Sections: Physics

Class: 7

Lesson type: learning new material.

Goals and objectives of the lesson:

• Educational:
  • introduce the basic concepts of mechanical motion: relativity of motion, trajectory, distance traveled, uniform and non-uniform motion;
  • introduce the concept of speed as a physical quantity, the formula and units of its measurement.
• Educational:
  • develop cognitive interests, intellectual and creative abilities, interest in the study of physics;
• Educational:
  • develop the skills of self-acquisition of knowledge, organization of educational activities, setting goals, planning;
  • to form the ability to systematize, classify and generalize the acquired knowledge;
  • develop students' communication skills.

DURING THE CLASSES

I. Organizational moment

II. Homework:§§13-14, ex. 3 (oral).

III. Explanation of new material

1. Start the lesson with an announcement new topic lesson and try to answer the question: "What allows us to judge whether the body is moving or at rest?". After the students' answers, we quote an excerpt from A.S. Pushkin's poem "Movement" (see Fig. 1).
In the passage, a very important point was made, necessary for reasoning about whether the body is moving or at rest. Namely, relative to which bodies the movement occurs or does not occur. How can you tell if a body is moving or at rest?

Rice. one ( Presentation, slide 2)

2. Relativity of motion.

In order to single out such a characteristic feature of mechanical motion as relativity, let us consider and analyze a simple experiment with a cart moving on a table. Let us consider in relation to which topics it moves, and in relation to which it rests (see Fig. 2, 3).

Rice. 2 (Slides 4-10).

Rice. 3 (Slide 11).

IV. In order to consolidate the material, we solve the following tasks:

Task 1. Indicate in relation to which bodies the following bodies are at rest and in relation to which - in motion: a passenger in a moving truck; a car following a truck at the same distance, a load in a car trailer.

Task 2. Relative to what bodies is the person standing on the pavement at rest and relative to what bodies does he move?

Rice. 4 (Slide 12).

Task 3. List the bodies in relation to which the driver of a moving tram is at rest.

Pupils usually answer that a person is at rest relative to the sidewalk, tree, traffic light, house and moving relative to a car driving along the road. In this situation, students should pay attention to the fact that a person, like the Earth, moves at a speed of 30 km / s relative to the Sun.

3. Trajectory of movement.

Next, we introduce the concept of a trajectory and, depending on its shape, distinguish two types of motion: rectilinear and curvilinear. First of all, we draw the attention of students to the movement of such bodies, the trajectories of which are clearly visible (see Fig. 5). Here we introduce the concept of the distance traveled as a physical quantity measured by the length of the trajectory along which the body moves for a certain period of time. In this regard, we repeat the basic units of length measurement known from the course of mathematics.

Rice. 5 (Slide 15).

Task 4. Match the example of mechanical movement with the type of toolpath.

EXAMPLE TYPE OF TRAJECTORY

A) meteor fall 1) circle
B) movement of the stopwatch hand 2) curve
C) a raindrop falling into a calm 3) a straight line
weather.

Task 5. Express the distance traveled in meters:

65 km
0.54 km
4 km 300 m
2300 cm
4 m 10 cm

(Slide 16).

4. Rectilinear uniform motion

Consider further what types of movement exist? Let's define what kind of motion is called uniform. A movement in which a body travels equal distances in equal intervals of time. Consider an example of rectilinear uniform motion (see Fig. 6).

Rolling the body down an inclined plane (Fig. 2);

Rice. 2. Rolling the body down an inclined plane ()

Free fall (Fig. 3).

All these three types of movement are not uniform, that is, the speed changes in them. In this lesson, we'll look at uneven movement.

Uniform movement - mechanical movement, at which the body travels the same distance in any equal time intervals (Fig. 4).

Rice. 4. Uniform movement

Movement is called uneven., at which the body covers unequal distances in equal intervals of time.

Rice. 5. Uneven movement

The main task of mechanics is to determine the position of the body at any time. With uneven movement, the speed of the body changes, therefore, it is necessary to learn how to describe the change in the speed of the body. For this, two concepts are introduced: average speed and instantaneous speed.

It is not always necessary to take into account the fact of changing the speed of a body during uneven movement; when considering the movement of a body over a large section of the path as a whole (we do not care about speed at each moment of time), it is convenient to introduce the concept of average speed.

For example, a delegation of schoolchildren travels from Novosibirsk to Sochi by train. The distance between these cities is railway is approximately 3300 km. The speed of the train when it just left Novosibirsk was , does this mean that in the middle of the way the speed was the same, but at the entrance to Sochi [M1]? Is it possible, having only these data, to assert that the time of movement will be (Fig. 6). Of course not, since the residents of Novosibirsk know that it takes about 84 hours to drive to Sochi.

Rice. 6. Illustration for example

When considering the motion of a body over a long section of the path as a whole, it is more convenient to introduce the concept of average velocity.

medium speed called the ratio of the total movement that the body made to the time for which this movement was made (Fig. 7).

Rice. 7. average speed

This definition is not always convenient. For example, an athlete runs 400 m - exactly one lap. The athlete's displacement is 0 (Fig. 8), but we understand that his average speed cannot be equal to zero.

Rice. 8. Displacement is 0

In practice, the concept of average ground speed is most often used.

Average ground speed- this is the ratio of the full path traveled by the body to the time for which the path has been traveled (Fig. 9).

Rice. 9. Average ground speed

There is another definition of average speed.

average speed- this is the speed with which a body must move uniformly in order to cover a given distance in the same time for which it traveled it, moving unevenly.

From the course of mathematics, we know what the arithmetic mean is. For numbers 10 and 36 it will be equal to:

In order to find out the possibility of using this formula to find the average speed, we will solve the following problem.

A task

A cyclist climbs a slope at a speed of 10 km/h in 0.5 hours. Further, at a speed of 36 km / h, it descends in 10 minutes. Find the average speed of the cyclist (Fig. 10).

Rice. 10. Illustration for the problem

Given:; ; ;

To find:

Solution:

Since the unit of measurement for these speeds is km/h, we will find the average speed in km/h. Therefore, these problems will not be translated into SI. Let's convert to hours.

The average speed is:

The full path () consists of the path up the slope () and down the slope () :

The way up the slope is:

The downhill path is:

The time taken to complete the path is:

Answer:.

Based on the answer to the problem, we see that it is impossible to use the arithmetic mean formula to calculate the average speed.

The concept of average speed is not always useful for solving the main problem of mechanics. Returning to the problem about the train, it cannot be argued that if the average speed over the entire journey of the train is , then after 5 hours it will be at a distance from Novosibirsk.

The average speed measured over an infinitesimal period of time is called instantaneous body speed(for example: the speedometer of a car (Fig. 11) shows the instantaneous speed).

Rice. 11. Car speedometer shows instantaneous speed

There is another definition of instantaneous speed.

Instant Speed- the speed of the body at a given moment of time, the speed of the body at a given point of the trajectory (Fig. 12).

Rice. 12. Instant speed

To better understand this definition, consider an example.

Let the car move in a straight line on a section of the highway. We have a graph of the dependence of the displacement projection on time for a given movement (Fig. 13), let's analyze this graph.

Rice. 13. Graph of displacement projection versus time

The graph shows that the speed of the car is not constant. Suppose you need to find the instantaneous speed of the car 30 seconds after the start of observation (at the point A). Using the definition of instantaneous speed, we find the modulus of the average speed over the time interval from to . To do this, consider a fragment of this graph (Fig. 14).

Rice. 14. Graph of displacement projection versus time

In order to check the correctness of finding the instantaneous speed, we find the module of the average speed for the time interval from to , for this we consider a fragment of the graph (Fig. 15).

Rice. 15. Graph of displacement projection versus time

Calculate the average speed for a given period of time:

We received two values ​​of the instantaneous speed of the car 30 seconds after the start of the observation. More precisely, it will be the value where the time interval is less, that is, . If we decrease the considered time interval more strongly, then the instantaneous speed of the car at the point A will be determined more precisely.

Instantaneous speed is a vector quantity. Therefore, in addition to finding it (finding its module), it is necessary to know how it is directed.

(at ) – instantaneous speed

The direction of instantaneous velocity coincides with the direction of movement of the body.

If the body moves curvilinearly, then the instantaneous velocity is directed tangentially to the trajectory at a given point (Fig. 16).

Exercise 1

Can the instantaneous speed () change only in direction without changing in absolute value?

Solution

For a solution, consider the following example. The body moves along a curved path (Fig. 17). Mark a point on the trajectory A and point B. Note the direction of the instantaneous velocity at these points (the instantaneous velocity is directed tangentially to the trajectory point). Let the velocities and be identical in absolute value and equal to 5 m/s.

Answer: maybe.

Task 2

Can the instantaneous speed change only in absolute value, without changing in direction?

Solution

Rice. 18. Illustration for the problem

Figure 10 shows that at the point A and at the point B instantaneous speed is directed in the same direction. If the body is moving with uniform acceleration, then .

Answer: maybe.

In this lesson, we began to study uneven movement, that is, movement with varying speed. Characteristics of non-uniform motion are average and instantaneous speeds. The concept of average speed is based on the mental replacement of uneven motion with uniform motion. Sometimes the concept of average speed (as we have seen) is very convenient, but it is not suitable for solving the main problem of mechanics. Therefore, the concept of instantaneous velocity is introduced.

Bibliography

1. G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10. - M .: Education, 2008.
2. A.P. Rymkevich. Physics. Problem book 10-11. - M.: Bustard, 2006.
3. O.Ya. Savchenko. Problems in physics. - M.: Nauka, 1988.
4. A.V. Peryshkin, V.V. Krauklis. Physics course. T. 1. - M .: State. uch.-ped. ed. min. education of the RSFSR, 1957.

1. Internet portal "School-collection.edu.ru" ().
2. Internet portal "Virtulab.net" ().

Homework

1. Questions (1-3, 5) at the end of paragraph 9 (p. 24); G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics 10 (see list of recommended reading)
2. Is it possible, knowing the average speed for a certain period of time, to find the movement made by the body for any part of this interval?
3. What is the difference between instantaneous speed in uniform rectilinear motion and instantaneous speed in non-uniform motion?
4. While driving a car, speedometer readings were taken every minute. Is it possible to determine the average speed of the car from these data?
5. The cyclist rode the first third of the route at a speed of 12 km per hour, the second third at a speed of 16 km per hour, and the last third at a speed of 24 km per hour. Find the average speed of the bike for the entire journey. Give your answer in km/h

Preparation for ZNO. Physics.
Synopsis 2. Uneven movement.

5. Univariate (uniformly accelerated) movement

Uneven movement– movement with variable speed.
Definition. Instant Speed- the speed of the body at a given point of the trajectory, at a given time. It is found by the ratio of the movement of the body to the time interval ∆t, during which this movement was made, if the time interval tends to zero.

Definition. Acceleration - a value showing how much the speed changes over a time interval ∆t.

Where is the final, and is the initial speed for the considered time interval.

Definition. Equally variable rectilinear motion (uniformly accelerated)- this is a movement in which for any equal time intervals the speed of the body changes by an equal value, i.e. is a movement with constant acceleration.

Comment. Saying that the motion is uniformly accelerated, we consider that the speed increases, i.e. acceleration projection when moving along the reference direction (velocity and acceleration coincide in direction), and speaking - equally slowed down, we consider that the speed decreases, i.e. (velocity and acceleration are directed towards each other). In school physics, both of these movements are usually called uniformly accelerated.

Displacement equations, m:

Graphs of uniformly variable (uniformly accelerated) rectilinear motion:

The graph is a straight line parallel to the time axis.

The graph is a straight line that is built “by points”.

Comment. The speed graph always starts from the initial speed.

The purpose of the lesson: we continue to form the concepts of average, instantaneous and relative speeds; we improve the ability to analyze, compare, build graphs.

During the classes

1. Examination homework through independent work

Option 1

a) What kind of movement is considered uniform?

B) Write down the equation of rectilinear uniform motion of a point in vector form.

C) The movements of two bodies are given by the equations: x1=5 – t,

Describe the nature of the movement of bodies. Find the initial coordinates, modulus and direction of their velocities. Plot motion graphs, velocity graphs Vx(t). Determine analytically and graphically the time and place of the meeting of these bodies.

Option - 2

a) What is the speed of rectilinear and uniform motion?

B) Write down the equation of rectilinear motion of a point in coordinate form.

C) The movement of two cyclists is described by the equations: x1=12t;

Describe the nature of the movement of each cyclist, find the modulus and direction of their velocities, Vx(t). Determine graphically and analytically the time and place of the meeting.

2. Learning new material

The concept of the average velocity vector: this is the ratio of the displacement vector to the time during which this displacement occurred. Vcr= Δr/Δt

Knowing the modulus of the average velocity vector, it is impossible to determine the path traveled by the body, since the modulus of the displacement vector is not equal to the path traveled in the same time.

The concept of the average speed module (ground speed) Vav=S/Δ t

Medium speed module is equal to the ratio path S to the time interval Δt, during which this path has been passed.

The concept of instantaneous speed (conversation with students)

What is the speed of the alternating motion shown by the car's speedometer?

About what speed in question in the following cases:

A) the train traveled between cities at a speed of 60 km/h;

B) the speed of the hammer on impact is 8 m/s;

C) an express train passed a traffic light at a speed of 30 km/h

The average speed measured over such a small period of time that during this period the movement can be considered uniform is called instantaneous speed or simply speed.

Vcr= Δr/Δt; at t→ 0 Vav→Vmgn (v)

The direction of the average velocity vector coincides with the displacement vector Δr, at the time interval Δt → 0, when the vector Δr decreases in absolute value and its direction coincides with the direction of the tangent at a given point of the trajectory.

The concept of relative speed

The addition of velocities is carried out according to the formula: S2= S1+S, where S1 is the displacement of the body relative to the moving frame of reference; S is the displacement of the moving frame of reference; S2 is the movement of the body relative to the fixed frame of reference.

Let's change the notation taking into account knowledge about the radius-vector:

Dividing both sides of the equation by Δt, we get: Δr2/Δt= Δr1/Δt + Δr/Δt or V2= V1+V where

V1 is the speed of the body relative to the first (moving) frame of reference;

V is the speed of the moving frame of reference:

V2 is the speed of the body relative to the second (fixed) frame of reference.

Solving problems to consolidate the studied material

The motorcyclist traveled 90 km in the first 2 hours, and moved at a speed of 50 km/h for the next 3 hours. What is the average speed of the motorcyclist for the entire journey?

T \u003d 2 h Average speed formula: Vav \u003d S / t

S=90 km