Physics material point reference system. Material point
The purpose of the lesson:
Lesson objectives:
educational:
developing:
educational:
Equipment:
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"Material point. reference system."
Lesson 1/1
Subject: Material point. Reference system.
The purpose of the lesson: to form concepts: a material point, a frame of reference.
Lesson objectives:
educational:
introduction of concepts: material point, reference system, trajectory.
developing:
development of skills to highlight the main thing, compare, generalize, draw conclusions, argue one's own opinion;
development of students' speech through the organization of dialogical communication in the classroom,
development of motor memory - students fixing information in a notebook,
development of auditory memory - pronunciation of definitions;
development of visual memory - making notes on the board;
educational:
aesthetic design of notes in notebooks and on the board.
Equipment: Tripod with clutch and foot, chute, ball, body on a thread.
During the classes:
1.Introduction.
Introduction to the textbook.
Safety precautions in the office and when performing laboratory work.
Teaching supplies necessary for the lesson.
2.Updating knowledge.
Answer the questions:
What is matter? ( definition).
What is mechanical movement? ( definition).
3. Study of new material.
Physics is a science that studies the most general properties of the world around us. This is an experimental science.
Find the most general laws nature
Explain specific processes by the action of these general laws.
Main sections of physics:
Mechanics
Thermodynamics
Electrodynamics
Mechanics is the science of motion and interaction of macroscopic bodies.
Classical mechanics consists of three parts:
Kinematics studies how the body moves.
Dynamics explains the reasons for the movement of the body.
Statics explains why the body is at rest.
To describe the movement in kinematics, special concepts are introduced: a material point, a frame of reference, a trajectory and quantities: path, displacement, speed, acceleration, which are important not only in kinematics, but also in other branches of physics.
The first thing that catches your eye when observing the world around you is its variability.
Answer the questions:
What changes do you notice?
Bottom line: frequent responses are associated with a change in the position of bodies relative to each other.
Change in the position of a body in space relative to other bodies over timecalled mechanical movement.
Demonstration:
rolling a ball down a chute,
pendulum oscillations.
Relativity of motion. (examples animation rel motion )
A material point is a body whose size and shape can be neglected under given conditions.
Criteria for replacing a body with a material point:
a) the path traveled by the body is much more sizes moving body.
b) the body is moving forward. (examples animation checkmate dot)
Answer the questions:
How to determine the position of the body?
You need a body of reference and a frame of reference.
Reference system: reference body, coordinate system, clock.
The reference system can be:
One-dimensional, when the position of the body is determined by one coordinate
Two-dimensional, when the position of the body is determined by two coordinates
Three-dimensional, when the position of the body is determined by three coordinates.
4.Fixing the material.
Answer the questions:
1. In which case is the body a material point of the body:
a) a sports disc is made on the machine;
b) the same disk after the throw of the athlete flies to a distance of 55 m.
2. What coordinate system (one-dimensional, two-dimensional, three-dimensional) should be chosen to determine the position of bodies:
- tractor in the field;
- helicopter in the sky;
- train;
- chess piece.
Independent work: write and fill in the gaps.
Any body can be considered as a material point in cases where the distances traveled by the points of the body are very large compared to ...
The movement is called translational if all points of the body are moving at any moment in time ...
The body, the size and shape of which in the case under consideration can be neglected, is called ...
All together: a) a reference body, b) a coordinate system, c) a device for determining time, - form ...
With a rectilinear motion of the body, the position of the body is determined by ... coordinates (s) (s).
5. Reflection.
Homework: § one.
Lesson #1
Topic. Mechanical movement and its types. The main task of mechanics and ways to solve it in kinematics. Physical body and material point. Reference system
Purpose: to characterize the tasks of studying the section "Kinematics", to acquaint with the structure of the textbook; give an idea of mechanical motion, the main task of mechanics and ways to solve it in kinematics; to form the concept of translational motion of bodies, a material point, a reference system; show the role of knowledge in mechanics in other sciences, in technology; show that mechanical motion is one of the forms of existence of matter, one of the many types of changes in nature, and a material point is a model, an ideal object of classical mechanics.
Type of lesson: lesson of studying new educational material.
Visual: demonstration of the translational motion of the body, cases when the body can (and cannot) be considered a material point, PPS "Physics-9" from "Kvazar-Micro".
Expected results. After the lesson, students:
Distinguish between a physical body and a material point, rectilinear and curvilinear motion of a material point;
They will be able to substantiate the content of the main (direct) task of mechanics;
They will learn to explain the essence of physical idealizations - a material point and a frame of reference.
II. Announcement of the topic and purpose of the lesson
Formation of new concepts. During a conversation using a demonstration experiment and teaching staff "Physics-9" from "Kvazar-Micro", consider the following questions:
Mechanical movement and its types;
The main task of mechanics and ways to solve it in kinematics;
What does kinematics study?
Physical body and material point, reference system.
We often call some bodies mobile, others immobile.
Trees, various buildings, bridges, river banks are motionless. The water in the river, the planes in the sky, the cars on the road are moving.
What gives us grounds for dividing bodies into mobile and immovable? How do they differ from each other?
When we talk about a car that is moving, we mean that at a certain point in time it was next to us, and at other times the distance between us and the car changed. The motionless bodies during the entire observation do not change their position relative to the observer.
An experience. Place the vertical poles on the table at some distance from each other in a straight line. Let's put a cart with a thread near the first of them and start pulling it. First, it moves from the first pole to the second, then to the third, and so on. That is, the cart will change its position relative to the towers.
Mechanical movement is a change in the position of a body relative to other bodies or one of its parts relative to others. Examples of mechanical movement: the movement of stars and planets, aircraft and cars, artillery shells and rockets, a person walks relative to the Earth, the movement of arms relative to the body.
Other examples of mechanical movement are shown in fig. one.
The mechanical movements of the surrounding bodies are divided into: translational, rotational and oscillatory (the system periodically returns to the equilibrium position, for example, the vibration of leaves on a tree under the influence of wind) movements (Fig. 2).
Features of translational movement (movement of passengers along with an escalator, movement of a lathe cutter, etc.):
An arbitrary straight line in the body remains parallel to itself;
All points have the same trajectories, speeds, accelerations.
These conditions are not met for the rotational movement of the body (the movement of a car wheel, Ferris wheel, the Earth around the Sun and its own axis, etc.).
Mechanical movement is often part of more complex non-mechanical processes, such as thermal ones. The branch of physics that deals with the study of mechanical motion is called mechanics.
The mechanical form of the motion of matter is studied by the section of physics "Mechanics". The main task of mechanics is to find the position of a body in space at any given time. Mechanical movement occurs in space and time. The concepts of space and time are fundamental concepts that cannot be defined through any simpler ones. To study the mechanical movement that occurs in space and time, you must first of all be able to measure intervals of time and distance. A special case of motion is rest, therefore mechanics also considers the conditions under which bodies are at rest (these conditions are called equilibrium conditions).
To formulate the laws of mechanics and learn how to apply them, you must first learn how to describe the position of the body and its movement. Description of motion is the content of the section of mechanics, called kinematics.
To describe mechanical motion, as well as other physical processes occurring in space and time, a reference system is used. A reference system is a combination of a reference body, a coordinate system associated with it (Cartesian or other) and a device for timing (Fig. 3).
The reference system in kinematics is chosen, guided only by considerations about how it is most convenient to describe the movement mathematically. There are no advantages of one system over another in kinematics. Due to the complexity of the physical world, the real phenomenon that is being studied always has to be simplified and instead of the phenomenon itself, an idealized model should be considered. So, for simplification in the conditions of certain tasks, the dimensions of the bodies can be neglected. An abstract concept that replaces a real body that moves forward and whose dimensions can be neglected in a real problem is called a material point. In kinematics, when solving a problem, the question of what exactly moves, where it moves, why it moves in this way, is generally not considered. The main thing is how the body moves.
III. Consolidation of what has been learned. Problem solving
1. Independent work on the material of the teaching staff "Physics-9" from "Kvazar-Micro", during which students make a reference note.
IV. Homework
1. Learn the outline of the lesson; corresponding section of the textbook.
2. Solve problems:
It seems to a small child that the second hand of the clock is moving, and the minute and hour hand motionless. How to prove to a child that she is wrong?
Give examples of problems in which the Moon: a) can be considered a material point; b) cannot be considered a material point.
3. Additional task: prepare presentations.
Topic: "Material point. Reference system"
Objectives: 1. to give an idea of the kinematics;
2. to acquaint students with the goals and objectives of the physics course;
3. introduce the concepts: mechanical movement, trajectory path; prove that rest and motion are relative concepts; justify the need to introduce an idealized model - a material point, a reference system.
4. Learning new material.
During the classes
1. Introductory conversation with students about the goals and objectives of the 9th grade physics course.
What does kinematics study? dynamics?
What is the main task of mechanics?
What phenomena should be able to explain?
problematic experiment.
Which body falls faster: a piece of paper or a book?
Which body falls faster: an unfolded sheet of paper or the same sheet folded several times?
Why doesn't water flow out of a hole in a jar when the jar falls?
What happens if you put a bottle of water on the edge of a piece of paper and jerk it sharply in a horizontal direction? If you pull the paper slowly?
2. Examples of bodies at rest and moving bodies. Demos.
A ball rolling down an inclined plane.
The movement of a ball up an inclined plane.
О Movement of the trolley on the demonstration table.
Z. Formation of concepts: mechanical movement, body trajectory, rectilinear and curvilinear movements, the path traveled.
Demos.
O The movement of a hot flashlight bulb in a darkened auditorium.
О A similar experiment with a light bulb mounted on the rim of a rotating disk.
4. Formation of ideas about the reference system and the relativity of motion.
1. Problem experiment.
The movement of the cart with the bar on the demonstration table.
Is the block moving?
Is the question clearly stated? Formulate the question correctly.
2. Frontal experiment to observe the relativity of motion.
Lay the ruler on a sheet of paper. press one end of the ruler with your finger and use a pencil to move it to a certain angle in the horizontal plane. In this case, the pencil should not move relative to the ruler.
What is the trajectory of the end of the pencil relative to the sheet of paper?
What type of movement is the movement of the pencil in this case?
What state is the end of the pencil in relation to the sheet of paper? About the line?
a) It is necessary to introduce a reference system as a combination of a reference body, a coordinate system and a device for determining time.
b) The trajectory of the body depends on the choice of reference system.
5. Substantiation of the need to introduce an idealized model - a material point.
6. Acquaintance with the translational movement of the body.
Demozh9soiratsiya.
Ф Movements of a large book with a line drawn on it (Fig. 2). (A feature of the movement is that any straight line drawn in the body remains parallel to itself)
The movements of a torch smoldering from both ends in a darkened auditorium.
7. Solving the main problem of mechanics: determining the position of the body at any time.
a) On a straight line - a one-dimensional coordinate system (a car on a highway).
X= 300 m, X= 200 m
b) On a plane - a two-dimensional coordinate system (a ship at sea).
c) In space - a three-dimensional coordinate system (an airplane in the sky).
C. Solution of qualitative problems.
Answer the questions in writing (yes or no):
When calculating the distance from the Earth to the Moon?
When measuring its diameter?
When landing a spacecraft on its surface?
When determining the speed of its movement around the Earth?
Going from home to work?
Performing gymnastic exercises?
Traveling by boat?
What about measuring a person's height?
III. Historical information.
Galileo Galilei in his book Dialogue a prime example relativity of the trajectory: "Imagine an artist who is on a ship sailing from Venice across the Mediterranean. The artist draws on paper with a pen a whole picture of figures drawn in thousands of directions, an image of countries, buildings, animals and other things .." The trajectory of the pen in relation to the sea, Galileo represents "a line of extension from Venice to the final place ...
more or less undulating, depending on how much the ship swayed along the way."
IV. Lesson results.
V. Homework: §1, exercise 1 (1-3).
Theme: "Moving"
Purpose: 1. to justify the need to introduce a displacement vector to determine the position of the body in space;
2. to form the ability to find the projection and the modulus of the displacement vector;
3. repeat the rule of addition and subtraction of vectors.
During the classes
1. Actualization of knowledge.
front poll.
1. What does mechanics study?
2. What movement is called mechanical?
3. What is the main task of mechanics?
4. What is called a material point?
5 What is progressive movement?
b. What branch of mechanics is called kinematics?
7. Why is it necessary to single out special reference bodies when studying mechanical motion?
8. What is called a reference system?
9. What coordinate systems do you know?
10. Prove that motion and rest are relative concepts.
11. What is called a trajectory?
12. What types of trajectory do you know?
13. Does the trajectory of the body depend on the choice of reference system?
14. What movements exist depending on the shape of the trajectory?
15. What is the distance covered?
Solving quality problems.
1. The cyclist moves uniformly and in a straight line. draw the trajectories of movement:
a) the center of the bicycle wheel relative to the road;
b) points of the wheel rim relative to the center of the wheel;
c) the points of the wheel rim relative to the bicycle frame;
d) the points of the wheel rim relative to the road.
2. Which coordinate system should be chosen (one-dimensional, two-dimensional, three-dimensional) to determine the position of the following bodies:
a) a chandelier in the room, e) a submarine,
b) train, f) chess piece,
c) helicopter g) plane in the sky
d) an elevator, h) an airplane on the runway.
1. Substantiation of the need to introduce the concept of displacement vector.
a) task. Determine the final position of the body in space if it is known that the body left point A and traveled a distance of 200 m?
b) Introduction of the concept of displacement vector (definition, designation), module of displacement vector (designation, unit of measure). The difference between the modulus of a displacement vector and the distance travelled. When do they match?
2. Formation of the concept of displacement vector projection. When is the projection considered positive, when is it negative? In what case is the projection of the displacement vector equal to zero? (Fig. 1)
3. Addition of vectors.
a) The rule of the triangle. To add two movements, the beginning of the second movement should be aligned with the end of the first. The closing side of the triangle will be the total displacement (Fig. 2).
b) Parallelogram rule. Construct a parallelogram on the vectors of added displacements S1 and S2. The diagonal of the parallelogram OD will be the resulting displacement (Fig. 3).
4. Frontal experiment.
a) Place the square on a sheet of paper, near the sides right angle put points D, E and A (Fig. 4).
b) Move the end of the pencil from point 1) to point E, leading it along the sides of the triangle in the direction 1) A B E.
c) Measure the path with the drawn end of the pencil relative to the sheet of paper.
d) Construct the vector of movement of the end of the pencil relative to the sheet of paper.
E) Measure the magnitude of the displacement vector and the distance traveled by the end of the pencil and compare them.
III. Problem solving. -
1. Do we pay for the journey or transportation when traveling by taxi, by plane?
2. the dispatcher, accepting the car at the end of the working day, made a note in waybill: "Increase meter reading 330 km". What is this entry about: the path traveled or the movement?
3. The boy threw the ball up and caught it again. Assuming that the ball has risen to a height of 2.5 m, find the path and movement of the ball.
4. The elevator car descended from the eleventh floor of the building to the fifth, and then went up to the eighth floor. Assuming that the distances between floors are 4 m, determine the path and movement of the cabin.
IV. Lesson results.
V. homework: § 2, exercise 2 (1.2).
Topic: "Determining the coordinates of a moving body"
1. to form the ability to solve the main problem of mechanics: to find the coordinates of the body at any time;
2. determine the value of the displacement vector projections on the coordinate axis and its module.
During the classes
1. Knowledge update
front poll.
What quantities are called vector quantities? Give examples of vector quantities.
What quantities are called scalars? What is called displacement? How are the movements? What is the projection of a vector onto a coordinate axis? When is the projection of a vector considered positive? negative?
What is the modulus of a vector?
Problem solving.
1. Determine the signs of the projections of the displacement vectors S1, S2, S3, S4, S5, S6 on the coordinate axes.
2. The car drove along the street for a distance of 400 m. Then it turned right and drove along the lane for another 300 m. Considering the movement to be straight on each of the segments of the path, find the path and movement of the car. (700 m; 500 m)
3. The minute hand of a clock makes a complete revolution in one hour. What path does the end of the arrow 5 cm long cover in this case? What is the linear displacement of the end of the arrow? (0.314 m; 0)
11. Learning new material.
Solution of the main problem of mechanics. Determining the coordinates of a moving body.
III. Problem solving.
1. In fig. 1 shows the initial position of point A. Determine the coordinate of the end point, build the displacement vector, determine its module if $x=4m and $y=3m.
2. The coordinates of the beginning of the vector are: X1 = 12 cm, Y1 = 5 cm; end: X2 = 4 cm, Y2 = 11 cm. Build this vector and find its projections on the coordinate axes and the module of the vector (Sx = -8, Sy = b cm, S = 10 cm). (On one's own.)
H. The body has moved from a point with coordinates X0=1 m, Y0=4 m to a point with coordinates X1=5 m, Y1=1 m. 3 cm, S = 5 m).
IV. Lesson results.
V. Homework: 3, exercise 3 (1-3).
Topic: "Rectilinear uniform motion"
1. form the concept of rectilinear uniform motion;
2. find out the physical meaning of the speed of the body;
3. to continue the formation of the ability to determine the coordinates of a moving body, to solve problems in a graphical and analytical way.
During the classes
Knowledge update.
Physical dictation
1. Change is called mechanical movement ...
2. A material point is a body ...
3. Trajectory is a line…
4. The path traveled is called ...
5. The frame of reference is…
b. The displacement vector is a segment ...
7. Displacement vector modulus is…
8. Vector projection is considered positive if…
9. Vector projection is considered negative if…
10. The projection of a vector is equal to O if the vector ...
11. The equation for finding the coordinates of the body at any time has the form ...
II. Learning new material.
1. Definition of rectilinear uniform motion. Vector character of speed. Velocity projection in one-dimensional coordinate system.
2. Movement formula. Dependence of displacement on time.
3. Coordinate equation. Determining the coordinates of the body at any time.
4. International system of units
The unit of length is the meter (m),
The unit of time is the second (s),
The unit of speed is meter per second (m/s).
1 km/h =1/3.6 m/s
Im/s=3.6 km/h
Historical information.
Old Russian measures of length:
1 inch \u003d 4.445 cm,
1 arshin \u003d 0.7112m,
1 sazhen \u003d 2, IZZbm,
1 verst = 1.0668 km,
1 Russian mile = 7.4676 km.
English measures of length:
1 inch = 25.4mm,
1 foot = 304.8 mm,
1 land mile = 1609 m,
1 mile nautical 1852
5. Graphical representation of the movement.
Graph of the dependence of the projection of speed on the change of motion.
Velocity projection modulus plot.
Graph of the dependence of the projection of the displacement vector on the time of movement.
Graph of dependence of the module of projection of the displacement vector on the time of movement.
Graph I - the direction of the velocity vector coincides with the direction of the coordinate axis.
Graph I I - the movement of the body occurs in the direction opposite to the direction of the coordinate axis.
6. Sx = Vxt. This product is numerically equal to the area of the shaded rectangle (Fig. 1).
7. Historical reference.
Velocity graphs were first introduced in the middle of the 11th century by the archdeacon of Rouen Cathedral, Nicolas Oresme.
III. Solving graphic problems.
1. In fig. 5 shows the graphs of the projection of the vectors of two cyclists moving along parallel lines.
Answer the questions:
What can be said about the direction of movement of cyclists in relation to each other?
Who is moving faster?
Draw a graph of the dependence of the module of the projection of the displacement vector on the time of movement.
What is the distance traveled by the first cyclist in 5 seconds of movement?
2. The tram is moving at a speed of 36 km/h, and the speed vector coincides with the direction of the coordinate axis. Express this speed in meters per second. Draw a graph of the dependence of the projection of the velocity vector on the time of movement.
IV. Lesson results.
V. homework: § 4, exercise 4 (1-2).
Topic: "Rectilinear uniformly accelerated motion. Acceleration"
1. introduce the concept of uniformly accelerated motion, a formula for accelerating a body;
2. explain its physical meaning, introduce a unit of acceleration;
3. to form the ability to determine the acceleration of the body with uniformly accelerated and uniformly slow movements.
During the classes
1. Actualization of knowledge (frontal survey).
Define uniform rectilinear motion.
What is the speed of uniform motion?
Name the unit of speed in the International System of Units.
Write down the formula for the projection of the velocity vector.
In what cases is the projection of the velocity vector of uniform motion onto the axis positive, in which cases is it negative?
Write down the formula for the day of the displacement vector projection?
What is the coordinate of the moving body at any moment of time?
How can speed expressed in kilometers per hour be expressed in meters per second and vice versa?
The car "Volga" is moving at a speed of 145 km/h. What does this mean?
11. Independent work.
1. How much more is the speed of 72 km/h than the speed of 10 m/s?
2. The speed of an artificial satellite of the Earth is 3 km / h, and rifle bullets are 800 m / s. Compare these speeds.
3 With uniform motion, a pedestrian travels a distance of 12 m in b s. What distance will he cover when moving at the same speed in 3 s?
4. Figure 1 shows a graph of the distance traveled by a cyclist versus time.
Determine the speed of the cyclist.
Draw a graph of the modulus versus time of motion.
II. Learning new material.
1. Repetition of the concept of non-uniform rectilinear motion from the course of physics? class.
How can average speed be determined?
2. Acquaintance with the concept of instantaneous speed: the average speed for a very small finite period of time can be taken as instantaneous, the physical meaning of which is that it shows how fast the body would move if, starting from a given point in time, its movement became uniform and straight.
Answer the question:
What speed are we talking about in the following cases?
o The speed of the courier train "Moscow - Leningrad" is 100 km/h.
o A passenger train passed a traffic light at a speed of 25 km/h.
Z. Demonstration of experiments.
a) Rolling a ball down an inclined plane.
b) On an inclined plane along its entire length, strengthen the paper tape. Place an easy-moving cart with a dropper on the board. Release the cart and examine the location of the drops on the paper.
4. Definition of uniformly accelerated motion. Acceleration: definition, physical meaning, formula, unit of measure. The acceleration vector and its projection onto the axis: in which case is the acceleration projection positive, in which case is it negative?
a) Uniformly accelerated motion (velocity and acceleration are co-directed, the module of speed increases; ax> O).
b) Uniformly slow motion (velocity and acceleration are directed in opposite directions, the speed modulus decreases, ah
5. Examples of accelerations encountered in life:
Suburban electric train 0.6 m/s2.
Aircraft IL-62 with a takeoff run of 1.7 m/s2.
The acceleration of a freely falling body is 9.8 m/s2.
Rocket at satellite launch 60 m/s.
A bullet in the barrel of a Kalashyavkov submachine gun was 105 m/s2.
6. Graphical representation of acceleration.
Graph I - corresponds to uniformly accelerated motion with acceleration a=3 m/s2.
Graph II - corresponds to uniformly slow motion with acceleration
III. Problem solving.
An example of problem solving.
1. The speed of a car moving in a straight line and uniformly increased from 12 m/s to 24 m/s in 6 seconds. What is the acceleration of the car?
Solve the following problems according to the model.
2. The car moved uniformly accelerated, and within 10 seconds its speed increased from 5 to 15 m/s. Find the acceleration of the car (1 m/s2)
H. When braking, the vehicle speed decreases from 20 to 10 m/s within 5 s. Find the acceleration of the car, provided that it remained constant during the movement (2 m/s2)
4. The acceleration of a passenger aircraft during takeoff lasted 25 s, by the end of the acceleration the aircraft had a speed of 216 km/h. Determine the acceleration of the aircraft (2.4 m/s2)
IV. Lesson results.
V. Homework: § 5, exercise 5 (1 - Z).
Topic: "Speed of rectilinear uniformly accelerated motion"
1. enter a formula for determining the instantaneous speed of a body at any time;
2. to continue the formation of the ability to build graphs of the dependence of the projection of speed on time;
3. Calculate the instantaneous speed of the body at any given time.
During the classes
Independent work.
1 option
1. What movement is called uniformly accelerated?
2. Write down the formula for determining the projection of the acceleration vector.
H. The acceleration of the body is 5 m/s2, what does this mean?
4. The speed of the parachutist's descent after opening the parachute decreased from 60 to 5 m/s in 1.1 s. Find the skydiver's acceleration. (50m/s2)
II option
1 What is acceleration?
2, Name the units of acceleration.
3. The acceleration of the body is 3 m/s2. What does this mean?
4. With what acceleration does the car move if in 10 seconds its speed has increased from 5 to 10 m / s? (0.5 m/s2)
II. Learning new material.
1. Derivation of a formula for determining the instantaneous speed of a body at any time.
1. Actualization of knowledge.
a) Graph of the dependence of the projection of the velocity vector on the time of movement Y (O.
2. Graphical representation of the movement. -
III. Problem solving.
Examples of problem solving.
1. The train is moving at a speed of 20 m/s. When the brakes were applied, it began to move with a constant acceleration of 0.1 m/s2. Determine the speed of the train through 30 s after the start of movement.
2. The speed of the body is given by the equation: V = 5 + 2 t (the units of speed and acceleration are expressed in SI). What is the initial velocity and acceleration of the body? Plot a graph of the speed of the body and determine the speed at the end of the fifth second.
Solve problems according to the model
1. A car with a speed of 10 m/s started moving with a constant acceleration of 0.5 m/s2 directed in the same direction as the velocity vector. Determine the speed of the car after 20 seconds. (20 m/s)
2. The projection of the speed of a moving body changes according to the law
V x= 10 -2t (values are measured in SI). Define:
a) initial velocity projection, module and direction of the initial velocity vector;
b) acceleration projection, module and direction of the acceleration vector;
c) plot the dependence Vх(t).
IV. Lesson results.
V Homework: § 6, exercise 6 (1 - 3); compose questions of mutual control to § 6 of the textbook.
Topic: "Moving with rectilinear uniformly accelerated motion"
1. to acquaint students with a graphical method for deriving a formula for moving in a rectilinear uniformly accelerated motion;
2. to form the ability to determine the movement of the body using formulas:
During the classes
Knowledge update.
Two students come to the blackboard and ask each other questions prepared in advance on the topic. The rest of the students act as experts: they evaluate the performance of the students. Then the next couple is invited, and so on.
II. Problem solving.
1. In fig. 1 shows a plot of the speed modulus versus time. Determine the acceleration of a rectilinear moving body.
2. In fig. 2 shows a graph of the projection of the speed of rectilinear motion of the body on time. Describe the nature of the movement in individual sections. Draw a graph of the projection of acceleration versus time of motion.
Sh. The study of new material.
1. Conclusion of the formula for moving with uniformly accelerated movement in a graphical way.
a) The path traveled by the body in time is numerically equal to the area of the trapezoid ABC
b) Dividing the trapezoid into a rectangle and a triangle, we find the area of these figures separately:
III. Problem solving.
An example of a problem solution.
A cyclist moving at a speed of 3 m/s starts downhill with an acceleration of 0.8 m/s2. Find the length of the mountain if the schiusk took b s,
Solve problems according to the model.
1. The bus is moving at a speed of 36 km/h. At what minimum distance from the stop should the driver start braking if, for the convenience of passengers, the acceleration during braking of the bus should not exceed 1.2 m/s? (42 m)
2. Space rocket starts from the spaceport with acceleration
45 m/s2. What speed will it have after flying 1000 m? (300 m/s)
3. A sled rolls down a 72 m long mountain in 12 s. Determine their speed at the end of the path. The initial speed of the sled is zero. (12m/s)
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BASICS OF KINEMATICS Lesson 1. TOPIC: “Material point. Reference system»
Mechanics is a branch of physics that studies motion. The main task of mechanics is to determine the position of a body in space at any time.
Kinematics is a section of mechanics that studies how to describe motion and the relationship between the quantities that characterize this motion. Dynamics is a branch of mechanics that studies the causes of mechanical motion. Statics studies the laws of equilibrium of a system of bodies.
Mechanical motion is a change in the position of a body in space over time relative to other bodies.
Translational motion is a movement in which all points of the body move in the same way, at the same speed. A material point is a body whose dimensions can be neglected, under the conditions of a given problem being solved. A reference body is any body conventionally taken as immovable, relative to which the motion of other bodies is considered.
For example, the Earth is often considered as a material point if its motion around the Sun is studied.
For example, But if we solve a problem related to the daily rotation of the planets, then it is necessary to take into account the shape and size of the planet. For example, if you want to determine the time of sunrise in different places on the globe.
What is forward movement? A body moves forward if all its points move in the same way. or A body moves translationally if a straight line drawn through two points of this body moves parallel to its original position when it moves.
Examples of translational motion Translational movement of the elevator car Translational motion of the ferris wheel
To determine the position of a body (material point) in space, it is necessary to: set the reference body; choose a coordinate system; have a device for counting time (clock)
The body of reference, the coordinate system associated with it, and the clock for counting the time of motion form the reference frame.
What is a reference body? A reference body is a body relative to which the position of other (moving) bodies is determined. For example, it can be a tree when considering the movement of a bus, or the Earth when calculating the movement of a rocket.
Coordinate system The position of the body in space can be determined using 2 coordinates ( two-dimensional system coordinates) The position of the body in space can be determined using 3 coordinates (three-dimensional coordinate system)
With a rectilinear motion of the body, one coordinate axis is sufficient
A trajectory is a line along which a body moves.
Path - the length of the path. [L] Displacement - a vector drawn from the initial position of a material point to its final position.
On the topic: methodological developments, presentations and notes
Dynamics. Inertial reference systems. Newton's first law.
Lesson objectives: to form the concept of ISO; study Newton's first law; show the importance of such a branch of physics as "Dynamics"; cultivate a sense of respect for various professions....
summary of the lesson "Movement. Material point. Reference system. Relativity of motion."
This work can be used when studying the topic in grade 9: "Kinematics". The material is intended to repeat and generalize the topic. The work can be used as a repetition material...
Lesson for grade 9 on the topic “Material point. Reference system»
The purpose of the lesson: form students about the material point; to form in students the skill of determining situations in which the concept of a material point can be applied; to form in students the concept of a reference system; consider the types of reference systems.
LESSON PLAN:
5. Homework (1 min)
DURING THE CLASSES:
1. Organizational stage (1 min)
At this stage, there is a mutual greeting of the teacher and students; checking for missing logs.
2. Motivational stage (5 min)
Today in the lesson we have to return to the study of mechanical phenomena. In the 7th grade, we already encountered mechanical phenomena, and before starting to study new material, let's remember:
What is mechanical movement?
What is uniform mechanical motion?
- What is speed?
- What is average speed?
- How to determine the speed if we know the distance and time?
In the 7th grade, you and I solved fairly simple problems to find the path, time or speed of movement. If you remember, then challenging task was to find the average speed.
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.
We write the number and the topic of the lesson “Material point. Reference system»
Today in the lesson we have to answer the following questions:
What is a material point?
Is it always possible to apply the concept of a material point?
What is a reference system?
What is the reference system?
What types of reference systems exist?
3. Learning new material (25 min)
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.
Most simple view movement is the mechanical movement already known to us.
When solving any problems related to mechanical movement, it is necessary to be able to describe this movement. What does it mean to "describe the motion of a body"?
This means that you need to define:
1) the trajectory of movement;
2) speed of movement;
3) the path traveled by the body;
4) the position of the body in space at any time
and etc.
For example, when launching a rover to Mars, astronomers carefully calculate the position of Mars at the moment the rover lands on the planet's surface. And for this you need to calculate how the direction and module of the velocity of Mars and the trajectory of Mars change over time.
From the course of mathematics, we know that the position of a point in space is specified using a coordinate system.
And what should we do if we do not have a point, but a body? After all, each body consists of a huge number of points, each of which has its own coordinate.
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 its 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 less speed at the points.
How then to be? How to describe the movement of a body that has a size?
It turns out that in many cases it is possible to use the concept, which implies that the size of the body disappears, as it were, 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.
There are situations in which the body can be taken as a material point:
1) If the distance traveled by each point of the body is much greater than the size of the body itself.
For example, the Earth is often considered as a material point if its motion around the Sun is studied. Indeed, the daily rotation of the planet will have little effect on the annual revolution around the Sun. But if we solve the problem with a daily rotation, then we must take into account the shape and size of the planet. For example, if you want to determine the time of sunrise or sunset.
2) With the translational movement of the body
Very often there are cases when the movement of the body is progressive. This means that all points of the body move in the same direction and at the same speed.
For example, a person is going up an escalator. Indeed, the person is simply standing, but each point is moving in the same direction and at the same speed as the person.
A little later, we will practice to determine situations in which it is possible to take the body as a material point, and in which it is not.
In addition to the material point, we need another tool that can be used to describe the movement of the body. This tool is called a frame of reference.
Any reference system consists 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. Those. To describe the movement, we need a starting point from which we will measure the distance and generally evaluate the position of the body in space. Such a body is calledreference body .
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 needclock .
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 needcoordinate system .
In this way,A reference system is a system that consists of a reference body, a coordinate system associated with it, and a clock.
There are many types of reference systems. We will consider the types of reference system in coordinate systems.
Reference system:
polar reference system | spherical reference system | |
one-dimensional | ||
two-dimensional | ||
three-dimensional |
We will use the Cartesian system of two types: one-dimensional and two-dimensional.
4. Consolidation of the studied material (13 min)
Presentation assignments; + No. 3.5.
5. Homework (1 min)
§ 1 + №№ 1,4,6.
Write out the definitions in the physical dictionary:
- mechanical movement;
- progressive movement;
- material point;
- reference system.