Molchanova Larisa Anatolievna
physics and science teacher
MBOU secondary school №150, Krasnoyarsk
Topic 1 "Laws of motion and interaction of bodies"
Lesson 1.1 Material point. Reference system
The purpose of the lesson: Get to know the basic characteristics of the movement. Consider the concept of a material point and the principles of its application. Explain the components of a reference system.
During the classes
1. Organizational moment
Marking those present. Announcement of the topic and the name of the lesson (slide 1).
2. Learning new material
1) Introductory speech of the teacher:
We begin to consider with you the issues of the interaction of bodies, a material point, a reference system from the main question -movement . In general, any changes that occur in nature can be called movement.
In the 9th grade physics course, we will begin the study of motion with the simplest type of motion - mechanical movement(slide 2).
Consider several types of movement. This is, first of all, progressive, the simplest, quite rare; rotational and oscillatory (slide 3).
In addition, we can talk about the shape of the trajectory of the body, that is, the line along which the body moves (slide 4).
Please note that when studying movement, we should consider issues related to the body. To characterize the movement, the following quantities are used: first of all, the distance traveled, speed, trajectory, as well as very important things - these are the coordinates of the body (slide 5).
Let's see where all these quantities meet. First of all, it is necessary to note the value familiar from the 7th grade - the distance traveled. It is denoted by the letter S and is expressed in meters. The distance traveled is the length of the trajectory, and the trajectory is the line along which the body moves (slides 6, 7).
The next characteristic is speed. From the 7th grade course, we can recall that speed is a value that characterizes the speed of movement. It is denoted by the Latin letter V and is measured in m / s (slide 8).
And so next feature are the coordinates. I draw your attention to the fact that from mathematics you remember that in order to determine the location of the body, you must specify its coordinates. Until the middle of the last millennium, only one coordinate was used - we call it the OX axis or the abscissa axis. But today you know that our space is three-dimensional, and therefore the coordinates along three axes are used: x, y andz(slide 9). By setting these points (coordinates), we can determine the location of the body.
A very important issue that should be noted here is how to consider the body in a given coordinate system. The fact is that bodies can be very different in size - large, super-large (some cosmic bodies), small, microscopic, therefore, in order to make it more convenient to use the characteristics of the movement of a body, it is necessary to introduce such a thing as a material point (slide 10).
If we consider, for example, a train that approaches the station, then in this case we cannot consider it as a material point compared to the station, since their sizes are comparable (slide 11). In this case, if the sizes of the bodies are comparable, then they cannot be considered MT. But if we consider the movement of the train, for example, from Moscow to Krasnoyarsk, then in this case the distance that the train overcomes is much larger (incommensurable) with its size. Therefore, in this case, we can talk about the train as a MT (slide 12). In this case, it is convenient to set the coordinates of the body (points) and talk about how it moves.
Consider how to determine the location of the body in space. In order to do this, you need to know the coordinates. If we are dealing with one-dimensional motion, that is, the body moves along one straight line along the OX axis, then there will be only one coordinate - x. If the movement is two-dimensional, then there will be two coordinates - x and y, in this case we will use a rectangular coordinate system. And if three-dimensional, then three coordinates. This coordinate system is calledcartesian system coordinates.
It should also be noted that the body is moving in time, so we need to say what coordinates the body has at a given time. And here we come to a very important conclusion: to characterize the movement, it is necessary to introducereference system.
We call the reference system three components - this is the coordinate system, the reference body and the reference time device - the clock (slide 13). I draw your attention to the fact that another MT can also be the reference body, in this case we can say that the origin of coordinates coincides with the reference point. In general, this will be the reference system used throughout the world. In addition to such a reference system, others are also used - containing not only a rectangular coordinate system, but also the so-called radius vector. Using such a system, you can also set the location of the body, for example, this is widely used in navigation.
3. Consolidation of the studied
Performing exercise 1 page 9 of the textbook (frontal analysis).
4. Summary of the lesson
In conclusion of the lesson, it should be noted that we characterize any movement by a reference system, coordinates. It must be remembered that we can use such a concept as MT. You also need to remember that sometimes we can consider not the whole body as a whole, but some part of it and take this part as MT. In the next lessons, we will get acquainted with other characteristics of movement.
Homework: §1.
In this lesson, the topic of which is: “Material point. Reference system”, we will get acquainted with the definition of a material point, consider the determination of the position of different bodies using coordinates. In addition, consider what a reference system is and why it is needed.
Imagine that you are sitting at home, in your room, and you are asked the question: “Where are you?”. How will you answer it? You can answer "at home" and that would be the correct answer. You can answer “in your room, at the table”, or name the city, or say that you are in Russia. The answer to the question "where are you?" will be given, all of these options are correct.
How, then, do we choose what to answer? Depends on how exactly you need to know the location. If the mother asks, who has entered the apartment, she wants to know what room you are in. If a friend from another city asks on the phone to meet you, then he doesn’t care if you are in your room or in the kitchen, and even more so it doesn’t matter which part of your legs is under the table and which part of your hands lies on the table. He just needs to know if you've left town.
Answering a simple question, we discarded everything superfluous, simplified and answered as accurately as required in each specific case.
We use simplifications at every step, describing objects or processes from the standpoint of what interests us.
One more example - geographic Maps(see fig. 1).
Rice. 1. Geographic map
It would be possible to place satellite photographs of the area in atlases, but no one does this. When studying geography, we do not care what each object looks like, and not all objects are of interest to us, therefore, when making maps, the unnecessary is discarded. On physical map remains the relief and water bodies (see Fig. 2), political map- state borders and Largest cities(see fig. 3)
And how do you show your position on the map? Put a point that has nothing to do with the real you, but describes your situation, and looking at the point on the map, you understand everything (see Fig. 4).
Rice. 4. Designation on the map
In physics, we will also use simplifications.
A simplified representation of something that we need to study or describe with a given degree of correspondence to reality is called model.
Man thinks in models. Imagine a bicycle. Now try to draw it as accurately as possible.
It's amazing how many of you will struggle, and everyone knows what a bike looks like and everyone presented it with ease. But the imaginary picture is quite approximate: two wheels, a steering wheel, pedals, a seat, these parts are connected by a frame, but we don’t think about how exactly they are connected, what shape and what color they are.
What details do we omit and what do we pay attention to? IN Everyday life- at your discretion, depending on the needs. In science, accuracy and certainty are needed, therefore, in physics, we will clearly stipulate the models that we will study and which will correspond to reality with a given accuracy.
Model
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When we say the word "model" in physics, most often we mean a reduced copy of something, some image of an object, its description, verbal or mathematical. Such a copy is not the original, but gives a simplified view of it. The degree of simplification can be different depending on what information we have enough. Let's take a model car. Some collect models that look like real ones, that is, they give an idea of the appearance of the car (see Fig. 5).
Rice. 5. Car model At the same time, such a model will not show the device of the engine, but for our purpose, the appearance is enough. If you tell a friend how you were overtaken by another car, you do not need to have collectible models of these cars, you do not care appearance, the movement and location of cars is important to you. You just need to take two rectangular objects, such as mobile phones, and simulate overtaking on the table (see Fig. 6). Rice. 6. Overtaking cars Another example: you are asked to buy bread. The concept of "bread" is a simplified model, in the phrase "Buy bread" there is no information about the bakery-manufacturer, nor about the composition, nor about the exact mass of the loaf. We only specify whether to buy white or black, we will omit all other details. If some details are important, then we will be asked to "Buy a small loaf of white bread." This will be another more accurate model: it will already specify the size of the loaf and the type of bread, but will also omit everything else. We use models all the time - by choosing the accuracy of extracting or transmitting information, we are already modeling reality. |
We will study mechanical motion. Motion is the movement of bodies over time.
We are interested in the fact that the body was in one place, and after a while it ended up in another. How would you describe it? For example, the car was in the parking lot in the morning, and then drove up to the house. Looking out of the window, you will point with your finger where he was in the morning, and then show where he is now (see Fig. 7).
Rice. 7. Car position
How to draw on paper your way home from school? After you mark the school, the house, and a few key objects, such as the bus stop, the subway station, the intersection where you turn, you mark with dots: first I am here, then I go here, and I arrive here (see Fig. 8) .
Rice. 8. Way home from school
Please note that in these examples, as in many other cases, we do not need to pay attention to the size and shape of the moving bodies. One student or another is walking from school, a car is driving or an elephant is running - we will mark them on paper with the same dots. This is very convenient, and we will apply this model where possible.
This model is called material point- a model of the body, the size and shape of which in this problem can be neglected.
Other models in kinematics
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In mechanics physical model The moving body can be a material point, the dimensions of which can be neglected in this problem, or a body that has a shape and dimensions, if they are important for us in this problem (see Fig. 9).
Rice. 9. Movement patterns The motion models we will be using are uniform motion in a straight line uniformly accelerated motion in a straight line and uniform motion in a circle. Anyone who has tried to ride a bike along a narrow straight path or crossbar knows how difficult it is to keep a perfectly straight path, the path is always curved, but we can ignore such inaccuracies, ignore the movement up and down the bumps at all, and we can reduce the movement to one of studied models. |
It must be understood that any model has its own limits of application and not all bodies and not in all cases can be considered material points. The same car, if we consider its movement from the parking lot to the house, can be considered a material point, its dimensions are not important (see Fig. 10).
Rice. 10. Car - material point
But if we consider how it will fit in a parking lot between two adjacent cars, its size and shape must be taken into account.
We will study the motion of a material point. Movement is a change in position over time. How to describe the situation?
Choose an object in your room, and now tell me where it is. Let's say you chose a cup from which you recently drank tea and have not yet taken it to the kitchen. You will say something like “she is on the table half a meter to the left of the keyboard” or “she is right in front of the diary” (see Fig. 11).
Rice. 11. The position of the cup on the table
Now try to indicate its position without mentioning any other items like a keyboard or a diary. Will not work. Describing the position of a body or a point, you need to select another body and set the position relative to it, that is, the coordinates.
Coordinates- this is a way to accurately indicate the place, the address of this place. This address should not only identify a place, but also help to find it, indicate its position in an ordered series of similar points (the term “coordinate” comes from the word ordinare, which means “arrange”, with the prefix co-, which means “together, jointly , agreed").
number properties
For example, the coordinate of a house on the street is its number, which is counted from the edge of the street, which is taken as the beginning. The house number not only indicates what kind of house we are talking about (about the same, for example, five-story building, with a hairdresser on the ground floor), but also tells where it can be found: if we passed houses No. 8 and No. 10, then house number 16 should be somewhere ahead (see Fig. 12).
Rice. 12. House number
Whereas the name of the street often only identifies it (we hear about Pushkinskaya Street and understand what kind of street it is), but does not contain information about its position among other streets (there is no order).
In a movie theater, the row number and seat number are chair coordinates: we know where the origin is (usually to the left of the screen), so if we see the fifth row, we know where to look for large row numbers. The same with places: if we are looking for place No. 13, we go immediately to the end of the row, and, having seen place No. 11, we understand that we are close (see Fig. 13).
Rice. 13. The desired place in the cinema
The number is not only a name (the inscription on the chair), but also a guideline in the search (orderliness).
Everyone who has played naval combat knows that the position of a cell can be uniquely set by a couple of parameters: in this case, a letter indicating a column and a number indicating a row, and columns and rows are counted from the upper left corner of the field (see Fig. 14) .
Rice. 14. The game "Sea battle"
You can determine the position by determining the direction and distance, for example, 50 kilometers from the city to the northeast (see Fig. 15).
Rice. 15. Position detection
Examples of coordinate systems
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In any case, when we set the position of something, we use its coordinates in one form or another. For example: - in the photo they write “in the first row, second from the left, Ivanov” (see Fig. 16). The coordinates are a row and a place in it;
Rice. 16. The position of the person in the photo: Ivanov is second from the left - on the tickets they write the number of the row and the number of the seat: the coordinates of the row and seat (see Fig. 17);
Rice. 17. Ticket - street, house number - coordinates: street and numbers; - “you will leave the subway“ such and such ”, turn left and walk 100 m; - The position of the body on the surface of the Earth can be set in different ways: - 30 km north of Moscow, 40 km east. In this case, the coordinates are a pair of numbers: distance east/west and north/south; - 50 km to the northeast. Here the coordinates are the direction angle relative to the east/west axis + the length of the radius vector (see Fig. 18).
Rice. 18. Position on the world map |
In mechanics, we will most often use a rectangular (or Cartesian) coordinate system. In it, the position of a point on the plane is given as follows. There is a reference point, that is, the origin of coordinates, and there are two mutually perpendicular directions. The position of a point is given by the distance that must be passed from the origin of coordinates in one and the other direction to get to this point (see Fig. 19), as in a movie theater when moving along the rows and along the row to seats.
So, we describe the motion of a material point. To describe it, we need a body of reference, relative to which to set the position of the point. You need a coordinate system to accurately and unambiguously set the position (see Fig. 20).
Rice. 20. Reference system
But movement is movement over time, so you still need to decide on the measurement of time. It would seem that a second on everyone's watch lasts the same, except for faulty watches, then what's the problem with measuring time? Imagine: if the beginning of the movement is detected by the clock, which shows 14:40, and the end - by the stopwatch, which stops at 02:36:41, and it is not known when it is started. Therefore, with the device for measuring time and the moment the measurement begins, we also need to decide how we determine the reference body and coordinate system.
Now we have all the tools that are needed to describe the movement: the reference body, the coordinate system and the time measuring device. Together they make reference system.
When solving problems, we will independently choose a frame of reference in which the process described in the problem will be considered most conveniently for us.
This concludes our lesson, thank you for your attention.
Bibliography
1. Sokolovich Yu.A., Bogdanova G.S. Physics: Handbook with examples of problem solving. - 2nd edition redistribution. - X .: Vesta: Publishing house "Ranok", 2005. - 464 p.
2. Peryshkin A.V., Gutnik E.M. Physics. Grade 9: textbook. for general education institutions - 14th ed., stereotypical. - M.: Bustard, 2009. - 300 p.
Homework
1. Define a material point.
2. What is a frame of reference?
3. What is the model?
4. Determine the coordinates of three points:
The mechanical motion of a body is a change in its position in space relative to other bodies over time. To judge whether a given body is moving or not, one must first select a reference body, and then see if its position of the considered body changes relative to the selected reference body. In this case, the body can move relative to one reference body and rest relative to another.
It is possible to take a body as a material point even if its dimensions are commensurate with the distance it has traveled. For example, a person stands motionless on the step of an escalator. At any moment in time, all points of his body move in the same way. Such a movement is called progressive.
But if it is necessary to determine the path that the body has traveled for a certain period of time, then we will need more instruments for measuring time - watches. The coordinate system associated with the reference body and the clock for timing form a reference system that allows you to determine the position of a moving body at any time.
Municipal educational institution
"Razumenska average comprehensive school№2"
Belgorodsky district of the Belgorod region
Physics lesson summary
in 9th grade
« »
prepared
math and physics teacher
Elsukova Olga Andreevna
Belgorod
2013
Subject: Laws of interaction and motion of bodies.
Lesson topic: Material point. Reference system.
Form of the lesson:lesson
Type: I + II(a lesson in the study of knowledge and methods of activity)
Place of the lesson in the section:1
Goals and objectives:
to ensure the perception, comprehension and primary memorization by students of the concepts of a material point, translational movement, reference system;
organize the activities of students to reproduce the studied material;
generalize knowledge about the concept of "material point";
check the practical application of the studied material;
develop cognitive independence and creativity students;
develop the skills of creative assimilation and application of knowledge;
develop the communication skills of students;
develop oral speech students;
Lesson equipment: board, chalk, textbook.
During the classes:
Organization of the beginning of the training session:
Greet students;
Check the sanitary and hygienic condition of the class ( is the class ventilated, the board is washed, the presence of chalk), if there are discrepancies with sanitary and hygienic standards, ask the students to correct them together with the teacher.
Get to know the students, mark those absent from the lesson;
Preparation for the active work of students:
Today in the lesson we have to return to the study of mechanical phenomena. In the 7th grade, you have already encountered mechanical phenomena and before starting to study new material, let's remember:
What is mechanical movement?
Mechanical movement- called the change in the position of the body in space over time.
What is uniform mechanical motion?
Uniform mechanical movement is movement at a constant speed.
What is speed?
Speed- This physical quantity, which characterizes the speed of movement of the body, numerically equal to the ratio of movement in a small period of time to the value of this gap.
What's happened average speed?
average speed is the ratio of the total distance traveled to the total time.
How to determine the speed if we know the distance and time?
In 7th grade you decided enough simple tasks to find the path, time or speed of movement. This year we will take a closer look at what types of mechanical motion exist, how to describe mechanical motion of any kind, what to do if the speed changes during the motion, etc.
Already today we will get acquainted with the basic concepts that help to describe both quantitatively and qualitatively mechanical movement. These concepts are very handy tools when considering any kind of mechanical motion.
Learning new material:
Everything in the world around us is in constant motion. What is meant by the word "movement"?
Movement is any change that occurs in the environment.
The simplest type of motion is the mechanical motion already known to us.
When solving any problems related to mechanical movement, it is necessary to be able to describe this movement. And this means that you need to determine: the trajectory of movement; movement speed; the path traveled by the body; the position of the body in space at any given time.
For example, during exercises in the Republic of Armenia, in order to launch a projectile, you need to know the flight path, how far it will fall.
From the course of mathematics, we know that the position of a point in space is specified using a coordinate system. Suppose we need to describe the position not of a point, but of the whole body, which, as we know, consists of many points, and each point has its own set of coordinates.
When describing the motion of a body that has dimensions, other questions arise. For example, how to describe the movement of a body if, during movement, the body also rotates around own axis. In such a case, in addition to its own coordinate, each point of the given body has its own direction of motion and its own modulus of speed.
An example is any of the planets. When the planet rotates, opposite points on the surface have the opposite direction of motion. Moreover, the closer to the center of the planet, the lower the speed of the points.
How then to be? How to describe the movement of a body that has a size?
To do this, you can use the concept, which implies that the size the body seems to disappear, but the mass of the body remains. This concept is called a material point.
Let's write the definition:
The material point is called a body whose dimensions can be neglected under the conditions of the problem being solved.
Material points do not exist in nature. A material point is a model of a physical body. With the help of a material point, it is enough to solve a large number of tasks. But it is not always possible to apply the replacement of a body by a material point.
If, under the conditions of the problem being solved, the size of the body does not have a special effect on the movement, then such a replacement can be made. But if the size of the body begins to affect the movement of the body, then the replacement is impossible.
For example, a soccer ball. If it flies and moves quickly across the football field, then it is a material point, and if it lies on the shelves of a sports store, then this body is not a material point. The plane flies in the sky - a material point, landed - its size can no longer be neglected.
Sometimes it can be taken as a material point of the body, the dimensions of which are comparable. For example, a person is going up an escalator. He just stands, but each of his points moves in the same direction and at the same speed as a person.
Such a movement is called progressive. Let's write down the definition.
translational movement – This is the movement of a body in which all its points move in the same way. For example, the same car makes forward movement along the road. More precisely, only the body of the car performs translational motion, while its wheels perform rotational motion.
But with the help of one material point, we will not be able to describe the motion of the body. Therefore, we introduce the concept of a reference system.
Every frame of reference is made up of three elements:
1) The very definition of mechanical motion implies the first element of any frame of reference. "The motion of a body relative to other bodies". The key phrase is about other bodies. Count body - this body, relative to which the movement is considered
2) Again, the second element of the reference system follows from the definition of mechanical motion. The key phrase is over time. This means that in order to describe the movement, we need to determine the time of movement from the beginning at each point of the trajectory. And for counting time we need watch.
3) And we already voiced the third element at the very beginning of the lesson. In order to set the position of the body in space, we need coordinate system.
Thus, A reference system is a system that consists of a reference body, a coordinate system associated with it, and a clock.
Reference systems We will use two types of Cartesian system: one-dimensional and two-dimensional.
