is a closed body body? Give examples of the manifestation of the impulse conservation law. # 17. Task: 1.

Task: on a fixed cart weighing 100 kg. Jumping a man with a mass of 50 kg. At a speed of 6 m / s. How fast will the trolley be moving with a man?

Signatures for slides:

11/13/2015 Newton's laws

What is the question called inertial? Neinercial? Examples. In which case the body moves uniformly? What is called material point? Formulate Newton's first law? Why stumbling a person falls forward, and slipped back? Why doesn't the ball be resting on the inclined plane?

Questions 1. What is called force? 2. What is the power characterized? 3. How are the forces acting on the body? 4. How is the acceleration of the body? 5. Word the Second Newton Law? 6. What role does the mass play in motion? 7. How does the body move if f \u003d 0? 8. How does the body move, if the power acts on it?

Questions 1. Formulate the third law of Newton? 2. What are the features of this law? 3. Create an example of fulfilling the III of the law. 4. The body is thrown at an angle to the horizon. Where is the acceleration of the body, if the air resistance is not taken into account?

Newton First Law Second Law Third Law Border Applicability Macroscopic Body System Two Bodies Model Material Point System Two Materials Described Phenomenon Condition of Peace or RPD ORD Interaction Body Body Body If F \u003d 0, then V \u003d Const F 12 \u003d - F 21

At this lesson, the topic of which: "Determination of the coordinates of the moving body" we will talk about how to determine the location of the body, its coordinate. Let's talk about reference systems, consider for example the task, and also recall what movement is

Imagine: You have abandoned the ball. How to determine where it will be in two seconds? You can wait two seconds and just see where it is. But, without even looking, you can approximately predict where the ball will be: the throw was stronger than the usual, directed at a large angle to the horizon, it means that it will fly high, but not far ... Using the laws of physics, it will be possible to accurately determine the position of our ball.

Determine the position of a moving body at any point in time - this is the main task of kinematics.

Let's start with the fact that we have a body: how to determine its position, how to explain to someone where it is? We say about the car: it is on the road 150 meters before the traffic light or 100 meters per intersection (see Fig. 1).

Fig. 1. Definition of the location of the machine

Or on the track 30 km south of Moscow. On the phone on the table, say: it is centimeters to 30 right of the keyboard or near the distant corner of the table (see Fig. 2).

Fig. 2. Position of the phone on the table

Note: We will not be able to determine the position of the car without mentioning other objects without attaching to them: traffic lights, city, keyboard. We define the situation, or coordinates, always relative to something.

Coordinates are a set of data by which the position of one or another object is determined, its address.

Examples of ordered and disordered names

The coordinate of the body is his address for which we can find it. He is ordered. For example, knowing a number and place, we define exactly where our place is located in the cinema hall (see Fig. 3).

Fig. 3. Cinema Hall

The letter and digit, for example E2, the position of the figure on the chessboard is accurately set (see Fig. 4).

Fig. 4. Position of the figure on the board

Knowing the address of the house, for example Sunny 14, we will look for it on this street, on the even side, between houses 12 and 16 (see Fig. 5).

Fig. 5. Search at home

The names of the streets are not ordered, we will not look for a sunny street according to the alphabet between the streets of Pink and Turgenev. Also not ordered phone numbers, license plates of cars (see Fig. 6).

Fig. 6. Disordered names

These numbers going in a row are just a coincidence that does not mean neighborhood.

We can set the position of the body in different coordinate systems, as we are comfortable. For the same car, you can set accurate geographical coordinates (latitude and longitude) (see Fig. 7).

Fig. 7. Longitude and latitude of terrain

Fig. 8. Location relative to the point

Moreover, if we choose different such points, we will get different coordinates, although they will set the position of the same car.

So, the position of the body relative to different bodies in different coordinate systems will be different. What is the movement? Movement is a change in body position with time. Therefore, we will describe the movement in different reference systems in different ways, and it makes no sense to consider the body movement without reference system.

For example, how is a glass of tea with tea on the table in a train, if the train itself goes? Watching what. Regarding the table or passenger sitting near the seat, the glass is resting (see Fig. 9).

Fig. 9. Movement of a glass of passenger

Regarding the tree near the railway, the glass is moving along with the train (see Fig. 10).

Fig. 10. Stacker movement along with the train relative to the tree

Regarding the globe, the glass and the train together with all points of the earth's surface will also move around the circle (see Fig. 11).

Fig. 11. The movement of a glass with the rotation of the Earth relative to the earth's axis

Therefore, it makes no sense to talk about the movement in general, the movement is considered in the reference to the reference system.

All we know about the movement of the body can be divided into the observed and calculated. Recall an example with the ball that we threw. The observed is its position in the selected coordinate system, when we only throw it (see Fig. 12).

Fig. 12. Observation

This is the moment of time when we threw it; The time that passed after the throw. Let the ball there are no speedometer that would show the ball speed, but its module, like the direction, can also be found using, for example, slow motion.

With the help of the observed data, we can predict, for example, that the ball falls after 5 seconds 20 m from the place of the throw or after 3 seconds will fall into the top of the tree. The position of the ball at any time is in our case the calculated data.

What determines every new position of the moving body? It determines the movement, because moving is a vector characterizing the change in position. If the beginning of the vector is combined with the initial body position, the end of the vector will indicate a new position of the moving body (see Fig. 13).

Fig. 13. Vector of movement

Consider several examples on determining the coordinates of the moving body by its movement.

Let the body moved straightly from point 1 to point 2. We construct the movement of the movement and denote it (see Fig. 14).

Fig. 14. Moving the body

The body moved along one straight line, it means that we will be enough one axis of coordinates directed along the movement of the body. Suppose we are observing the movement from the part, compatible the beginning of the reference with the observer.

Moving - vector, it is more convenient to work with the projections of the vectors on the axis of the coordinates (we have one). - vector projection (see Fig. 15).

Fig. 15. Projection of vector

How to determine the coordinate of the starting point, point 1? Lower perpendicular from point 1 on the coordinate axis. This perpendicular cross the axis and mark the point of the point 1. Also define the point 2 coordinate (see Fig. 16).

Fig. 16. Lower the perpendicular to the axis oh

Travel projection is:

With this direction of the axis and movement, it will be equal to the module itself.

Knowing the initial coordinate and movement, to find the final coordinate of the body - the matter of mathematics:

The equation

The equation is equality containing an unknown member. What is his meaning?

Any task is that something we know, and something is no, and the unknown needs to find. For example, the body from a certain point moved 6 m in the direction of the axis of the coordinate and turned out to be at the point with the coordinate 9 (see Fig. 17).

Fig. 17. Starting point

How to find from what point the body starts the movement?

We have a pattern: the projection of movement is the difference of the final and initial coordinates:

The meaning of the equation will be that we know the movement and the final coordinate () and we can substitute these values, and we do not know the initial coordinate, it will be unknown in this equation:

And already solving the equation, we will get the answer: the initial coordinate.

Consider another case: moving is directed to the side opposite to the direction of the coordinate axis.

The coordinates of the initial and endpoints are determined in the same way as before, the perpendicular to the axis is lowered (see Fig. 18).

Fig. 18. The axis is directed to the other side

Projection of movement (nothing changes) is equal to:

Note that more than, and the projection of movement, when it is directed against the axis of the coordinates, will be negative.

The final coordinate of the body from the equation for the projection of the movement is:

As you can see, nothing changes: In the projection on the coordinate axis, the final position is equal to the initial position plus the projection of movement. Depending on which side the body has moved, the projection of the movement will be positive or negative in this coordinate system.

Consider the case when the movement and axis of coordinates are directed at an angle to each other. Now one axis of coordinate is not enough for us, the second axis is needed (see Fig. 19).

Fig. 19. The axis is directed to the other side

Now the move will have a non-zero projection on each coordinate axis. These displacement projections will be determined, as before:

Note, the module of each of the projections in this case is less than the movement module. The movement module can be easily found using the Pythagora theorem. It can be seen that if you build a rectangular triangle (see Fig. 20), then its katenets will be equal and, and hypotenuse is equal to the movement module or, as often written, simply.

Fig. 20. Triangle Pythagora

Then, on the Pythagora theorem, we write:

The car is 4 km east of the garage. Take advantage of one axis of coordinates aimed at east, with the start of reference in the garage. Specify the car coordinate in a given system after 3 minutes if the car was driving with this time at a speed of 0.5 km / min to the west.

In the task, nothing is said that the car turned or changed the speed, so we consider the movement uniformly straightforward.

I will depict the coordinate system: the origin of the coordinate at the garage, the X axis is directed to the east (see Fig. 21).

The car was originally at the point and moved under the condition of the task to the West (see Fig. 22).

Fig. 22. Movement of the car to the West

Projection of movement, as we repeatedly wrote, is equal to:

We know that the car drove 0.5 km every minute, it means to find the total move, you need to multiply the speed by the number of minutes:

On this physics ended, it remains to mathematically to express the desired coordinate. Express it from the first equation:

Substitute moving:

It remains to substitute the numbers and get the answer. Do not forget that the car moved to the West against the direction of the axis X, it means that the projection of speed is negative :.

The task is solved.

The main thing is how we used today to determine the coordinates - the expression for the projection of the movement:

And from it we have already expressed a coordinate:

At the same time, the projection of the movement can be set, can be calculated as in the task of a uniform straight line movement, it can be calculated more complicated that we still have to study, but in any case the coordinate of the moving body (where the body turned out to be determined by the initial coordinate (where was the body) and on the projection of movement (where it moved).

On this, our lesson is over, goodbye!

Bibliography

1. Sokolovich Yu.A., Bogdanova GS Physics: Handbook with examples of solving problems. - 2nd edition, redid. - X.: Vesta: Publishing House "Rocky", 2005. - 464 p.
2. Pryrickin A.V., Godnik E.M. Physics: Grade 9. Textbook for general education institutions. - 14th ed. - M.: Drop, 2009.

1. Class-fizika.narod.ru ().
2. AV-PHYSICS.NAROD.RU ().
3. Class-fizika.narod.ru ().

Homework

1. What is moving, path, trajectory?
2. How can I define the coordinates of the body?
3. Record the formula to determine the projection of movement.
4. How will the movement module be determined if the movement has a projection into two axes of coordinates?