Uniformly accelerated rectilinear motion. Graphs of the dependence of kinematic quantities on time in uniformly accelerated motion. Variable movement. Average speed. Acceleration. Units of measurement of acceleration all bodies are made up of particles: atoms, molecules and ions
(topic " Font and paragraph formatting»)Text 1
Newton's second law
Body mass
Strength
Newton's second law
Text 2
Newton's second law
The properties of a body, on which its acceleration depends when interacting with other bodies, is called inertia.
A quantitative measure of the inertia of the body is the mass of the body. Body mass is a physical quantity that characterizes inertia.
With uneven translational motion, the speed of the body changes over time. The process of changing the speed of a body is characterized by acceleration.
For a quantitative expression of the action of one body on another, the concept of "force" is introduced. Strength is a vector quantity, i.e. characterized by direction. To quantitatively characterize the process of body movement, the concept of speed of movement is introduced. Velocity is expressed in meters per second.
The relationship between the force and acceleration of the body is established Newton's second law. The force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force.
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Rice. 4
The coordinate system, the reference body with which it is associated, and the indication of the origin of the time reference form the reference frame, relative to which the motion of the body is considered.
The trajectory of the movement of the body, the distance traveled and the displacement depend on the choice of the frame of reference. In other words, mechanical motion is relative.
Speed. To quantitatively characterize the process of body movement, the concept of speed of movement is introduced.
The instantaneous speed of the translational motion of a body at a point in time is the ratio of a very small displacement to a small time interval during which this displacement occurred:
Instantaneous speed is a vector quantity.
With a successive decrease in the duration of the time interval, the direction of the displacement vector approaches the tangent at the point A the trajectory of motion through which the body passes at the moment of time (Fig. 5). Therefore, the velocity vector lies on the tangent to the trajectory of the body at the point A and directed in the direction of body movement.
Rice. five
Formula (1.1) allows you to set the unit of speed.
In the International System (SI), the unit of distance is the meter, the unit of time is the second; so the speed is expressed in meters per second:
A meter per second is equal to the speed of a rectilinearly and uniformly moving point, at which the point moves a distance of 1 m in a time of 1 s.
Uniform rectilinear motion. Movement with a constant modulo and direction speed is called uniform rectilinear motion. In uniform rectilinear motion, the body moves in a straight line and for any equal intervals of time covers the same path.
Let us find out how the velocities of the body in different frames of reference are related to each other. Let's consider such an example. The car moves along a straight section of the railway track uniformly at a speed relative to the Earth. The passenger moves relative to the car with the speed , the speed vectors and have the same direction. Find the speed of the passenger relative to the Earth. The movement of a passenger relative to the Earth in a short period of time is equal to the sum of the movements of the car relative to the Earth and the passenger relative to the car during this period of time (Fig. 6):
or 
.
Rice. 6
Hence the speed of the passenger relative to the Earth is
We have obtained that the speed of the passenger in the frame of reference associated with the Earth is equal to the sum of the velocities of the passenger in the frame of reference associated with the car and the car relative to the Earth.
This conclusion is valid for any direction of the velocity and velocity vectors. The law expressed by formula (1.2) is called the classical law of addition of velocities.
The movement of any body in real conditions is never strictly uniform and rectilinear. A motion in which a body makes unequal movements in equal intervals of time is called non-uniform motion.
Acceleration. With uneven translational motion, the speed of the body changes over time. The process of changing the speed of a body is characterized by acceleration. Acceleration is a vector quantity equal to the ratio of a very small change in the velocity vector to a small period of time for which this change occurred.
Job #9
Development of a hypertext document
Option 1
Using the snippets below, develop a hypertext document on Newton's Second Law, identifying key words and establishing links between the snippets.
Fragment 1. The property of a body on which its acceleration depends when interacting with other bodies is called inertia.
Fragment 2. A quantitative measure of the inertia of the body is the mass of the body. Body mass is a physical quantity that characterizes inertia.
Fragment 3. With uneven translational motion, the speed of the body changes over time. The process of changing the speed of a body is characterized by acceleration.
Fragment 4. For a quantitative expression of the action of one body on another, the concept of "force" is introduced. Force is a vector quantity, that is, it is characterized by direction. The unit of force is the force that imparts an acceleration of 1 m/s to a body with a mass of 1 kg.
Fragment 5. To quantitatively characterize the process of body movement, the concept of speed of movement is introduced. Velocity is expressed in meters per second.
Fragment 6. The relationship between force and acceleration of a body is established by Newton's second law. The force acting on a body is equal to the product of the mass of the body and the acceleration imparted by this force.
Option 2
Using the fragments below, develop a hypertext document on the topic "Musical scale", arranging the fragments from simpler to more complex concepts, identifying keywords and establishing links between fragments:
Fragment 1. Musical sound is distinguished by the following properties: height, strength, duration and timbre. The pitch of the sound depends on the vibration frequency of the elastic body; strength (loudness) - from the breadth of the range of oscillations; duration - on how long the elastic body is excited; timbre is a kind of coloring of sounds.
Fragment 2. All musical sounds, if they are arranged in height from the lowest to the highest, form a musical scale. Each sound of the musical scale corresponds to sounds similar in sound, but different in height. They are called octaves, and the group of sounds between them is called an octave.
Fragment 3. Sound is a phenomenon that occurs as a result of the rapid vibration of an elastic body and is perceived by the organ of hearing - the ear.
Fragment 4. The entire scale is divided into nine octaves: seven complete and two incomplete. Names of octaves in order of their location: subcontroctave, counteroctave, large octave, small octave, first octave, second octave, third octave, fourth octave, fifth octave.
Fragment 5. A full octave contains twelve sounds of different pitches. Of these, only seven main ones have independent names: do, re, mi, fa, salt, la, si.
Fragment 6. The shortest distance between two adjacent sounds is called a semitone. Two semitones make up a whole tone. The distance between the sounds do-re, re-mi, fa-sol, la-si is equal to a whole tone, and between the sounds mi-fa and si-do - a semitone.
Option 3
Develop a testing hypertext document on the topic "Battle of Poltava". Questions should be displayed on the screen and options for answers should be offered. In case of a correct answer, display the corresponding fragment of text with a message, and in case of an incorrect answer, display the correct answer, after which - return to the current question. Organize the connection between the fragments by highlighting the keywords by which the transition from fragment to fragment will be made.
Fragment 1. Which armies participated in the Battle of Poltava?
1. Russia and France 2. Russia and Poland 3. Sweden and Russia
Fragment 2. In what year did the Battle of Poltava take place?
Fragment 3. Who was at the head of the Swedish army?
Fragment 4. What was the size of the Russian army?
1. 20 000 2. 32 000 3. 56 000
Fragment 5. The answer is correct.
Return to question: 1 2 3 4
Fragment 6. The armies of Russia and Sweden participated in the Battle of Poltava.
Fragment 7. The Battle of Poltava took place in 1709.
Fragment 8. King Charles XII was at the head of the Swedish army.
Fragment 9. The number of the Russian army was 32,000 people.
Purpose of the test
The methodology is designed to assessknowledge , under the section "Mechanics". The material is intended forstudents first year SPO.
Instructions for the test
Exactly given to complete the test60 min. Don't stay too long on one task. Perhaps you are on the wrong track and it is better to move on to the next task. But don't give up too easily either; most of the tasks can be solved if you - show a little perseverance. The answer to the task consists of choosing the correct answer in your opinion. Sometimes you need to make a choice from several possibilities. Write your answer in the space provided. If you are unable to solve the problem - do not write the answer at random. The test does not contain "tricky" tasks, but you always have to consider several solutions. Before proceeding with the decision, make sure that you correctly understand what is required of you. You will be wasting your time if you take on a decision without understanding what the problem is.
Registration of works
You need to write down the answers to the test in your notebook for verification work in the form:
1 a
2 a, b
MECHANICAL TASKS
a) moving
b) trajectory
c) line of motion
a) coordinate system
b) reference body
c) clock
d) moving a point
a) moving
b) travel time
c) distance traveled
b) He is small.
5. The clock system does:
a) rotation
b) forward movement
c) rectilinear motion
a) 11 m/s
b) 9 m/s
c) 1 m/s
a) movement.
b) instantaneous speed
c) body coordinates
d) acceleration
a) constant in direction
b) constant modulo
a) -2 m/s
b) 2 m/s
c) 50 m/s
a) kinematics
b) dynamics
c) static
a) momentum
b) inertia
c) uniformly accelerated movement
but ) Newton's first law
b) Newton's second law
c) Newton's third law
a) internal structure
b) features of the external environment
a) fly
b) man
c) trolleybus
a) moving
b) acceleration
c) application of force
a) 0.5 m/s2
b) 200 m/s2
c) 2 m/s2
a) -20 N
b) 0 N
c) 40 N
19. The gravitational constant G is:
a) 6.67x10
b) 6.67x10
c) 9.8
a) force of elasticity
b) gravity
c) body weight
a) overload
b) weightlessness
c) free fall
a) gravity
b) body weight
c) elastic force
a) gravity
b) the force of elasticity
c) body weight
d) equal to gravity
a) 1 m/s
b) 2 m/s
c) 0 m/s
a) with the ground
b) with vacuum
27. The work done by the force F is positive if the angle between the vector F and S:
but)
b)
in)
a) 3 s
b) 40 s
c) 160 s
a) 50 J
b) 200J
c) 2000J
a) 10 J
b) 100 J
c) 1000 J
a) kinetic energy
b) potential energy
c) mechanical work
a) 2000 J
b) 10000 J
c) -2000 J
a) 0.5 m/s
b) 1.5 m/s
c) 2 m/s
a) 0.5 J
b) 2 J
c) 5000 J
a) 0.4 N
b) 2.5 N
c) 10 N
a) 98 kg
b) 100 kg
c) 9800 kg
but ) 0.1 m/s
b) 10 m/s
c) 90 m/s
a) 0 m
b) 2.5 m
c) 5 m
39. The equation for determining the coordinates of a material point has the form Use it to determine the acceleration.
a) -3 m/s2
b) 4 m/s2
c) 8 m/s2
a) uniform
b) uniformly accelerated
c) equally slow
Key to the test
1. The line along which the point of the body moves is called-
a) moving
b) trajectory
c) line of motion
2. What constitutes a reporting system.
a) coordinate system
b) reference body
c) clock
d) moving a point
3. What does a taxi passenger pay for:
a) moving
b) travel time
c) distance traveled
4. The cyclist rides on the road. In which case can it be considered as a material point:
a) He moves non-stop for 60 meters.
b) He is small.
c) He travels a distance of 60 km.
5. The clock system does:
a) rotation
b) forward movement
c) rectilinear movement
6. The train travels at a speed. The passenger goes against the movement of the train at a speed of 1 m / s, relative to the car. Determine the speed of the passenger relative to the ground.
a) 11 m/s
b) 9 m/s
c) 1 m/s
7. The process of changing the speed of the body is characterized by:
a) movement.
b) instantaneous speed
c) body coordinates
d) acceleration
8. Uniformly accelerated is the movement with acceleration:
a) constant in direction
b) constant modulo
c) constant in direction and modulus
9. Vehicle speed changes from 20m/s to 10m/s in 5 seconds. Determine the acceleration of the car.
a) -2 m/s
b) 2 m/s
c) 50 m/s
10. Using the equation x \u003d x, you can determine:
a) moving with uniform acceleration
b) coordinates of the body with uniform motion
c) coordinates of the body during uniformly accelerated motion
11. The section of mechanics that studies the laws of interaction of bodies is called:
a) kinematics
b) dynamics
c) static
12. The phenomenon of maintaining the speed of a body in the absence of external influences is called:
a) momentum
b) inertia
c) uniformly accelerated movement
13. Which of Newton's laws has the following formulation: there are such reporting systems, relative to which a progressively moving body keeps its speed constant if no other bodies act on them, or their actions are compensated.
a) Newton's first law
b) Newton's second law
c) Newton's third law
14. The reason for the change in the speed of movement of the body is:
a) internal structure
b) features of the external environment
c) interaction with other bodies
15. Which body is more inert:
a) fly
b) man
c) trolleybus
a) moving
b) acceleration
c) application of force
17. On a body weighing 10 kg. a force of 20N is applied. Determine how fast the body is moving.
a) 0.5 m/s2
b) 200 m/s2
c) 2 m/s2
18. The weight acts on the scales with a force of 20 N. With what force do the scales act on the weight.
a) -20H
b) 0 N
c) 40 N
19. Gravitational constantGis equal to:
a) 6.67x10
b) 6.67x10
c) 9.8
20. The force with which the body acts on a horizontal support or vertical suspension is called:
a) force of elasticity
b) gravity
c) body weight
21. The disappearance of the weight during the movement of the support with the acceleration of free fall is called:
a) overload
b) weightlessness
c) free fall
22. Using this formula, you can determine:
a) gravity
b) body weight
c) elastic force
23. The force resulting from deformation and directed in the direction opposite to the movement of body particles during deformation is called:
a) gravity
b) the force of elasticity
c) body weight
24. Choose all the correct answers. Friction force:
a) is equal in absolute value to the external force
b) directed in the direction of movement of the body.
c) is directed in the opposite direction of movement
d) equal to gravity
25. Two trolleys weighing 200 kg each. moving towards each other at a speed of 1m/s. With what speed will they move after an inelastic impact.
a) 1 m/s
b) 2 m/s
c) 0m/s
26. What does a jet rocket interact with when moving:
a) with the ground
b) with vacuum
c) with gases formed during combustion.
27. Work done by forceF, is positive if the angle between the vectorFAndS:
but)
b)
in)
28. A crane with a power of 2 kW., did the work of 0.08 MJ. How long was the work done?
a) 3 s
b) 40from
c) 160 s
29. Determine the potential energy of a person weighing 100 kg, at a height of 2 meters
a) 50 J
b) 200J
c) 2000J
30. Determine the kinetic energy of a bullet with a mass of 2 grams flying at a speed of 100 m / s.
a) 10 J
b) 100 J
c) 1000 J
31. The formula allows you to determine:
a) kinetic energy
b) potential energy
c) mechanical work
32. The kinetic energy of the body has changed from 4000J to 6000J. Define body work:
a) 2000 J
b) 10000 J
c) -2000 J
33. A railway car weighing 15 tons moves at a speed of 2 m / s, catches up with a stationary car weighing 5 tons. What will be the speed of the cars after their collision?
a) 0.5 m/s
b) 1.5m/s
c) 2 m/s
34. A sleigh moving uniformly under the action of a force of 50 N has moved 100 meters. What work do they do with it?
a) 0.5 J
b) 2 J
c) 5000 J
35. Determine the force under which a body of mass 5 kg. Acquires an acceleration of 2m/s?
a) 0.4 N
b) 2.5 N
c) 10 N
36. Determine the mass of the body if the force of gravity is 980 N.
a) 98 kg
b) 100kg
c) 9800 kg
37. A car, moving evenly, traveled 30 meters in 3 seconds. Determine its speed.
a) 0.1 m/s
b) 10m/s
c) 90 m/s
38. A boy threw the ball to a height of 2.5 m and caught it again. Determine the movement of the ball.
a) 0 m
b) 2.5 m
c) 5 m
39. The equation for determining the coordinates of a material point has the form. Use it to determine the acceleration.
a) -3 m/s2
b) 4 m/s2
c) 8 m/s2
40. The projection of the speed of a moving body changes according to the law. Describe the nature of the movement:
a) uniform
b) uniformly accelerated
c) equally slow
The movement of any body in real conditions is never strictly uniform and rectilinear. With uneven translational motion, the speed of the body changes over time. The process of changing the speed of a body is characterized by acceleration.
Acceleration - this is the value that determines the rate of change in the speed of the body, and is equal to the limit to which the change in speed tends with an infinite decrease in the time interval Δt:
Uniform motion can be uniformly accelerated or uniformly slowed down.
Uniformly accelerated motion - this is the movement of a body (material point) with a positive acceleration, that is, with such a movement, the body accelerates with a constant acceleration. In the case of uniformly accelerated motion, for any equal time intervals, the speed increases by the same amount and the direction of acceleration coincides with the direction of the speed of motion.
∆ And but> 0
Uniformly slow motion - this is the movement of a body (material point) with negative acceleration, that is, with such a movement, the body slows down uniformly. With uniformly slow motion, the velocity and acceleration vectors are opposite, and the velocity modulus decreases with time.
¯ ∆ and but 0
In mechanics, any rectilinear motion is accelerated, so slow motion differs from accelerated motion only by the sign of the projection of the acceleration vector onto the selected axis of the coordinate system.
Acceleration is measured in meters per second squared.
With uniformly accelerated movement with an initial speed of 0, the acceleration is .
where is the speed at time t, then the speed of uniformly variable motion is equal to
0 + t or υ = ±υ 0 ± a t(3.3)
The distance traveled during rectilinear uniformly accelerated motion is equal to the displacement modulus and is determined by the formula:
where the plus sign refers to accelerated motion and the minus sign refers to slow motion.
If the time of motion of the body is unknown, another displacement formula can be used:
where υ is the final speed of movement;
υ 0 - initial speed
The coordinates of the body during uniformly accelerated motion at any time can be determined by the formulas:
where x 0; y 0 – initial body coordinates; υ 0 - the speed of the body at the initial moment of time; but- acceleration of movement. The sign "+" and "-" depend on the direction of the OX axis and the direction of the vectors and .
Projection displacement
on the OX axis is: S x \u003d x-x 0
on the y axis is: S y \u003d y-y 0
Graph of body displacement versus time for
υ 0 = 0 is shown in fig. 1.9.
The speed of the body at a given time t 1 is equal to the tangent of the slope between the tangent to the graph and the time axis υ=tgα.
The graph of the x(t) coordinate is also a parabola (as is the displacement graph), but the vertex of the parabola generally does not coincide with the origin. At
but < 0 и х 0 = 0 ветви параболы направлены вниз (рис. 1.10).
Velocity versus time is a linear function whose graph is a straight line
(Fig. 1.11). The tangent of the slope of the straight line to the time axis is numerically equal to the acceleration.
In this case, the displacement is numerically equal to the area of \u200b\u200bthe figure 0abc (Fig. 1.11). The area of a trapezoid is half the sum of the lengths of its bases times the height. The bases of the trapezoid 0abc are numerically equal: 0a = υ 0 bc = υ.