Topic: The equation of rectilinear uniform motion.
The purpose of the lesson: to find out what kind of movement is taken as a rectilinear uniform; what is meant by the speed of rectilinear uniform motion; learning to solve problems.
During the classes
I. Examination homework in the form of a face-to-face survey
1) What is meant by the trajectory of movement?
2) Depending on the shape of the trajectory of movement, there can be ...?
3) How do you graphically represent the trajectory of movement:
The center of the car's wheel relative to the highway?
Points on the tire of the wheel relative to the center of the wheel and relative to the highway when the car is moving?
4) How can you describe the motion of a material point?
5) Write down the equations of motion of a material point in coordinate form.
6) What is the frame of reference?
7) What is called a displacement vector?
8) What is the displacement modulus:
If the direction of the coordinate axis is the same as the direction of the vector?
If the vector is directed at an angle α to the direction of the coordinate axis?
II. Learning new material by the method of heuristic conversation:
1) Describe in detail the movement of the car on the highway. Does it always move uniformly?
3) What is called rectilinear uniform motion?
4) What is called the speed of rectilinear uniform motion?
5) What is the formula for the speed of rectilinear uniform motion? (ʋ=s/t)
6) What is the modulus of speed? (ʋ=∆s/ ∆t)
The equation of motion of a material point for rectilinear uniform motion in vector form is written as follows: r=r 0 +ʋt
In coordinate form, only without a sign - a vector. x \u003d x o +ʋ x t; y= y o +ʋ y t; z=z o +ʋ z t
On the graph, uniform rectilinear motion is depicted as - the area of \u200b\u200ba rectangle which is equal to: s \u003d ʋ x t from this equation follows: x - x o \u003d ʋ x t. This means that the change in the coordinate of the body is numerically equal to the area of the rectangle.
III. Solving problems to consolidate the acquired knowledge
1. The point moves uniformly and rectilinearly in the positive direction of the Ox axis. At the initial moment of time, the point had the coordinate x o = -10m. Find the coordinate of the point after 5s from the beginning of the time reference, if the modulus of its speed is equal to ʋ=2m/s. What is the distance traveled by the point during this time?
IV. Summarize the lesson
V. Reflection
VI. Homework:§ 4, learn the formulas and notation of quantities.
Outline of a physics lesson in grade 7 “Schedule of uniform rectilinear motion»
Author: Ganovicheva Maria Anatolyevna, Communal government agency « high school No. 13 "of the akimat of the city of Ust-Kamenogorsk, a teacher of physics.Purpose: exchange of experience with colleagues in the organization learning activities students in physics lessons.
Description: This abstract is intended for teachers of physics during the initial acquaintance and study of the topic "Graph of uniform rectilinear motion." The material has a close relationship with the subject of mathematics, so it can be used to conduct an integrated lesson.
The purpose of the lesson: familiarity with the equation and a graphical method for describing rectilinear uniform motion.
Tasks:
Tutorials:
To teach how to read and build graphs of rectilinear uniform motion for various bodies (moving with negative and positive speed, with and without an initial coordinate);
Developing:
Develop an understanding of the meaning of physical quantities;
Develop functional literacy, namely: the ability to compare, analyze, use formulas, record data in tabular and graphical form, perform calculations;
Educational:
To cultivate cognitive interest in the subject, attentiveness and observation, to strengthen interdisciplinary connections,
Cultivate a culture of making notes in notebooks;
Develop the ability to work independently and in a team.
Lesson type: lesson of studying and primary consolidation of new knowledge.
Interdisciplinary communication: mathematics, geography, technology, drawing.
Devices and materials: handout: coordinate systems, task cards ( see Appendices 1,2); presentation "Graph of uniform rectilinear motion", illustrations, posters on the topic of the lesson.
During the classes:
1. Organizational moment.Preliminary organization of the class (checking absent, jobs).
I want to start our lesson with the phrase of N. Rothschild: "Who owns the information, he owns the world."
In order to possess information or information about something, one must be able to receive it.
How can information be received and transmitted?
Student responses: In words, text, tabular, depict with a diagram or drawing, draw in the form of a graph.
Read the topic of the lesson, think what What do we have to do in class today? How?
Student responses: get acquainted with graphs, compare movement, build graphs.
You have already met with a graphical way of presenting information: weather forecasts, a class graph (it is easy to see subjects for which there are a lot of good grades), a cardiogram, comparative stock reports.
Working with graphs is very convenient and useful and will be useful to us in the future.
2. Actualization of the studied material.
We answer questions:
1. What does the science of physics study?
Physics is the science of nature that studies the most general forms motions of matter and their mutual transformations
2. What is called mechanical movement?
The mechanical motion of a body is the change in its position in space relative to other bodies over time.
3. What is called a trajectory?
The line described in space by this point as it moves.
4. What is speed? Speed is constant, equal to the ratio of the movement of the body to the time during which the movement occurred
5. Calculation formula
6. Name the types of movement according to the figure
A) along the trajectory: rectilinear or curvilinear B) along the speed: uniform or non-uniform
The simplest type of movement: rectilinear uniform (the path is equal to the displacement, the speed is constant), which we met in the last lesson.
Using the example of such a movement, we will begin to work with one of the ways to describe and study physical processes – graphic way.
3. Learning new material.
Today we will recall from the course of geography the concept coordinate
.
Geographical coordinates are quantities that determine the position of a point on earth's surface using latitudes and longitudes.
Coordinate in physics also a numeric value indicating where the point is at a given time.
Designated - X, measured in meters.
When calculating and constructing, it is important to take into account the reference system.
That is, at the moment of the beginning of the movement, the body can be at the point that we take as the origin (its coordinate will be “o”) or it can be displaced and have - X0 the initial coordinate.
The equation of rectilinear uniform motion allows us to solve the main problem of mechanics - to find the position of the body at any time.
Please note that the speed and the initial coordinate do not change, the coordinate and time will change in the equation.
From the course of mathematics, we know a similar equation - this is the equation of a straight line (linear dependence):
Therefore, graphically both dependencies will look the same.
We build the abscissa axis and the ordinate axis. The teacher supervises the performance by students of all stages of work in notebooks.
The axes must be signed not only with values, but also with units of measurement.
To build a graph of rectilinear uniform motion, you need to know at least two points. Numeric values It is customary to write in the form of a table next to the coordinate axes.
Example 1
Let's build a graph of the monitor lizard movement if it is known that it moves from the origin of coordinates and its speed is 3 m/s.
Next, students are given a sheet with completed axes and a table for speed of execution. further work.
(Appendix 1)
Example 2
Let's build a motion graph if it is known that a cyclist is moving at a speed of 5 m/s from a point with an initial coordinate of 10 m.
The example of the movement of a cyclist shows us how important it is to choose the right scale for the image on the graph.
In geography, this is the ratio of the length of a segment on a map or plan to its actual size. In drawing and technology, this is the ratio of the dimensions of an object in a drawing to its actual dimensions.
For us today scale is the ratio of the sizes of physical quantities on a conditional graphic image.
In one cell, we can accept both 1 m and 2 m and 5 m and 10 m vertically. Horizontally, you can take 0.25s, 0.5s, 1s or more.
Example 3:
Let's build a graph of the movement of the helicopter in the same coordinate system, if it is known that it is moving at a speed of -20m/s from a point with an initial coordinate of 15m.
4. Consolidation of the studied material
Students are grouped into groups of 3. Groups are formed by the teacher, taking into account abilities and psychological compatibility. The task involves discussion and joint implementation: plotting two (and if there is enough time, more) bodies on one sheet.
One student performs the graphic part of the task: builds axes, selects a scale, finds points and connects them, signs the work.
Two other students receive task cards (Annex 2) perform calculations and complete tables. After completing the task, you need to evaluate your work in the group for each participant.
For strong students, additional tasks should be provided. For example, if the group had cards No. 1 and 2, then in case of quick completion, these students can be offered more cards No. 3 and 4.
5. Summing up.
The verbal or textual form of information transmission, which is not always familiar to us, is the most effective.
What have we learned today and what have we learned?
Children's answers: In this lesson, we learned how to describe the DRP graphically, build, compare and understand graphs; use formulas, record data in tabular and graphical form, perform calculations; correctly draw up notes in notebooks; work independently and in a team, understood the relationship of physics with other sciences.
And now let's, everyone will think and evaluate their collective work.
Self-esteem. Correct solutions are posted on the board.
Submit your grades on the group sheet.
1. Rectilinear motion
Rectilinear motion body is a motion in which the body moves in a straight line in a given frame of reference.
To describe rectilinear motion in the chosen reference system, it is necessary to turn on the clock at the moment of the beginning of the motion and measure the coordinate of the body at different points in time. The measurement results are presented in the form of a table (a tabular way of describing the movement) or a graph of the movement in the axes: time - coordinate
(graphical way to describe the movement).
If the graphical dependence of the body coordinate on time is known in the form continuous line , then the movement of the body is described completely, i.e., you can:
- Define coordinate bodies at any time of movement (answer the question "where?").
- Define moment of time, in which the body had a given coordinate (to answer the question "when?").
- Characterize the movement of the body (indicate whether the body was at rest, whether it moved in the positive or negative direction of the coordinate axis, how quickly its coordinate changed over time).
2. Uniform movement
The rectilinear motion of a body is called uniform, if the body for any equal time intervals passes equal distances in the same direction. The change in the coordinates of the body over a period of time from the moment t1 until the moment t2 called difference x 2 - x 1 between the end and start values of the coordinate.
rectilinear uniform motion is characterized by the fact that the change in the coordinate of the body per unit of time (it is usually denoted by the Latin letter v) is a constant value. Coordinate plot X bodies from time t for such a movement is straight line . In this case, the dependence of the body coordinate on time has the form:
x \u003d x 0 + v t,
where x 0- initial coordinate of the body, t- moment of time after the start of movement, v- a constant value equal to the change in the coordinates of the body per unit of time, X- coordinate of the body at the moment of time t.
3. Speed of rectilinear uniform motion
If the body moves uniformly in a straight line, then the physical quantity v, numerically equal to the change in its coordinates per unit time, is called the value of the speed of uniform rectilinear motion. In SI, the unit of speed is meter per second (m/s) .
Speed- a vector quantity, which is characterized not only by its module, but also by its direction. If the speed value is positive, then the speed is in the positive direction of the X-axis. If the value of the speed is negative, then the speed is in the negative direction of the X-axis.
Lesson type: practical lesson
Lesson form: on-line
Technology: elements of problem-search technology
Expected Result:
be able to apply theoretical knowledge of kinematics in solving experimental problems;
own terminology in Kazakh, Russian and English, according to kinematics.
Lesson structure:
Organization of the beginning of the lesson - 2 min
Actualization of basic knowledge - 2min
Awareness and comprehension educational material- 3 min
Checking homework -3 min
Solving experimental problems - 30 min
Summing up the lesson. -2 minutes
Homework - 1 min
Reflection - 2 min
During the classes:
If I have seen farther than others, it is only because I have stood on the shoulders of giants.
I. Newton
(slide number 3)
I .Organization of the beginning of the lesson ( Psychological mood for the lesson)
Walking along the roads of discovery, we met great scientists, whose life creative feat did not leave us indifferent. But in each of their discoveries there was an invaluable contribution of their predecessors. Once the great English scientist Isaac Newton said: "If I have seen farther than others, it is only because I was standing on the shoulders of giants." These words can serve as an epigraph to our lesson.
II .Updating basic knowledge
Block diagram (Types of mechanical movement)
(slide number 4)
III .Awareness and comprehension of educational material.
Repetition of basic concepts and formulas of physical quantities
A) Rectilinear uniform motion
B) Rectilinear uniformly accelerated motion ing
B) Decision graphic task
In the last lesson, we considered a graphical method for determining the path traveled by the body over a certain time interval, as one of the optimal methods for solving problems. We use this method to find average speed on a certain section of the road.
The path traveled by a body in a certain time interval is equal to the area of the figure, limited schedule speed.
D) Terminological dictionary
| Kazakh | English | |
| Mechanics | Mechanics | mechanics |
| Kinematics | k kinematics | kinematics |
| mechanics қozgalys | mechanical movement |
|
| materialyk nүkte | material point |
|
| Coordinate | coordinate | coordinate |
| moving | oryn auystyru | transfer ring |
| Speed | zhyldamdyk | speed |
| Acceleration | Udeu | acceleration |
IV . Checking homework
At the last lesson, the task was given to make a device for studying the law of falling bodies, and using the main property uniformly accelerated motion prove that free fall is uniformly accelerated.
Take six identical weights (for example, six identical buttons, screws or nuts) and tie them to an ordinary thread so that the distance between the weights is related to each other as 1:3:5:7:9. If you take the first distance equal, for example, 7 cm, then the second should be 21 cm, the third - 35 cm, the fourth - 49 cm, the fifth - 63 cm.
Hold the appliance by the sixth weight so that the first weight rests on the seat or, even better, on the bottom of the bucket or basin.
Release the weight and listen for the beats. These strikes must be made at regular intervals, although all loads travel different distances. Why? Prove analytically.
V .Solving experimental problems
Task #1
Investigate the dependence of the speed of uniformly accelerated motion on time
Target: check the statement that the speed of a body moving uniformly accelerated in a straight line changes in direct proportion to the time of motion.
Equipment : tripod, tilt rail, carriage, stopwatch, sensors.
From the definition of acceleration it follows that the speed of the body V, moving in a straight line with constant acceleration, after some time t after the start of movement can be determined from the equation: V = V + at ( one). If the body began to move without having initial speed, that is, when Vo = 0, this equation becomes simpler: V = at (2). It follows that the body, moving from rest with a constant acceleration a, after time t 1 from the moment the movement starts, will have a speed V 1 = at 1 After some time t 2 his speed will be V 2 = at 2 , After some time t 3 - speed V 3 = at 3 etc. Moreover, it can be argued that V 2 : V 1 = t 2 : t b ; V 3 : V , = t 3 : t 1 etc. (3).
The movement that the carriage will make when moving between the sensors is measured;
The carriage is started and the time of its movement between the sensors is measured;
Repeat the start of the carriage 6-7 times, each time recording the stopwatch readings;
Calculate the average time of movement of the carriage t cf in the area;
The formula determines the speed with which the carriage moved at the end of the first section;
Increase the distance between the sensors by 5 cm and repeat a series of experiments for 2S, and calculate the value of the body velocity at the end of the second section: V 2
Two more series of experiments are carried out, increasing the distance between the sensors by 5 cm in each series. This is how the speed values \u200b\u200bare found V 3 and V 4 .
According to the data obtained, the validity of the relationship is checked: V 2 : V 1 = t 2 : t 1 V 3 : V 1 = t 3 : t 1 E) final result
Task #2
Estimate the reaction time of the experimenter using a wooden school ruler
30 cm long .
The assistant holds the ruler so that it hangs down, and zero division, it is convenient to have it from below. Experimenter holding thumb and forefinger right hand so that the lower end of the ruler is between the fingers and it is easy for him to grab the falling ruler. The assistant suddenly releases the ruler, the experimenter pinches it with his fingers as quickly as he can. The ruler will have time to fly some distance - it can be measured by its own divisions, it is convenient to first hold your fingers opposite the zero division. From this distance, we determine the time of fall, considering the motion of the ruler to be uniformly accelerated. Such movements were studied in the 16th century by Galileo Galilei. He found that these movements are uniformly accelerated, and the acceleration is directed vertically down. His experiment, in which he threw objects down from the Leaning Tower of Pisa and found for the first time that light objects fall down as quickly as heavy ones, was included in the 10 best experiments of the century. Consider Galileo's thought experiment
mental e Galileo Galilei's experiment
Video #4
Summarizing.
Observation and experience are the surest means of understanding nature.
Galileo Galilei
Homework:
We see that the ratio of displacement to time for such a movement will be a constant value. This allows us to introduce such a relation as main characteristic rectilinear uniform motion, which we call the speed of uniform rectilinear motion.
speed rectilinear uniform motion is the ratio of the displacement of the body to the time t:
Speed is a vector quantity. The modulus of velocity is numerically equal to the modulus of displacement of the body per unit time, and the direction of velocity coincides with the direction of displacement.
Knowing the definition of speed, we can formulate that if a body makes the same movements for any equal time intervals, then it is obvious that this is a movement at a constant speed. Rectilinear uniform motion is a motion when a body moves at a constant speed not only in absolute value, but also in direction.
Knowing the speed of uniform rectilinear motion, it is easy to determine the movement that the body makes in any period of time, that is, it is easy to solve the main problem of mechanics.
It follows from the definition of speed that the displacement vector is equal to the product of the speed vector and the time : =
in projections on the coordinate axes, this will look like this:
= · ; = · ; = ·
Since the radius vector of the body at any time is given by the relation
Then we get = + ·
We have obtained the solution of the main problem of mechanics in vector form. In projections on the coordinate axes, we get: x = x 0 + V x t
y = y 0 + Vy t
z = z 0 + Vz t
For uniform rectilinear motion, it is most convenient to choose one of the axes along the trajectory of the body, and the trajectory is a straight line, then it is obvious that one formula is enough to describe the motion. For example, x \u003d x 0 + V x t, most often it is written x \u003d x 0 + V t without the x icon in the velocity projection. It should be remembered that V is not the speed modulus, but its projection. The difference is that the modulus cannot be negative, but the projection can. If we consider the movement of cars moving towards each other, then the movement will be one-dimensional, it is enough for us to choose one axis to describe this movement. The projection of the speed of one of the cars will be positive, and the other negative. If the velocity projection is negative, then the body is moving in the direction opposite to the selected axis.
A car is moving along a straight road at a constant speed of 72 km/h. Write down the equation of the dependence of its coordinates on time, directing the Ox axis in the direction of movement, choosing the origin of coordinates at the gas station, and the time reference - at the moment when the car has another 500 m left to drive to the gas station (Fig. 2, 3).
Rice. 2. Task example 1 ()
Converting kilometers and hours to meters and seconds, and seeing that the direction of the velocity projection coincides with the direction of the axis, we can write:
Rice. 3. Solution of problem 1 ()
We can determine the position of the body at any point in time by substituting the value of the variable t.
Describe the motion of the body along the x-axis, if the dependence of the coordinate on time has the form: x = -5 + 3t
Let's write down the law that is given to us in the condition of the problem: x(t) = -5 + 3t
We need to describe the movement of the body. It means to describe:
- How did the body move?
- Record the characteristics of the movement.
From the problem statement, we see that:
- The body moved uniformly in a straight line x(t) = x 0 + V x t
- The initial coordinate of the body x 0 = -5 m; velocity modulus V = 3 m/s and coincides with the direction of the axis, i.e. positively V x › 0
x 0 \u003d -5 m; V = 3 m/s; Vx › 0
We have fully described this movement, the problem is solved.
We have solved the main problem of mechanics for uniform rectilinear motion, then we will learn how to work with graphs of uniform rectilinear motion.
Bibliography
- Tikhomirova S.A., Yavorsky B.M. Physics ( a basic level of) - M.: Mnemozina, 2012.
- Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
- Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.
Homework
- Define uniform rectilinear motion.
- What equation describes rectilinear uniform motion?
- Internet portal Av-physics.narod.ru ().
- Internet portal Eduspb.com ().
- Internet portal Lass-fizika.narod.ru ().