We know that all bodies attract each other. In particular, the Moon, for example, is attracted to the Earth. But the question arises: if the Moon is attracted to the Earth, why does it revolve around it instead of falling towards the Earth?
In order to answer this question, it is necessary to consider the types of motion of bodies. We already know that movement can be uniform and uneven, but there are other characteristics of movement. In particular, depending on the direction, a distinction is made between straight and curvilinear movement.
Straight-line movement
It is known that a body moves under the influence of a force applied to it. You can do a simple experiment showing how the direction of movement of a body will depend on the direction of the force applied to it. To do this, you will need an arbitrary small object, a rubber cord and a horizontal or vertical support.
Ties the cord at one end to the support. At the other end of the cord we attach our object. Now, if we pull our object a certain distance and then release it, we will see how it begins to move in the direction of the support. Its movement is caused by the elastic force of the cord. This is how the Earth attracts all bodies on its surface, as well as meteorites flying from space.
Only instead of the elastic force, the force of attraction acts. Now let’s take our object with an elastic band and push it not in the direction towards/away from the support, but along it. If the object were not secured, it would simply fly away. But since it is held by a cord, the ball, moving to the side, slightly stretches the cord, which pulls it back, and the ball slightly changes its direction towards the support.
Curvilinear movement in a circle
This happens at every moment of time; as a result, the ball does not move along the original trajectory, but also not straight to the support. The ball will move around the support in a circle. The trajectory of its movement will be curvilinear. This is how the Moon moves around the Earth without falling on it.
This is how the Earth's gravity captures meteorites that fly close to the Earth, but not directly at it. These meteorites become satellites of the Earth. Moreover, how long they will stay in orbit depends on what their initial angle of motion was relative to the Earth. If their movement was perpendicular to the Earth, then they can remain in orbit indefinitely. If the angle was less than 90˚, then they will move in a descending spiral, and will gradually fall to the ground.
Circular motion with a constant modulus speed
Another point to note is that the speed of curvilinear motion around a circle varies in direction, but is the same in value. And this means that movement in a circle with a constant absolute speed occurs uniformly accelerated.
Since the direction of movement changes, it means that the movement occurs with acceleration. And since it changes equally at each moment of time, therefore, the movement will be uniformly accelerated. And the force of gravity is the force that causes constant acceleration.
The Moon moves around the Earth precisely because of this, but if suddenly the Moon’s movement ever changes, for example, a very large meteorite crashes into it, then it may well leave its orbit and fall to the Earth. We can only hope that this moment never comes. Such things.
Topic: Curvilinear motion. Uniform movement material point around the circumference.
Lesson objectives: to develop students’ understanding of curvilinear motion, frequency, angular movement, and period. Introduce formulas for finding these quantities and units of measurement.
Tasks:
Educational
:
to give students an idea of the curvilinear movement of its trajectory, the quantities that characterize it, the units of measurement of these quantities and formulas for calculation.
Developmental
:
continue to develop the ability to apply theoretical knowledge to solve practical problems, develop interest in the subject and logical thinking.
Educational
:
continue to develop students' horizons; the ability to keep notes in notebooks, observe, notice patterns in phenomena, and justify their conclusions.
Lesson type: combined
Methods: visual, verbal, elements of critical thinking, demonstration experiment.
Equipment: inclined chute, ball, ball on a string, toy car, spinning top, model of a clock with hands, multimedia projector, presentation.
PROGRESS OF THE LESSON
Psychological mood. Physical minute.
Checking homework.
Frontal survey pp. 24-25 Questions for self-control.
Checking the solution house. problems Exercise 5(2,3)
3.Call.
– What types of movement do you know?
How do body movements differ from each other?
– What is the difference between rectilinear and curvilinear movements?
– In what frame of reference can we talk about these types of motion?
– Compare trajectory and path for straight and curved motion.
2. Explanation of new material in combination with a demonstration experiment and conversation.
Teacher. Demonstration: a ball falling vertically, rolling down a chute, a ball spinning on a string, a toy car moving on a table, a tennis ball thrown at an angle to the horizon falling.
Teacher. How do the motion trajectories of the proposed bodies differ? (Students' answers)
Try to give it yourself definitions
curvilinear and rectilinear movements. (Record in notebooks):
– straight motion– movement along a straight path, and the direction of the force and velocity vectors coincide ;
– curvilinear movement – movement along an indirect trajectory.
Consider two examples of curvilinear movement: along a broken line and along a curve
Teacher: How do these trajectories differ?
Student. In the first case, the trajectory can be divided into straight sections and each section can be considered separately. In the second case, you can divide the curve into circular arcs and straight sections. Thus, this movement can be considered as a sequence of movements occurring along circular arcs of different radii
Teacher. Give examples of rectilinear and curvilinear motion that you have encountered in life.
Teacher. Circular motion is often characterized not by the speed of movement, but by the period of time during which the body makes one full revolution. This quantity is called circulation period and is denoted by the letter T. (Write down the definition of the period).
Student message. A period is a quantity that occurs quite often in nature and technology. Yes, we know. That the Earth rotates around its axis and the average rotation period is 24 hours. A complete revolution of the Earth around the Sun occurs in approximately 365.26 days. The impellers of hydraulic turbines make one full revolution in a time of 1 second. A helicopter rotor has a rotation period of 0.15 to 0.3 seconds. The period of blood circulation in humans is approximately 21-22 seconds.
Teacher. The movement of a body in a circle can be characterized by another quantity - the number of revolutions per unit time. They call her frequency circulation: ν = 1/T. Frequency unit: s –1 = Hz. ( Write definition, unit and formula)
Student message. The crankshafts of tractor engines have a rotation speed of 60 to 100 revolutions per second. The gas turbine rotor rotates at a frequency of 200 to 300 rps. A bullet fired from a Kalashnikov assault rifle rotates at a frequency of 3000 rps.
To measure frequency, there are instruments, so-called frequency measuring circles, based on optical illusions. On such a circle there are black stripes and frequencies. When such a circle rotates, the black stripes form a circle at a frequency corresponding to this circle. Tachometers are also used to measure frequency .
Work on creating a concept table using§7
Circulation period
T = 1/ ν
T = t/n
the period of time during which a body makes one complete revolution
Frequency
s –1 = Hz.
ν = 1/T
ν = n/t
number of revolutions per unit time
Cyclic frequency
rad/s
= 2 ν
= 2/T
4. Reinforcing the material Teacher. In this lesson we became acquainted with the description of curvilinear motion, with new concepts and quantities. Answer me the following questions:
– How can you describe curvilinear movement?
– What is called angular movement? In what units is it measured?
– What are period and frequency called? How are these quantities related to each other? In what units are they measured? How can they be identified?
6. Control and self-test
Teacher. Next test task, as you have learned new material. Testing.
1. An example of curvilinear movement is...
a) falling of a stone;
b) turn the car to the right;
c) sprinter running 100 meters.
2. The minute hand of a clock makes one full revolution. What is the period of circulation?
a) 60 s; b) 1/3600 s; c) 3600 s.
3. A bicycle wheel makes one revolution in 4 s. Determine the rotation speed.
a) 0.25 1/s; b) 4 1/s; c) 2 1/s.
Test 2
1. An example of curvilinear movement is...
a) movement of the elevator;
b) a ski jump from a springboard;
c) a cone falling from the lower branch of a spruce tree in calm weather.
2. The second hand of the watch makes one full revolution. What is its circulation frequency?
a) 1/60 s; b) 60 s; c) 1 s.
3. The car wheel makes 20 revolutions in 10 s. Determine the period of revolution of the wheel?
a) 5 s; b) 10 s; c) 0.5 s.
Answers to test 1: b; V; A; V; V
Answers to test 2: b; A; V; V; b
7. Homework: § 7, compose problems to determine the period and frequency of circulation.
8. Summing up. Assessment using self-control cards
No.
Types of tasks
grade
Solving house problems
Drawing up a conceptual table
testing
Final grade
9. Reflection
"Self-assessment sheet."
Learned something new Learned
I'm upset Got joy
Surprised Didn't understand anything
Municipal budgetary educational institution "Chubaevskaya secondary school" of the Urmara district of the Chechen Republic
PHYSICS LESSON in 9TH GRADE
“Rectilinear and curvilinear movement.
Movement of a body in a circle."
Teacher: Stepanova E.A.
Chubaevo – 2013
Subject: Rectilinear and curvilinear movement. Movement of a body in a circle with a constant absolute speed.
Objectives of the lesson: to give students an idea of rectilinear and curvilinear motion, frequency, period. Introduce formulas for finding these quantities and units of measurement.
Educational objectives: to form the concept of rectilinear and curvilinear motion, the quantities that characterize it, the units of measurement of these quantities and formulas for calculation.
Developmental tasks: continue to develop the skills to apply theoretical knowledge to solve practical problems, develop interest in the subject and logical thinking.
Educational objectives: continue to develop students’ horizons; the ability to keep notes in notebooks, observe, notice patterns in phenomena, and justify their conclusions.
Equipment: Presentation. Computer. Multimedia projector Ball, ball on a string, inclined chute, ball, toy car, spinning top, clock model with hands, stopwatches
Lesson progress
I. Organizational moment. Introductory word from the teacher. Hello, my young friends! Let me start our lesson today with these lines: “Terrible mysteries of nature hang everywhere in the air” (N. Zabolotsky, poem “Mad Wolf”) (slide 1)
2. Updating knowledge
- What types of movement do you know?- What is the difference between rectilinear and curvilinear movements?- Compare trajectory and path for straight and curved movements. Teacher: We know that all bodies attract each other. In particular, the Moon, for example, is attracted to the Earth. But the question arises: if the Moon is attracted to the Earth, why does it revolve around it instead of falling towards the Earth? (sl-)In order to answer this question, it is necessary to consider the types of motion of bodies. We already know that movement can be uniform and uneven, but there are other characteristics of movement (slide)
3. Problem situation: How are the following movements different?
Demonstrations: falling a ball in a straight line, rolling a ball along a straight chute. And along a circular path, the rotation of a ball on a string, the movement of a toy car on the table, the movement of a ball thrown at an angle to the horizon...( by type of trajectory)
Teacher: Based on the type of trajectory, these movements can be divide for movement in a straight line and along a curved line .(slide)
Let's try to give definitions curvilinear and rectilinear movements. ( Writing in a notebook) rectilinear movement - movement along a straight path. Curvilinear movement is movement along an indirect (curved) trajectory.
4. So, the topic of the lesson
Rectilinear and curvilinear movement. Circular movement(slide)
Teacher: Let's consider two examples of curvilinear movement: along a broken line and along a curve (draw). How are these trajectories different?
Students: In the first case, the trajectory can be divided into straight sections and each section can be considered separately. In the second case, you can divide the curve into circular arcs and straight sections. T.ob. this movement can be considered as a sequence of movements occurring along circular arcs of different radii. Therefore, to study curvilinear motion, you need to study movement in a circle.(slide 15)
Message 1 Movement of a body in a circle
In nature and technology very often there are movements whose trajectories are not straight, but curved lines. This is a curvilinear movement. Planets and artificial satellites of the Earth move along curvilinear trajectories in outer space, and on Earth all kinds of means of transport, parts of machines and mechanisms, river waters, atmospheric air, etc.
If you press the end of a steel rod against a rotating grindstone, the hot particles coming off the stone will be visible in the form of sparks. These particles fly at the speed they had at the moment they left the stone. It is clearly seen that the direction of movement of the sparks coincides with the tangent to the circle at the point where the rod touches the stone. On a tangent Splashes from the wheels of a skidding car are moving. (Sketch.)
Direction and velocity module
Teacher: Thus, the instantaneous speed of the body in different points curvilinear trajectory has different direction. In absolute terms, the speed can be the same everywhere or vary from point to point. (slide)
But even if the speed module does not change, it cannot be considered constant. Speed - vector quantity. For a vector quantity, the magnitude and direction are equally important. And once speed changes, which means there is acceleration. Therefore, curvilinear movement is always accelerating movement, even if the absolute value of the speed is constant .(slide)(video1)
Acceleration body moving uniformly in a circle at any point centripetal, i.e. directed along the radius of the circle towards its center. At any point, the acceleration vector is perpendicular to the velocity vector. (Draw)
Modulus of centripetal acceleration: a c =V 2 /R ( write the formula), where V is the linear speed of the body, and R is the radius of the circle. (slide)
Centripetal force is a force acting on a body during curvilinear motion at any time, always directed along the radius of the circle towards the center (as well as centripetal acceleration). And the force acting on a body is proportional to acceleration. F=ma, then
Characteristics of body movement in a circle
Circular motion is often characterized not by the speed of movement, but by the period of time during which the body makes one full revolution. This quantity is called circulation period and is designated by the letter T. ( Write period definition). When moving in a circle, a body will return to its original point in a certain period of time. Therefore, the circular motion is periodic.
A period is the time of one complete revolution.
If a body makes N revolutions in time t, then how to find the period? (formula)
Let's find the connection between the period of revolution T and the magnitude of velocity for uniform motion in a circle of radius R. Because V=S/t = 2πR/T. ( Write the formula in your notebook)
Message2 A period is a quantity that occurs quite often in nature and technology. Yes, we know. That the Earth rotates around its axis and the average rotation period is 24 hours. A complete revolution of the Earth around the Sun occurs in approximately 365.26 days. The impellers of hydraulic turbines make one full revolution in a time of 1 second. A helicopter rotor has a rotation period of 0.15 to 0.3 seconds. The period of blood circulation in humans is approximately 21-22 seconds.
Teacher: The movement of a body in a circle can be characterized by another quantity - the number of revolutions per unit time. They call her frequency circulation: ν= 1/T. Frequency unit: s -1 =Hz. ( Write definition, unit and formula)(slide)
How to find the frequency if a body makes N revolutions in time t (formula)
Teacher: What conclusion can be drawn about the relationship between these quantities? (period and frequency are reciprocal quantities)
Message3 The crankshafts of tractor engines have a rotation speed of 60 to 100 revolutions per second. The gas turbine rotor rotates at a frequency of 200 to 300 rps. Bullet. Flying out of a Kalashnikov assault rifle, it rotates at a frequency of 3000 rps. To measure frequency, there are instruments, so-called frequency measuring circles, based on optical illusions. On such a circle there are black stripes and frequencies. When such a circle rotates, the black stripes form a circle at a frequency corresponding to this circle. Tachometers are also used to measure frequency. (slide)
Connection Rotation speed and rotation period
ℓ - circumference
ℓ=2πr V=2πr/T
Additional characteristics of circular motion. (slide)
Teacher: Let us remember what quantities characterize rectilinear motion?
Movement, speed, acceleration.
Teacher: by analogy, movement in a circle - the same quantities - angular displacement, angular velocity and angular acceleration.
Angular displacement: (slide) This is the angle between two radii. Designated – Measured in rad or deg.
Teacher: Let's remember from the algebra course how the radian is related to the degree?
2pi rad = 360 deg. Pi = 3.14, then 1 rad = 360/6.28 = 57 degrees.
Angular velocity w=
Unit of measurement of angular velocity - rad/s
Teacher:. Think about what the angular velocity will be equal to if the body has completed one full revolution?
Student. Since the body has completed a full revolution, the time of its movement is equal to the period, and the angular displacement is 360° or 2. Therefore, the angular velocity is equal to.
Teacher: So what did we talk about today? (about curvilinear motion)
5. Questions for consolidation.
What kind of movement is called curvilinear?
Which motion is a special case of curvilinear motion?
What is the direction of instantaneous velocity during curvilinear motion?
Why is acceleration called centripetal?
What are period and frequency called? What units are they measured in?
How are these quantities interrelated?
How can we describe curvilinear motion?
What is the direction of acceleration of a body moving in a circle with a constant velocity?
6. Experimental work
Measure the period and frequency of a body suspended on a thread and rotating in a horizontal plane.
(on your desks you have bodies suspended by strings, a stopwatch. Rotate the body in a horizontal plane evenly and measure the time of 10 complete rotations. Calculate the period and frequency)
7. Consolidation. Problem solving. (slide)
A.S. Pushkin. "Ruslan and Lyudmila"
There is a green oak near the Lukomorye,
Golden chain on the oak tree
Day and night the cat is a scientist
Everything goes around and around in a chain.
Q: What is this cat movement called? Determine the frequency and period and angular velocity if in 2 minutes. He does 12 laps. (answer: 0.1 1/s, T=10s, w=0.628 rad/s)
P.P. Ershov “The Little Humpbacked Horse”
Well, this is how our Ivan goes
Behind the ring on the okiyan
The little hunchback flies like the wind,
And the start for the first evening
I covered a hundred thousand versts
And I didn’t rest anywhere.
Q: How many times did the Little Humpbacked Horse circle the Earth during the first evening? The earth has the shape of a ball, and one mile is approximately 1066 m. (answer: 2.5 times)
8.Test Checking the assimilation of new material(tests on paper)
Test 1.
1. An example of curvilinear movement is...
a) falling of a stone;
b) turn the car to the right;
c) sprinter running 100 meters.
2. The minute hand of a clock makes one full revolution. What is the period of circulation?
a) 60 s; b) 1/3600 s; c) 3600 s.
3. A bicycle wheel makes one revolution in 4 s. Determine the rotation speed.
a) 0.25 1/s; b) 4 1/s; c) 2 1/s.
4. The propeller of a motor boat makes 25 revolutions in 1 s. What is the angular velocity of the propeller?
a) 25 rad/s; b) /25 rad/s; c) 50 rad/s.
5. Determine the rotation speed of the electric drill drill if its angular speed is 400 .
a) 800 1/s; b) 400 1/s; c) 200 1/s.
Answers: b; V; A; V; V.
Test 2.
1. An example of curvilinear movement is...
a) movement of the elevator;
b) a ski jump from a springboard;
c) a cone falling from the lower branch of a spruce tree in calm weather.
The second hand of a watch makes one full revolution. What is its circulation frequency?
a) 1/60 s; b) 60 s; c) 1 s.
3. The car wheel makes 20 revolutions in 10 s. Determine the period of revolution of the wheel?
a) 5 s; b) 10 s; c) 0.5 s.
4. The rotor of a powerful steam turbine makes 50 revolutions in 1 s. Calculate the angular velocity.
a) 50 rad/s; b)/50 rad/s; c) 10 rad/s.
5. Determine the rotation period of the bicycle sprocket if the angular velocity is equal.
a) 1 s; b) 2 s; c)0.5 s.
Answers: b; A; V; V; b.
Self-test
9. Reflection.
Let's fill it out together ZUH mechanism (I know, I found out, I want to know)
10.Summing up, grades for the lesson
11. Homework paragraphs 18,19,
home study: calculate, if possible, all the characteristics of any rotating body (bicycle wheel, minute hand of a clock)
Ya. I. Perelman. Entertaining physics. Book 1 and 2 - M.: Nauka, 1979.
S. A. Tikhomirova. Didactic material in physics. Physics in fiction. 7 – 11 grades. – M.: Enlightenment. 1996.
Rectilinear and curvilinear movement. Movement of a body in a circle with a constant absolute speed
Laws of interaction and motion of bodies
With the help this lesson You can independently study the topic “Rectilinear and curvilinear motion. Movement of a body in a circle with a constant absolute speed." First, we will characterize rectilinear and curvilinear motion by considering how in these types of motion the velocity vector and the force applied to the body are related. Next, we consider a special case when a body moves in a circle with a constant velocity in absolute value.
In the previous lesson we looked at issues related to the law of universal gravitation. The topic of today's lesson is closely related to this law; we will turn to the uniform motion of a body in a circle.
We said earlier that movement - This is a change in the position of a body in space relative to other bodies over time. Movement and direction of movement are also characterized by speed. The change in speed and the type of movement itself are associated with the action of force. If a force acts on a body, then the body changes its speed.
If the force is directed parallel to the movement of the body, then such movement will be straightforward(Fig. 1).
Rice. 1. Straight-line movement
Curvilinear there will be such a movement when the speed of the body and the force applied to this body are directed relative to each other at a certain angle (Fig. 2). In this case, the speed will change its direction.
Rice. 2. Curvilinear movement
So, when straight motion the velocity vector is directed in the same direction as the force applied to the body. A curvilinear movement is such a movement when the velocity vector and the force applied to the body are located at a certain angle to each other.
Let us consider a special case of curvilinear motion, when a body moves in a circle with a constant velocity in absolute value. When a body moves in a circle at a constant speed, only the direction of the speed changes. In absolute value it remains constant, but the direction of the velocity changes. This change in speed leads to the presence of acceleration in the body, which is called centripetal.
Rice. 6. Movement along a curved path
If the trajectory of a body’s movement is a curve, then it can be represented as a set of movements along circular arcs, as shown in Fig. 6.
In Fig. Figure 7 shows how the direction of the velocity vector changes. The speed during such a movement is directed tangentially to the circle along the arc of which the body moves. Thus, its direction is constantly changing. Even if the absolute speed remains constant, a change in speed leads to acceleration:
IN in this case acceleration will be directed towards the center of the circle. That's why it's called centripetal.
Why is centripetal acceleration directed towards the center?
Recall that if a body moves along a curved path, then its speed is directed tangentially. Velocity is a vector quantity. A vector has a numerical value and a direction. The speed continuously changes its direction as the body moves. That is, the difference in speeds at different moments of time will not be equal to zero (), in contrast to rectilinear uniform motion.
So, we have a change in speed over a certain period of time. The ratio to is acceleration. We come to the conclusion that, even if the speed does not change in absolute value, a body performing uniform motion in a circle has acceleration.
Where is this acceleration directed? Let's look at Fig. 3. Some body moves curvilinearly (along an arc). The speed of the body at points 1 and 2 is directed tangentially. The body moves uniformly, that is, the velocity modules are equal: , but the directions of the velocities do not coincide.
Rice. 3. Body movement in a circle
Subtract the speed from it and get the vector. To do this, you need to connect the beginnings of both vectors. In parallel, move the vector to the beginning of the vector. We build up to a triangle. The third side of the triangle will be the velocity difference vector (Fig. 4).
Rice. 4. Velocity difference vector
The vector is directed towards the circle.
Let's consider a triangle formed by the velocity vectors and the difference vector (Fig. 5).
Rice. 5. Triangle formed by velocity vectors
This triangle is isosceles (the velocity modules are equal). This means that the angles at the base are equal. Let us write down the equality for the sum of the angles of a triangle:
Let's find out where the acceleration is directed at a given point on the trajectory. To do this, we will begin to bring point 2 closer to point 1. With such unlimited diligence, the angle will tend to 0, and the angle will tend to . The angle between the velocity change vector and the velocity vector itself is . The speed is directed tangentially, and the vector of speed change is directed towards the center of the circle. This means that the acceleration is also directed towards the center of the circle. That is why this acceleration is called centripetal.
How to find centripetal acceleration?
Let's consider the trajectory along which the body moves. In this case it is a circular arc (Fig. 8).
Rice. 8. Body movement in a circle
The figure shows two triangles: a triangle formed by velocities, and a triangle formed by radii and displacement vector. If points 1 and 2 are very close, then the displacement vector will coincide with the path vector. Both triangles are isosceles with the same vertex angles. Thus the triangles are similar. This means that the corresponding sides of the triangles are equally related:
The displacement is equal to the product of speed and time: . Substituting this formula, we can obtain the following expression for centripetal acceleration:
Angular velocity denoted by the Greek letter omega (ω), it indicates the angle through which the body rotates per unit time (Fig. 9). This is the magnitude of the arc in degree measure traversed by the body over some time.
Rice. 9. Angular velocity
Please note that if solid rotates, then the angular velocity for any points on this body will be a constant value. Whether the point is located closer to the center of rotation or further away is not important, i.e. it does not depend on the radius.
The unit of measurement in this case will be either degrees per second () or radians per second (). Often the word “radian” is not written, but simply written. For example, let’s find what the angular velocity of the Earth is. The Earth makes a complete rotation in one hour, and in this case we can say that the angular velocity is equal to:
Also pay attention to the relationship between angular and linear speeds:
Linear speed is directly proportional to the radius. The larger the radius, the greater the linear speed. Thus, moving away from the center of rotation, we increase our linear speed.
It should be noted that circular motion at a constant speed is a special case of motion. However, the movement around the circle may be uneven. Speed can change not only in direction and remain the same in magnitude, but also change in value, i.e., in addition to a change in direction, there is also a change in the magnitude of velocity. In this case we are talking about the so-called accelerated motion in a circle.
What is a radian?
There are two units for measuring angles: degrees and radians. In physics, as a rule, the radian measure of angle is the main one.
Let's build central angle, which rests on an arc of length .
Lesson No. 26 Scenario
Lesson topic: Rectilinear and curvilinear motion. Movement of a body in a circle with a constant absolute speed.
Subject: physics
Teacher: Apasova N.I.
Grade: 9
Textbook: Physics. 9th grade: textbook / A. V. Peryshkin, E. M. Gutnik. - 3rd ed., stereotype. - M.: Bustard, 2016
Lesson type: lesson in discovering new knowledge
Lesson objectives:
Create conditions for students to develop an idea of curvilinear motion and the quantities that characterize it;
Promote the development of observation skills, logical thinking;
Contribute to the formation of a scientific worldview and interest in physics.
Lesson objectives:
- give examples of rectilinear and curvilinear motion of bodies; name the conditions under which bodies move rectilinearly and curvilinearly; calculate the module of centripetal acceleration; depict in drawings the vectors of velocity and centripetal acceleration when a body moves in a circle; explain the reason for the occurrence of centripetal acceleration during uniform circular motion (subject result);
- master the skills of independently acquiring new knowledge about the movement of the body in a circle; apply heuristic methods when deciding the cause of centripetal acceleration during uniform circular motion; master regulatory control methods when solving calculation and qualitative problems; develop monologue and dialogic speech (metasubject result);
Form cognitive interest to types of mechanical movement; develop creative abilities and practical skills in solving qualitative and calculation problems on the uniform movement of a point along a circle; be able to make independent decisions, justify and evaluate the results of their actions (personal result).
Teaching aids: textbook, collection of problems; computer, multimedia projector, presentation “Rectilinear and curvilinear motion”; inclined chute, ball, ball on a string, toy car, spinning top.
I. Organizational moment (motivation to educational activities)Goal of the stage: inclusion of students in activities at a personally significant level
Greeting, checking readiness for the lesson, emotional mood.
“We are truly free when we have retained the ability to reason for ourselves.” Cicero.
They listen and tune in to the lesson.
Personal: attention, respect for others
Communicative: planning educational cooperation
Regulatory: self-regulation
II. Updating knowledge
The purpose of the stage: repetition of the studied material necessary for the “discovery of new knowledge” and identification of difficulties in individual activities every student
Organizes mutual checking of homework and discussion on test questions
1. Formulate the law of universal gravitation. Write down the formula.
2. Is it true that attraction to the Earth is one of the examples of universal gravitation?
3. How does the force of gravity acting on a body change as it moves away from the Earth?
4. What formula can be used to calculate the force of gravity acting on a body if it is at a low altitude on Earth?
5. In what case will the force of gravity acting on the same body be greater: if this body is located in the equatorial region of the globe or at one of the poles? Why?
6. What do you know about the acceleration of gravity on the Moon?
No. 2,3 – orally
No. 4 – at the blackboard
We know that all bodies attract each other. In particular, the Moon, for example, is attracted to the Earth. But the question arises: if the Moon is attracted to the Earth, why does it revolve around it instead of falling towards the Earth?
In order to answer this question, it is necessary to consider the types of motion of bodies.
What types of movements have we studied?
What kind of motion is called uniform?
What is the speed of uniform motion called?
What kind of motion is called uniformly accelerated?
What is the acceleration of a body?
What is movement? What is a trajectory?
Answer questions
Peer review of the assignment
Answer questions
Cognitive: logical inferences; consciously and voluntarily construct a speech utterance in oral form
Regulatory: the ability to listen in accordance with the target setting; clarification and addition of student statements
IIӀ. Setting the goals and objectives of the lesson.
The purpose of the stage: creating a problem situation; fixing a new learning task
Statement of the problem.
Demonstration of experience: spinning a spinning top, spinning a ball on a string
How can you characterize their movements? What do their movements have in common?
This means that our task in today’s lesson is to introduce the concept of rectilinear and curvilinear motion. Body movements in a circle. Slide 1
To set goals, I suggest analyzing the mechanical movement pattern. Slide 2.
What goals will we set for our topic? Slide 3
They make an assumption
Write down the topic of the lesson, formulate goals
Regulatory: regulation of educational activities; ability to listen in accordance with the target setting
Personal: readiness and ability for self-development.
I V. Problematic explanation of new knowledge
The purpose of the stage: to ensure students’ perception, comprehension and initial consolidation of knowledge about curvilinear movement, quantities characterizing it
Explaining new material with showing a presentation, demonstrating experiments, organizing independent work students with textbook
Demonstration: a ball falling vertically, rolling down a chute, a ball spinning on a string, a toy car moving across a table, a ball thrown at an angle to the horizon falling.
How are the movements of the proposed bodies different?
Try to give it yourselfdefinitions
curvilinear and rectilinear movements.
– rectilinear movement – movement along a straight path
– curvilinear movement – movement along an indirect trajectory.
Task 1. Identify the main signs of rectilinear and curvilinear motion
1. Read § 17
2. Based on Fig. 34 p. 70 write down in your notebook the signs that a moving body has:
a) straight (1 b)
b) curvilinear (1 b)
3. Choose the correct statement: (2 b)
A: if the force vector and the velocity vector are directed along the same straight line, then the body moves rectilinearly
B: if the force vector and the velocity vector are directed along intersecting straight lines, then the body moves curvilinearly
1) only A 2) only B 3) both A and B 4) neither A nor B
Do conclusion What determines the type of movement trajectory?
The action of a force on a body in some cases can only lead to a change in the magnitude of the velocity vector of this body, and in others - to a change in the direction of the velocity.
Consider two examples of curvilinear movement: along a broken line and along a curve. Slides 7,8
How are these trajectories different?
Task 2. Imagine movement along any curved path as movement in a circle.
1. Consider Fig. 35 p. 71, analyze it based on the text of the textbook.
2. Draw your own curvilinear trajectory and imagine it as a set of circular arcs of different radii. (1 b)
That. this movement can be considered as a sequence of movements occurring along circular arcs of different radii. Slide 9
Task 3. Determine the direction of the linear velocity vector when moving in a circle.
1. Read § 18 p. 72.
2. Draw the velocity vector at points B and C in your notebook and draw a conclusion. (2b)
Give examples of curvilinear motion that you have encountered in life.
Planets and artificial satellites of the Earth move along curvilinear trajectories in outer space, and on Earth all kinds of means of transport, parts of machines and mechanisms, river waters, atmospheric air, etc. Slide 10.
If you press the end of a steel rod against a rotating grindstone, the hot particles coming off the stone will be visible in the form of sparks. These particles fly at the speed they had at the moment they left the stone. It is clearly seen that the direction of movement of the sparks coincides with the tangent to the circle at the point where the rod touches the stone.On a tangent splashes from the wheels of a skidding car are moving.
Thus, the instantaneous speed of the body at different points of the curvilinear trajectory has a different direction, and, please note: the vectors of speed and force acting on the body are directed along intersecting straight lines. Slide 11.
In absolute terms, the speed can be the same everywhere or vary from point to point. But even if the speed module does not change, it cannot be considered constant. Speed is a vector quantity. And oncethe velocity vector changes , that means there is acceleration. Therefore, curvilinear movement is alwaysaccelerating movement , even if the absolute speed is constant.(Slide 12).
Task 4. Study p concept of centripetal acceleration.
Answer the questions:
2) Where is the acceleration of a body directed when moving in a circle with a constant absolute speed? (1 b)
3) What formula can be used to calculate the magnitude of the centripetal acceleration vector? (1 b)
4) What formula is used to calculate the magnitude of the vector of force, under the influence of which a body moves in a circle with a constant velocity in magnitude? (1 b)
Acceleration of a body moving uniformly in a circle at any pointcentripetal
,
those. directed along the radius of the circle towards its center. At any point, the acceleration vector is perpendicular to the velocity vector. Slide 13
Centripetal acceleration module: a q = V 2 /R where V is the linear speed of the body, and R is the radius of the circle.
Slide 14
The formula shows that at the same speed, the smaller the radius of the circle, the greater the centripetal force. So, at road turns, a moving body (train, car, bicycle) should act towards the center of the curve, the greater the force, the sharper the turn, i.e., the smaller the radius of the curve.
According to Newton's II law, acceleration is always co-directed with the force that produces it. This is also true for centripetal acceleration.
How is the force directed at each point of the trajectory?
This force is called centripetal.
Centripetal force depends on linear speed: as speed increases, it increases. This is well known to all skaters, skiers and cyclists: what with higher speed the more difficult it is to make a turn. Drivers know very well how dangerous it is to turn a car sharply at high speed.
Centripetal force is created by all the forces of nature.
Give examples of the action of centripetal forces by their nature:
elastic force (stone on a rope);
gravitational force (planets around the sun);
friction force (turning motion).
Watching the demonstration
They answer the question: according to the type of trajectory, these movements can be divided into movements along a straight line and along a curved line
Definitions are given. Slide 4
Complete the task
Draw a conclusion
Slides 5,6
Answer the question: in the first case, the trajectory can be divided into straight sections and each section can be considered separately. In the second case, you can divide the curve into circular arcs and straight sections
Working with a textbook
Complete the task
Working with a textbook
Give examples
Working with a textbook
Write down the formula
Answer the question
Write the formula in your notebook
Give examples
Cognitive: highlighting essential information; logical conclusions; consciously and voluntarily construct a speech utterance in oral form; ability to formulate questions; analysis of the content of the paragraph.
Communicative: listening to the teacher and friends, constructing statements that are understandable to the interlocutor.
Regulatory: the ability to listen in accordance with the target setting; plan your actions; clarification and addition of student statements
V. Initial check of understanding
The purpose of the stage: pronunciation and consolidation of new knowledge; identify gaps in the primary understanding of the studied material, misconceptions of the student; make a correction
Problem solving
1. Solving quality problems
No. 1624-1629(P)
2. Solving calculation problems
Work in pairs
Participate in a collective discussion of problem solving
Regulatory: planning one’s activities to solve a given problem, self-regulation
Personal: self-determination in order to obtain the highest result
V ӀΙΙ. Lesson summary (activity reflection)
The purpose of the stage: students’ awareness of their educational activities, self-assessment of the results of their own and the entire class’s activities
The teacher invites students to summarize the acquired knowledge in the lesson. Calculate the number of points for correctly completed tasks and give yourself a grade.
21 -19 points – score “5”
18-15 points - score “4”
14-10 points – score “3”
Offers to return to the goals and objectives of the lesson and analyze their implementation
Have all goals been achieved?
What have you learned?
I didn't know...
Now I know...
Students enter into dialogue with the teacher, express their opinions, and summarize the lesson.
Cognitive: the ability to draw conclusions.
Communicative: be able to formulate your own opinion and position.
Regulatory: the ability to exercise self-control and self-esteem; adequately perceive the teacher's assessment
ΙХ. Homework
Goal: further independent application of acquired knowledge.
§17,18; answer questions to paragraphs
Exercise 17 – orally
Students write down homework, get advice
Regulatory: students’ organization of their learning activities.
Personal: assessing the level of difficulty of a task when choosing it for the student to complete independently