Kinematics- part of mechanics in which movement is studied material point without considering the reasons causing this movement.
Mechanical body movement is called the change in its position in space relative to other bodies over time.
The main task of mechanics- determine the position of the body in space at any time.
A movement in which all points of the body move equally is called forward movement of the body.
A body whose dimensions can be neglected under the conditions of the motion being studied is called material point
Reference body- this is any body conventionally accepted as motionless, relative to which the movement of other bodies is considered.
Watch- an instrument in which periodic motion is used to measure periods of time.
Reference system represents a reference body, an associated coordinate system and a clock.
TRAJECTORY, PATH AND MOVEMENT
Trajectory- a line that a material point describes during its movement.
The path is the length of the trajectory of the body.
By moving the body is a vector connecting the initial position of a body to its final position.
DISPLACEMENT AND SPEED DURING RIGHT LINEAR UNIFORM MOTION
Straight-line movement- a movement whose trajectory is a straight line.
A movement in which a body makes equal movements at any equal intervals of time is called uniform movement.
Speed of uniform rectilinear motion- the ratio of the vector of movement of a body over any period of time to the value of this interval:
Knowing the speed, you can find the displacement over a known period of time using the formula
With a straight line uniform motion the velocity and displacement vectors have the same direction.
Projection of movement onto the axis X: s x = x t . Since s x = x - x 0, then the body coordinate x = x 0 + s x. Similarly for the y-axis: y = y 0 + s y.
As a result, we obtain the equations of rectilinear uniform motion of a body in projections on the x and y axes:
RELATIVITY OF MOTION
The position of the body is relative, that is, it is different in different systems countdown. Therefore, its motion is also relative.
SPEED WITH UNEVEN MOTION
Uneven is a movement in which the speed of a body changes over time.
The average speed of uneven movement is equal to the ratio of the displacement vector to the travel time
Then the displacement during uneven movement
Instant speed is called the speed of a body this moment time or at a given point in the trajectory.
ACCELERATION. UNIFORMLY ACCELERATED MOTION
Uniformly accelerated is a movement in which the speed of a body changes equally over any equal intervals of time.
Acceleration of the body is the ratio of the change in the speed of a body to the time during which this change occurred.
Acceleration characterizes the rate of change in speed.
Acceleration is a vector quantity. It shows how the instantaneous speed of a body changes per unit time.
Knowing the initial speed of the body and its acceleration, from formula (1) you can find the speed at any time:
To do this, the equation must be written in projections onto the selected axis:
V x =V 0x + a x t
The speed graph for uniformly accelerated motion is a straight line.
DISPLACEMENT AND PATH IN RECTILINEAR UNIFORM ACCELERATED MOTION
Let us assume that the body has moved in time t, moving with acceleration. If the speed changes from to and given that,
Using a speed graph, you can determine the distance traveled by a body in known time way - it is numerical equal to area shaded surface.
FREE FALL OF BODIES
The movement of bodies in airless space under the influence of gravity is called free fall.
Free fall is uniformly accelerated motion. Acceleration free fall in a given place on the Earth is constant for all bodies and does not depend on the mass of the falling body: g = 9.8 m/s 2 .
For solutions various tasks From the "Kinematics" section, two equations are needed:
Example: A body, moving uniformly accelerated from a state of rest, covered a distance of 18 m in the fifth second. What is the acceleration and how far did the body travel in 5 s?
In the fifth second, the body has traveled the distance s = s 5 - s 4 and s 5 and s 4 are the distances traveled by the body in 4 and 5 s, respectively.
Answer: a body moving with an acceleration of 4 m/s2 travels 50 m in 5 s.
Tasks and tests on the topic "Topic 1. "Mechanics. Fundamentals of kinematics."
- Material point (Reference system)
Lessons: 3 Assignments: 9 Tests: 1
- Graphs of the dependence of kinematic quantities on time during uniformly accelerated motion - Laws of interaction and motion of bodies: basics of kinematics, grade 9
Lessons: 2 Assignments: 9 Tests: 1
Lessons: 1 Assignments: 9 Tests: 1
To complete tasks on the topic "Mechanics" you need to know Newton's laws, laws universal gravity, Hooke, conservation of momentum and energy, as well as the basic formulas of kinematics (equations of coordinates, velocity and displacement).
Strictly follow the order of studying theoretical material proposed in the recommendations for the Physics course.
When performing tasks in the Mechanics course, pay attention to the signs of the projection of vectors in the selected reference system. This standard error, which is admitted to high school students.
Don’t be lazy to draw diagrams (drawings) of problems - this can make solving the problem much easier for you.
Analyze the conditions of each specific task, compare the answers with the conditions and reality.
Don't invent your own problems using the original data!
Lesson plan on the topic “Uneven movement. Instant Speed"
date :
Subject: « »
Goals:
Educational : Provide and form a conscious assimilation of knowledge about uneven movement and instantaneous speed;
Developmental : Continue developing skills independent activity, group work skills.
Educational : Shape cognitive interest to new knowledge; develop behavioral discipline.
Lesson type: lesson in learning new knowledge
Equipment and sources of information:
Isachenkova, L. A. Physics: textbook. for 9th grade. public institutions avg. education with Russian language training / L. A. Isachenkova, G. V. Palchik, A. A. Sokolsky; edited by A. A. Sokolsky. Minsk: Narodnaya Asveta, 2015
Lesson structure:
Organizing time(5 minutes)
Updating basic knowledge (5 min)
Learning new material (14 min)
Physical education session (3 min)
Consolidation of knowledge (13min)
Lesson summary (5 min)
Organizing time
Hello, sit down! (Checking those present).Today in the lesson we must understand the concepts of uneven motion and instantaneous speed. And this means thatLesson topic : Uneven movement. Instantaneous speed
Updating of reference knowledge
We studied uniform linear motion. However, real bodies - cars, ships, airplanes, machine parts, etc. most often move neither rectilinearly nor uniformly. What are the patterns of such movements?
Learning new material
Let's look at an example. A car is moving along the section of road shown in Figure 68. On an ascent, the car’s movement slows down, and on a descent it accelerates. Car movementneither straight nor uniform. How to describe such a movement?
First of all, for this it is necessary to clarify the conceptspeed .
From 7th grade you know what average speed is. It is defined as the ratio of the path to the period of time during which this path is traveled:
(1 )
Let's call heraverage travel speed. She shows whatpath on average the body passed per unit of time.
In addition to the average travel speed, you must also enteraverage moving speed:
(2 )
What is the meaning of average moving speed? She shows whatmoving on average performed by the body per unit of time.
Comparing formula (2) with formula (1 ) from § 7, we can conclude:average speed< > equal to the speed of such uniform rectilinear motion, at which in a period of time Δ tthe body would move Δ r.
Average path speed and average moving speed - important characteristics any movement. The first of them is a scalar quantity, the second is a vector quantity. Because Δ r < s , then the module of the average speed of movement is not greater than the average speed of the path |<>| < <>.
Average speed characterizes movement over the entire period of time as a whole. It does not provide information about the speed of movement at each point of the trajectory (at each moment in time). For this purpose, it is introducedinstantaneous speed - speed of movement at a given time (or at a given point).
How to determine instantaneous speed?
Let's look at an example. Let the ball roll down an inclined chute from a point (Fig. 69). The figure shows the positions of the ball at different times.
We are interested in the instantaneous speed of the ball at the pointABOUT. Dividing the movement of the ball Δr 1 for the corresponding period of time Δ averagetravel speed<>= on the section Speed<>can be much different from the instantaneous speed at a pointABOUT. Consider a smaller displacement Δ =IN 2 . It will occur in a shorter period of time Δ. average speed<>= although not equal to the speed at the pointABOUT, but already closer to her than<>. With a further decrease in displacement (Δ,Δ , ...) and time intervals (Δ, Δ, ...) we will obtain average speeds that differ less and less from each otherAndfrom the instantaneous speed of the ball at a pointABOUT.
So that's enough exact value instantaneous speed can be found using the formula, provided that the time interval Δt very small:
(3)
Designation Δ t-» 0 reminds that the speed determined by formula (3), the closer to the instantaneous speed, the smallerΔt .
The instantaneous speed of curvilinear motion of a body is found in a similar way (Fig. 70).
What is the direction of the instantaneous speed? It is clear that in the first example the direction of the instantaneous velocity coincides with the direction of motion of the ball (see Fig. 69). And from the construction in Figure 70 it is clear that with curvilinear movementinstantaneous speed is directed tangentially to the trajectory at the point where the moving body is located at that moment.
Observe the hot particles coming off the grindstone (Fig. 71,A). The instantaneous speed of these particles at the moment of separation is directed tangentially to the circle along which they moved before separation. Similarly, the sports hammer (Fig. 71, b) begins its flight tangentially to the trajectory along which it moved when untwisted by the thrower.
Instantaneous speed is constant only when uniform straight motion. When moving along a curved path, its direction changes (explain why). With uneven movement, its module changes.
If the module of instantaneous speed increases, then the motion of the body is called accelerated , if it decreases - slow.
Give yourself examples of accelerated and decelerated movements of bodies.
IN general case When a body moves, both the instantaneous velocity module and its direction can change (as in the example with a car at the beginning of the paragraph) (see Fig. 68).
In what follows, we will simply call instantaneous speed speed.
Consolidation of knowledge
The speed of uneven movement on a section of the trajectory is characterized by average speed, and at a given point of the trajectory - by instantaneous speed.
Instantaneous speed is approximately equal to the average speed determined over a short period of time. The shorter this period of time, the smaller the difference between the average speed and the instantaneous speed.
Instantaneous speed is directed tangentially to the trajectory of motion.
If the module of instantaneous speed increases, then the movement of the body is called accelerated, if it decreases, it is called slow.
With uniform rectilinear motion, the instantaneous speed is the same at any point of the trajectory.
Lesson summary
So, let's summarize. What did you learn in class today?
Organization homework
§ 9, ex. 5 No. 1,2
Reflection.
Continue the phrases:
Today in class I learned...
It was interesting…
The knowledge I gained in the lesson will be useful
Key points:
Uneven movement is a movement with variable speed.
Instantaneous speed is vector physical quantity, equal to the limit of the ratio of the body's displacement to the period of time tending to zero.
If in arbitrary equal intervals of time a point traverses paths of different lengths, then the numerical value of its speed changes over time. This movement is called uneven. In this case, use a scalar quantity called average ground speed of uneven movement on this section of the trajectory. It is equal to the ratio of the distance traveled to the period of time during which this path was covered:
average speed with uneven movement - the ratio of the vector of movement of the body to the period of time during which this movement occurred.
To characterize changes in movement speed, the concept is introduced acceleration.
Medium acceleration uneven movement in the time interval from t to is called a vector quantity, equal to the ratio changes in speed to time interval:
Instant acceleration or acceleration material point at time t, there will be a limit of average acceleration:
Movement occurring with constant acceleration is called equally variable.
Equation of uniformly alternating motion: 
.
The acceleration vector is usually decomposed into two components: tangential and centripetal acceleration.
Tangential acceleration shows the speed of change in the velocity modulus, and normal acceleration characterizes the speed of change in the direction of speed during curvilinear motion.
Full acceleration of a body is the geometric sum of the tangential and normal components:
;
.
Control questions:
1. Define uneven motion.
2. What is called uniformly alternating motion?
3. Define instantaneous speed.
4. What is the direction of the instantaneous velocity vector?
5. Define instantaneous acceleration. In what units is it measured?
6. How are the tangential and centripetal acceleration directed relative to the curvature of the trajectory?
7. Define angular velocity. Its units of measurement.
Complete the tasks:
1. Write dependency formulas:
a) rotation speed versus period;
b) angular velocity versus period;
c) corner and linear speed;
d) angular velocity versus frequency;
e) centripetal acceleration versus speed;
e) linear speed versus rotational speed;
g) linear speed versus period.
Lesson plan on the topic " »
Date of:
Subject: Uneven (variable) movement. average speed
Goals:
Educational: formation of knowledge and ideas about uneven (variable) movement, as well as average speed;
Developmental: development and formation of practical skillsuse physical concepts and quantities to describe uniform linear motion;develop cognitive interest;
Educational: instill a culture of mental work, accuracy, teach to see the practical benefits of knowledge, continue the formation of communication skills, cultivate attentiveness and observation.
Lesson type: lesson in learning new knowledge
Equipment and sources of information:
Isachenkova, L. A. Physics: textbook. for 7th grade public institutions avg. education with Russian language training / L. A. Isachenkova, G. V. Palchik, A. A. Sokolsky; edited by A. A. Sokolsky. Minsk: Narodnaya Asveta, 2017.
Lesson structure:
Organizational moment (5 min)
Updating basic knowledge (5 min)
Learning new material (14 min)
Physical education minute (1 min)
Consolidation of knowledge (15 min)
Lesson summary (5 min)
Lesson content
Organizing time (checking those present in the class, checking the completion of homework, voicing the topic and main goals of the lesson)
Updating of reference knowledge
What does a path graph express?
For which motion the path graph is a straight line?
How to determine the distance traveled from the speed graph?
Learning new material
Analyze the movement of the bus. He slows down before stopping. Then, for a period of time, someone stands at a stop, i.e., his speed is zero, after which the speed increases. This means that the speed of the bus changes as it moves, i.e. it is a variable value.
Movement in which the speed changes is called uneven (variable).
Almost all movements observed in nature and technology are uneven.WITHFor example, people, birds (Fig. 103), dolphins (Fig. 104), trains, and falling objects move at varying speeds (Fig. 105). But how then to characterize this movement?
Uneven movement is characterized by average speed. How to determine average speed? Let's look at an example. You are going on an excursion to Brest by train. The train runs from Minsk to Brests= 330 km. It takes time to travel this patht = 4.5 hours. During this time, the train stands at the stations, moving either with increasing or decreasing speed.
Let's denote the average speed( v ) and write the formula:
Then the Minsk - Brest train moves at average speed
Weren't you surprised that we used the uniform motion formula? Yes indeed,formally we found the average speed as if the train was traveling all the ways= 330 km moved uniformly at constant speedv = 73 This, of course, does not mean that he actually moved evenly. On certain sections of the route, the speed of the train was significantly
greater(120 , and less than 73, and even equal to zero (Fig. 106).
Average speed gives only an approximate idea of how fast a body is moving. The description of variable motion is more complex than the description of uniform motion.
For example, if the speed of a train in the acceleration section increases from 0 to 90, then various points the trajectory she takes different meanings from this gap. Thus, we can talk not only about the average speed on a given section of the trajectory, but also about the speed at a given point on the trajectory. This speed is called in physicsinstantaneous speed.
Let's look at an example of solving the problem from page 66
Physical education minute
Consolidation of knowledge
Now let’s work with cards on the topic “Uneven (variable) movement. Average speed" (Appendix 1)
Fill the table.
Answer:
Movement during which the speed changes is called uneven (variable).The average speed is found by dividing the entire path by the entire period of time during which this path was covered.
Answer: With uniform motion, a body travels an equal distance in equal time, but with uneven motion, it covers a different distance.
Answer: according to the formula
Answer: “total” is the entire path that the body has traveled, “entire” is the entire time during which this path has been traveled
An apple fell from a heighth= 2.2 m over timet
Answer:
Answer: First, the motorcyclist accelerated to a speed of 6 m/s in 3 seconds, then rode for 6 seconds at a constant speed of 6 m/s, and then began to brake and stopped after 3.5 seconds.
Lesson summary
So, let's summarize:
The characteristic of uneven movement is the average speed.
To calculate the average speed, you need to divide the path by the entire period of time spent traveling this path.
Homework organization
§18, reply to Control questions.
Solve a problem:
Determine your average speed from home to school. Evaluate the result.
Reflection
Continue the phrases:
Today in class I learned...
It was interesting…
The knowledge I gained in class will come in handy.
Annex 1
Card on the topic “Uneven (variable) movement. Average speed"
Complete tasks and solve problems
Fill out the table, answer test questions orally, solve problems.
How does uneven motion of a body differ from uniform motion?
How to find the average speed of uneven motion?
What is the physical meaning of the words “total” and “entire” in the definition of average speed
An apple fell from a heighth= 2.2 m over timet= 0.67 s. Find the average speed of the apple falling.
Based on the graph data (see figure), describe the movement of the motorcyclist.
Fill the table.
