The theme of the lesson is “Uniform and not uniform motion. Speed"
Lesson Objectives:
introduce the concepts of uniform and uneven
motion;introduce the concept of speed as a physical
quantities, formula and units of its measurement.develop cognitive interests,
intellectual and creative abilities,
interest in studying physics;develop independent skills
acquisition of knowledge, organization of training
activities, goal setting, planning;develop the ability to organize
classify and generalize the acquired knowledge;develop communication skills
students
Educational:
Educational:
Educational:
During the classes:
1. Repetition
What is mechanical movement? Give examples
What is a trajectory? What are they?
What is a path? How is it denoted, in what units is it measured?
Translate:
in m 80cm, 5cm, 2km, 3dm, 12dm, 1350cm, 25000mm, 67km
in cm 2 dm, 5 km, 30 mm
2. Assimilation of new knowledge
Uniform movement A movement in which a body travels equal distances in equal intervals of time.
Uneven movement A movement in which a body travels unequal distances in equal intervals of time.
Examples of uniform and non-uniform motion
Speed of rectilinear uniform motion- a physical quantity equal to the ratio of the path to the time for which the path was traveled.
Let's check if our knowledge is enough to solve the following problem. Two cars started moving simultaneously from the village with the same speed of 60 km/h. Is it possible to say that in an hour they will be in the same place?
Conclusion: speed should be characterized not only by number, but also by direction. Such quantities, which, apart from numerical value also have a direction called vector.
Speed is a vector physical quantity.
Scalar quantities are quantities that are characterized only by a numerical value (for example, path, time, length, etc.)
To characterize non-uniform motion, the concept of average speed is introduced.
To determine average speed bodies with uneven movement, it is necessary to divide the entire distance traveled by the entire time of movement:
Working with the textbook table p.37
3. Checking the assimilation of new knowledge
Problem solving
1. Convert speed units to basic SI units:
36 km/h = __________________________________________________________________
120 m/min = ________________________________________________________________
18 km/h = _________________________________________________________________
90 m/min = _______________________________________________________________
2. The balloon is moving east at a speed of 30 km/h. Plot the velocity vector using the scale: 1 cm=10 km/h
Algorithm for solving problems in physics:
1. Carefully read the condition of the problem and understand the main question; present the processes and phenomena described in the condition of the problem.
2. Re-read the content of the problem in order to clearly present the main question of the problem, the purpose of its solution, the known values, based on which you can search for a solution.
3. Make a brief note of the problem condition using generally accepted letter designations.
4. Make a drawing or drawing for the task.
5. Determine which method will solve the problem; make a plan to solve it.
6. Write down the basic equations describing the processes proposed by the task system.
7. Record the solution in general view, expressing the required quantities in terms of the given ones.
8. Check the correctness of the solution of the problem in general terms by performing actions with the names of the quantities.
9. Perform calculations with the specified accuracy.
10. Make an assessment of the reality of the resulting solution.
11. Write down the answer in the required form
3. Find the speed of the French athlete Roman Zaballo, who in 1981 ran the distance between the French cities of Florence and Montpellier (510 km) in 60 hours.
4. Find the speed of a cheetah (the fastest mammal) if it runs 210 meters in 7 seconds.
5. V.I.Lukashik Problems No. 117,118,119
6. Homework: §14,15, exercise 4(4)
Lesson
Theme: Rectilinear uniformly accelerated motion. Speed in uneven motion.
Lesson Objectives:
Educational:
1. to form the concept of rectilinear uniformly accelerated motion, instantaneous speed, acceleration;
2. build an acceleration graph;
3. develop skills in solving graphic and calculation problems
Developing:
1. to develop the practical skills of students: the ability to analyze, generalize, highlight the main idea from the teacher's story and draw conclusions;
2. develop the ability to apply acquired knowledge in new conditions.
Educators:
1. to expand the horizons of students about the types of mechanical movement (in particular, about rectilinear uniformly variable (uniformly accelerated) motion);
2. develop curiosity, interest in studying physics and, attentiveness, discipline
Lesson type: Combined lesson.
During the classes.
1) Organizing time
Establish class readiness for the lesson.
2) Motivation
Movement is life. Each body moves differently: with its own purpose, trajectory, speed. your movements - development, which is impossible without obtaining new knowledge. So today, we will discover a new characteristic of movement, which is an integral part of our life.
3) Knowledge update
Independent work(20 minutes)
4) Learning new material
We have studied the uniform motion of a body when its speed remains unchanged and at any moment of time and at any distance can be found as the ratio of the distance traveled to the time.
Please give examples of uniform motion.
(students give examples).
How often can we observe such a movement?
(general opinion of students: rarely, almost always body speed change for any reason)
Indeed, such a movement is actually very rare and, as a rule, in mechanisms. But in the world around us, another movement is widespread.
fast motion is a fairly common type of movement. An example of such a movement is the movement of a load thrown from a certain height, the movement of a braking bus or a starting elevator.
In order to somehow characterize the accelerated movement, a quantity is introduced, which is calledacceleration body.
Acceleration is a physical quantity equal to the ratio of the change in speed to the time span for which it happened.
In addition, you can use the everyday definition: acceleration is the rate of change of speed.
Often, we consider acceleration in projection onto some axis (for example, onto the axis ), while the acceleration projection will take the form:
Note that the acceleration in all cases isvector magnitude, that is, it has not only magnitude, but also direction. Acceleration in the SI system is measured in meters divided by a second squared.
One meter per second squared is such an acceleration at which for every second the speed of the body changes by one meter per second.
We have figured out how to determine the acceleration module, now we will figure out how to determine the direction of acceleration. To do this, we depict the change in speed in vector form (Fig. 1).
Rice. 1. Change in body speed during accelerated movement
Accordingly, the acceleration of the body will be directed in the same direction as the vector .
One of the simplest types of non-uniform motion is uniformly accelerated motion.
Uniformly accelerated is a movement in which for any equal intervals of time the speed of the body increases by the same amount.In uniformly accelerated motion, the acceleration of the body is constant.
In addition, sometimes allocate the so-called equally slow motion. Uniformly decelerated motion is a movement in which the speed of the body is opposite to its acceleration.
Let's draw graphs of the dependence of the acceleration of the body on time for uniformly accelerated motion. Since the acceleration is constant during uniformly accelerated motion (Fig. 2):
Rice. 2. Acceleration of the body during uniformly accelerated motion
The red graph corresponds to the case when the acceleration projection is positive. The green graph corresponds to the case when the acceleration projection is zero. Blue - negative projection of acceleration.
In order to solve the main problem of kinematics, that is, to find the position of the body at any time, you must first find the speed of the body at any time. For this, we should write down the law of change of instantaneous speed from time for uniformly accelerated motion. This can be done by simply expressing the speed from the acceleration formula.
where – starting speed body, - acceleration. The law of speed change, written in vector form, is the most general, but it is rather inconvenient to use it to determine the speed at any point in time. Therefore, let us consider the law of change of instantaneous speed from time in the projection on the axis chosen along the direction of motion.
Consider four possible cases (Fig. 3):
Rice. 3. Four possible cases of directivity of the initial velocity and acceleration
in case a)the speed of the body and its acceleration are directed along the positive direction of the coordinate axis, and the law of change in speed will take the form:
in case in) the speed of the body is directed along the positive direction of the coordinate axis, and the acceleration is directed along the negative direction of the coordinate axis, we previously called such a movement uniformly slowed down, and its law of change in speed:
It can be seen from the form of the laws of change in speed over time that the projection of speed depends linearly on time, and accordingly, the graph of the dependence of the projection of speed on time will be a straight line (Fig. 4).
Rice. 4. Graphs of the dependence of the speed of the body on time for uniformly accelerated motion
The graph (Fig. 4a) shows the dependence of the velocity projection on time. The green straight line corresponds to the case, the body was at rest, and at the initial moment of time it began to move in the positive direction of the coordinate axis with increasing speed. The red straight line corresponds to the case when at the initial moment of time the body had some speed directed in the positive direction of the coordinate axis, and increases with time.
Figure 4b shows the relationship between the slope of the graph of the dependence of the speed of the body on time and the acceleration of the body during uniformly accelerated motion.
Finally, consider one special point on the graph of the dependence of the projection of the velocity of the body on time. Figure 5 shows the point at which the speed of the body changes its direction to the opposite. Such a point is calledturning point (Fig. 5).
Rice. 5. Turning point
So, in this lesson we learned about the concept of body acceleration. In addition, we considered the laws of change in the speed of the body from time to time. Next, we learned how to build graphs of body speed versus time, and finally introduced the concept of a turning point.
Homework
SPEED IN IRREGULAR MOVEMENT
Unevenis called a movement in which the speed of the body changes with time.
The average speed of uneven movement is equal to the ratio of the displacement vector to the travel time
Then the displacement with uneven motion
instantaneous speed called the speed of the body this moment time or at a given point in the trajectory.
Speedis a quantitative characteristic of the movement of the body.
average speed is a physical quantity equal to the ratio of the point displacement vector to the time interval Δt during which this displacement occurred. The direction of the average velocity vector coincides with the direction of the displacement vector . The average speed is determined by the formula:
Instant Speed , that is, the speed at a given time is a physical quantity, equal to the limit, to which the average speed tends with an infinite decrease in the time interval Δt:
In other words, the instantaneous speed at a given moment of time is the ratio of a very small movement to a very small period of time during which this movement occurred.
The instantaneous velocity vector is directed tangentially to the trajectory of the body (Fig. 1.6).
Rice. 1.6. Instantaneous velocity vector.
In the SI system, speed is measured in meters per second, that is, the unit of speed is considered to be the speed of such uniform rectilinear motion, in which in one second the body travels a distance of one meter. The unit of speed is denoted m/s. Often speed is measured in other units. For example, when measuring the speed of a car, train, etc. The commonly used unit of measure is kilometers per hour:
1 km/h = 1000 m / 3600 s = 1 m / 3.6 s
or
1 m/s = 3600 km / 1000 h = 3.6 km/h
Addition of speeds
The velocities of the body in different reference systems are connected by the classical law of addition of speeds.
body speed relative to fixed frame of reference is equal to the sum of the velocities of the body in moving frame of reference and the most mobile frame of reference relative to the fixed one.
For example, a passenger train is moving along a railroad at a speed of 60 km/h. A person is walking along the carriage of this train at a speed of 5 km/h. If we consider the railway to be motionless and take it as a frame of reference, then the speed of a person relative to the frame of reference (that is, relative to railway), will be equal to the addition of the speeds of the train and the person, that is, 60 + 5 = 65, if the person goes in the same direction as the train; and 60 - 5 = 55 if the person and the train are moving in different directions. However, this is only true if the person and the train are moving along the same line. If a person moves at an angle, then this angle will have to be taken into account, remembering that speed is vector quantity.
Now let's look at the example described above in more detail - with details and pictures.
So, in our case, the railway is fixed frame of reference. The train that is moving along this road is moving frame of reference. The car on which the person is walking is part of the train.
The speed of a person relative to the car (relative to the moving frame of reference) is 5 km/h. Let's call it C.
The speed of the train (and hence the wagon) relative to a fixed frame of reference (that is, relative to the railway) is 60 km/h. Let's denote it with the letter B. In other words, the speed of the train is the speed of the moving reference frame relative to the fixed reference frame.
The speed of a person relative to the railway (relative to a fixed frame of reference) is still unknown to us. Let's denote it with a letter.
Let's associate the XOY coordinate system with the fixed reference system (Fig. 1.7), and the X P O P Y P coordinate system with the moving reference system (see also the Reference System section). And now let's try to find the speed of a person relative to a fixed frame of reference, that is, relative to the railway.
For a short period of time Δt, the following events occur:
Then for this period of time the movement of a person relative to the railway:
H+B
This is displacement addition law. In our example, the movement of a person relative to the railway is equal to the sum of the movements of a person relative to the wagon and the wagon relative to the railway.
The law of addition of displacements can be written as follows:
= ∆ H ∆t + ∆ B ∆t
Subject. Uneven movement. average speed
The purpose of the lesson: to acquaint students with the simplest cases of uneven movement
Lesson type: combined
Lesson Plan
STUDY NEW MATERIAL
Uniform rectilinear motion happens relatively infrequently. Bodies move uniformly and rectilinearly only on small segments of their trajectory, while in other sections their speed changes.
Ø Movement at a variable speed, when a body travels different paths at the same time intervals, is called uneven.
To characterize the speed of uneven movement, average and instantaneous speeds are used.
Since the speed in the case of uneven movement changes in time, the formula for calculating the displacement cannot be used, because the speed is a variable, and it is not known which value should be substituted into this formula.
However, in some cases, displacements can be calculated by entering a value called the average speed. It shows what movement the body makes on average per unit of time, i.e.
This formula describes the so-called average vector speed. However, it is not always suitable for describing movement. Consider this example: a regular bus left the garage and returned at the end of the shift. The speedometer shows that the car has traveled 600 km. What is the average speed of movement?
Correct Answer: The mean vector speed is zero since the bus has returned to starting point, that is, the displacement of the body is zero.
In practice, the so-called average ground speed is often used, which is equal to the ratio of the path traveled by the body to the time of movement:
Since the path is a scalar quantity, the average ground speed (as opposed to the average speed) is also a scalar quantity.
Knowing the average speed does not make it possible to determine the position of the body at any time, even if the trajectory of its movement is known. However, this concept is convenient for performing some calculations, for example, calculating the time of movement.
If you observe the readings of the speedometer of a car that is moving, you will notice that they change over time. This is especially noticeable during acceleration and deceleration.
When they say that the speed of a body changes, they mean the instantaneous speed, that is, the speed of the body at a certain moment and at a certain point in the trajectory.
Ø Instantaneous speed is a value that is equal to the ratio of a very small movement to the period of time during which this movement occurred:
Instantaneous speed is the average speed measured over an infinitesimal amount of time.
Question to the students during the presentation of new material
1. The car drove 60 km per hour. Can it be argued that its movement was uniform?
2. Why is it impossible to talk about the average speed of variable movement in general, but can we only talk about the average speed for a certain period of time or about the average speed on a separate section of the path?
3. While driving, the speedometer readings were taken every minute. Is it possible to calculate the average speed of the car from this data?
4. The average speed for a certain period of time is known. Is it possible to calculate the displacement made in half of this interval?
CONFIGURATION OF THE STUDYED MATERIAL
1. The skier walked the first section of the path 12 m long in 2 minutes, the second, 3 m long - 0.5 minutes each. Calculate the average ground speed of the skier.
2. A person walked along a straight road 3 km in 1 hour, then returned at a right angle and walked another 4 km in 1 hour. Calculate the average and average ground speed at the first stage of movement, at the second stage and for the entire time of movement.
3. A person traveled the first half of the way in a car at a speed of 7 km/h, and the second half - on a bicycle at a speed of 2 km/h. Calculate the average ground speed for the entire journey.
4. A pedestrian walked at a speed of 3 km/h for two thirds of the time of his movement, the rest of the time at a speed of 6 km/h. Calculate the average and average ground speed of the pedestrian.
5. Material point moves along an arc of a circle with a radius of 4 m, while describing a trajectory that is half the arc of a circle. In this case, the first quarter of the circle, the point moves at a speed of 2 m/s, and the second quarter - at a speed of 8 m/s. Calculate the average ground and average vector speed for the entire movement.
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.