Which movement is uniform or uneven? School encyclopedia

Characteristics mechanical movement body:

- trajectory (the line along which the body moves),

- displacement (directed straight line segment connecting the initial position of the body M1 with its subsequent position M2),

- speed (ratio of movement to movement time - for uniform movement) .

Main types of mechanical movement

Depending on the trajectory, body movement is divided into:

Straight-line;

Curvilinear.

Depending on the speed, movements are divided into:

Uniform,

Uniformly accelerated

Equally slow

Depending on the method of movement, movements are:

Progressive

Rotational

Oscillatory

Complex movements (For example: a screw movement in which the body rotates uniformly around a certain axis and at the same time makes a uniform translational movement along this axis)

Forward movement - This is the movement of a body in which all its points move equally. In translational motion, any straight line connecting any two points of the body remains parallel to itself.

Rotational motion is the movement of a body around a certain axis. With such a movement, all points of the body move in circles, the center of which is this axis.

Oscillatory motion is a periodic motion that occurs alternately in two opposite directions.

For example, oscillatory motion makes a pendulum in a clock.

Translational and rotational movements are the most simple types mechanical movement.

Straight and uniform movement is called such a movement when, for any arbitrarily small equal intervals of time, the body makes identical movements . Let us write down the mathematical expression of this definition s = v? t. This means that the displacement is determined by the formula, and the coordinate - by the formula .

Uniformly accelerated motion is the movement of a body in which its speed increases equally over any equal intervals of time . To characterize this movement, you need to know the speed of the body in at the moment time or at a given point of the trajectory, t . e . instantaneous speed and acceleration .

Instantaneous speed- this is the ratio of a sufficiently small movement on the section of the trajectory adjacent to this point to the small period of time during which this movement occurs .

υ = S/t. The SI unit is m/s.

Acceleration is a quantity equal to the ratio of the change in speed to the period of time during which this change occurred . α = ?υ/t(SI system m/s2) Otherwise, acceleration is the rate of change of speed or the increase in speed for each second α. t. Hence the formula for instantaneous speed: υ = υ 0 + α.t.

The displacement during this movement is determined by the formula: S = υ 0 t + α . t 2 /2.

Equally slow motion motion is called when the acceleration is negative and the speed uniformly slows down.

At uniform motion circumferentially the angles of rotation of the radius for any equal periods of time will be the same . Therefore the angular speed ω = 2πn, or ω = πN/30 ≈ 0.1N, Where ω - angular speed n - number of revolutions per second, N - number of revolutions per minute. ω in the SI system it is measured in rad/s . (1/c)/ It represents the angular velocity at which each point of the body in one second travels a path equal to its distance from the axis of rotation. During this movement, the velocity module is constant, it is directed tangentially to the trajectory and constantly changes direction (see . rice . ), therefore centripetal acceleration occurs .

Rotation period T = 1/n - it's time , during which the body makes one full revolution, therefore ω = 2π/T.

Linear speed during rotational motion is expressed by the formulas:

υ = ωr, υ = 2πrn, υ = 2πr/T, where r is the distance of the point from the axis of rotation. The linear speed of points lying on the circumference of a shaft or pulley is called the peripheral speed of the shaft or pulley (in SI m/s)

With uniform motion in a circle, the speed remains constant in magnitude but changes in direction all the time. Any change in speed is associated with acceleration. Acceleration that changes speed in direction is called normal or centripetal, this acceleration is perpendicular to the trajectory and directed to the center of its curvature (to the center of the circle, if the trajectory is a circle)

α p = υ 2 /R or α p = ω 2 R(because υ = ωR Where R circle radius , υ - point movement speed)

Relativity of mechanical motion- this is the dependence of the trajectory of the body, the distance traveled, movement and speed on the choice reference systems.

The position of a body (point) in space can be determined relative to some other body chosen as the reference body A . The reference body, the coordinate system associated with it, and the clock constitute the reference system . The characteristics of mechanical movement are relative, t . e . they can be different in different reference systems .

Example: the movement of a boat is monitored by two observers: one on the shore at point O, the other on the raft at point O1 (see . rice . ). Let us mentally draw through the point O the XOY coordinate system - this is a fixed reference system . We will connect another X"O"Y" system to the raft - this is a moving coordinate system . Relative to the X"O"Y" system (raft), the boat moves in time t and will move at speed υ = s boats relative to raft /t v = (s boats- s raft )/t. Relative to the XOY (shore) system, the boat will move during the same time s boats where s boatsmoving the raft relative to the shore . Speed of the boat relative to the shore or . The speed of a body relative to a fixed coordinate system is equal to the geometric sum of the speed of the body relative to a moving system and the speed of this system relative to a fixed one .

Types of reference systems can be different, for example, a fixed reference system, a moving reference system, an inertial reference system, a non-inertial reference system.

In grade 7, you studied the mechanical motion of bodies occurring at a constant speed, i.e. uniform motion.

We now move on to consider uneven motion. Of all the types of non-uniform motion, we will study the simplest - rectilinear uniformly accelerated, in which the body moves along a straight line, and the projection of the body's velocity vector changes equally over any equal periods of time (in this case, the magnitude of the velocity vector can either increase or decrease).

For example, if the speed of an airplane moving along the runway increases by 15 m/s in any 10 s, by 7.5 m/s in any 5 s, by 1.5 m/s in every second, etc., then the plane moves with uniform acceleration.

In this case, the speed of an aircraft means its so-called instantaneous speed, i.e. the speed at each specific point of the trajectory at the corresponding moment in time (a more rigorous definition of instantaneous speed will be given in a high school physics course).

The instantaneous speed of bodies moving uniformly accelerated can change in different ways: in some cases faster, in others slower. For example, the speed of a normal passenger elevator Average power increases by 0.4 m/s for each second of acceleration, and speed power increases by 1.2 m/s. In such cases, they say that bodies move with different accelerations.

Let's consider what physical quantity called acceleration.

Let the speed of some body moving uniformly accelerated change from v 0 to v over a period of time t. By v 0 we mean the initial speed of the body, i.e. the speed at the moment t 0 = O, taken as the beginning of time. And v is the speed that the body had at the end of the time period t, counted from t 0 = 0. Then for each unit of time the speed changed by an amount equal to

This ratio is denoted by the symbol a and is called acceleration:

The acceleration of a body during rectilinear uniformly accelerated motion is a vector physical quantity equal to the ratio of the change in speed to the period of time during which this change occurred

Uniformly accelerated motion is motion with constant acceleration.

Acceleration is a vector quantity that is characterized not only by its magnitude, but also by its direction.

The magnitude of the acceleration vector shows how much the magnitude of the velocity vector changes in each unit of time. The greater the acceleration, the faster the speed of the body changes.

The SI unit of acceleration is the acceleration of such uniformly accelerated motion, in which the speed of the body changes by 1 m/s in 1 s:

Thus, the SI unit of acceleration is meter per second squared (m/s2).

Other units of acceleration are also used, for example 1 cm/s 2 .

You can calculate the acceleration of a body moving rectilinearly and uniformly accelerated using the following equation, which includes projections of the acceleration and velocity vectors:

Let us show with specific examples how acceleration is found. Figure 8, a shows a sled that is rolling down a mountain with uniform acceleration.

Rice. 8. Uniformly accelerated motion of a sled rolling down a mountain (AB) and continuing to move along the plain (CD)

It is known that the sled covered part of the path AB in 4 s. Moreover, at point A they had a speed of 0.4 m/s, and at point B they had a speed of 2 m/s (the sled is taken as a material point).

Let us determine with what acceleration the sled moved in section AB.

In this case, the beginning of the time count should be taken as the moment the sled passes point A, since according to the condition, it is from this moment that the period of time during which the magnitude of the velocity vector changed from 0.4 to 2 m/s is counted.

Now let’s draw the X axis parallel to the sled’s speed vector and directed in the same direction. Let us project the beginnings and ends of the vectors v 0 and v onto it. The resulting segments v 0x and v x are projections of the vectors v 0 and v onto the X axis. Both of these projections are positive and equal to the modules of the corresponding vectors: v 0x = 0.4 m/s, v x = 2 m/s.

Let's write down the conditions of the problem and solve it.

The projection of the acceleration vector onto the X axis turned out to be positive, which means that the acceleration vector is aligned with the X axis and with the speed of the sled.

If the velocity and acceleration vectors are directed in the same direction, then the speed increases.

Now let's consider another example, in which a sled, having rolled down a mountain, moves along a horizontal section CD (Fig. 8, b).

As a result of the friction force acting on the sled, its speed continuously decreases, and at point D the sled stops, i.e., its speed is zero. It is known that at point C the sled had a speed of 1.2 m/s, and they covered section CD in 6 s.

Let's calculate the acceleration of the sled in this case, i.e., determine how much the speed of the sled changed for each unit of time.

Let's draw the X axis parallel to the segment CD and align it with the speed of the sled, as shown in the figure. In this case, the projection of the sled's velocity vector onto the X axis at any moment of their movement will be positive and equal to the magnitude of the velocity vector. In particular, at t 0 = 0 v 0x = 1.2 m/s, and at t = 6 s v x = 0.

Let's record the data and calculate the acceleration.

The acceleration projection onto the X axis is negative. This means that the acceleration vector a is directed opposite to the X axis and, accordingly, opposite to the speed of movement. At the same time, the speed of the sled decreased.

Thus, if the velocity and acceleration vectors of a moving body are directed in one direction, then the magnitude of the body’s velocity vector increases, and if in the opposite direction, it decreases.

Questions

What type of motion - uniform or non-uniform - does rectilinear uniformly accelerated motion belong to?
What is meant by instantaneous speed of uneven motion?
Give the definition of acceleration of uniformly accelerated motion. What is the unit of acceleration?
What is uniformly accelerated motion?
What does the magnitude of the acceleration vector show?
Under what condition does the magnitude of the velocity vector of a moving body increase; is it decreasing?

Exercise 5

Human movement is mechanical, that is, it is a change in the body or its parts relative to other bodies. Relative movement is described by kinematics.

Kinematics – a branch of mechanics in which mechanical motion is studied, but the causes of this motion are not considered. The description of the movement of both the human body (its parts) in various sports and various sports equipment is an integral part of sports biomechanics and in particular kinematics.

Whatever material object or phenomenon we consider, it turns out that nothing exists outside of space and outside of time. Any object has spatial dimensions and shape, and is located in some place in space in relation to another object. Any process in which material objects participate has a beginning and an end in time, how long it lasts in time, and can occur earlier or later than another process. This is precisely why there is a need to measure spatial and temporal extent.

Basic units of measurement of kinematic characteristics in international system SI measurements.

Space. One forty-millionth of the length of the earth's meridian passing through Paris was called a meter. Therefore, length is measured in meters (m) and its multiple units: kilometers (km), centimeters (cm), etc.

Time– one of the fundamental concepts. We can say that this is what separates two successive events. One way to measure time is to use any regularly repeated process. One eighty-six thousandth of an earthly day was chosen as a unit of time and was called the second (s) and its multiple units (minutes, hours, etc.).

In sports, special time characteristics are used:

moment in time(t)- this is a temporary measure of the position of a material point, links of a body or system of bodies. Moments of time indicate the beginning and end of a movement or any part or phase of it.

Movement duration(∆t) – this is its temporary measure, which is measured by the difference between the moments of the end and the beginning of movement∆t = tcon. – tbeg.

Movement speed(N) – it is a temporal measure of the repetition of movements repeated per unit of time. N = 1/∆t; (1/s) or (cycle/s).

Rhythm of movements – this is a temporary measure of the relationship between parts (phases) of movements. It is determined by the ratio of the duration of the parts of the movement.

The position of a body in space is determined relative to a certain reference system, which includes a reference body (that is, relative to which the movement is considered) and a coordinate system necessary to describe at a qualitative level the position of the body in one or another part of space.

The beginning and direction of measurement are associated with the reference body. For example, in a number of competitions, the origin of coordinates can be chosen as the starting position. Various competitive distances in all cyclic sports are already calculated from it. Thus, in the selected “start-finish” coordinate system, the distance in space that the athlete will move when moving is determined. Any intermediate position of the athlete’s body during movement is characterized by the current coordinate within the selected distance interval.

For precise definition of a sports result, the rules of the competition stipulate at what point (reference point) the counting is carried out: at the toe of a skater’s skate, at the protruding point of a sprinter’s chest, or at the back edge of the footprint of a landing long jumper.

In some cases, to accurately describe the movement of the laws of biomechanics, the concept of a material point is introduced.

Material point – this body, size and internal structure which in these conditions can be neglected.

The movement of bodies can be different in nature and intensity. To characterize these differences, a number of terms are introduced in kinematics, presented below.

Trajectory – a line described in space by a moving point of a body. When biomechanical analysis of movements, first of all, the trajectories of movements of characteristic points of a person are considered. As a rule, such points are the joints of the body. Based on the type of movement trajectories, they are divided into rectilinear (straight line) and curvilinear (any line other than a straight line).

Moving – is the vector difference between the final and initial position of the body. Therefore, displacement characterizes the final result of the movement.

Path – this is the length of the trajectory section traversed by a body or a point of the body during a selected period of time.

In order to characterize how quickly the position of a moving body changes in space, the special concept of speed is used.

Speed – This is the ratio of the distance traveled to the time it takes to complete it. It shows how quickly the position of a body in space changes. Since velocity is a vector, it also indicates in which direction the body or point on the body is moving.

Medium speed of a body on a given section of the trajectory is called the ratio of the distance traveled to the time of movement, m/s:

If the average speed is the same in all parts of the trajectory, then the movement is called uniform.

The issue of running speed is important in sports biomechanics. It is known that the speed of running over a certain distance depends on the magnitude of this distance. The runner can support maximum speed only for a limited time (3-4 seconds, highly skilled sprinters up to 5 - 6 seconds). Average speed stayers are much lower than sprinters. Below is the dependence of the average speed (V) on the length of the distance (S).

World sports records and the average speed shown in them

Type of competition and distance	Men		Women
Type of competition and distance		Average speed m/s	Time shown on the course	Average speed m/s
Running
100 m	9.83 s	10,16	10.49 s	9,53
400 m	43.29 s	9,24	47.60 s	8,40
1500 m	3 min 29.46 s	7,16	3 min 52.47 s	6,46
5000 m	12 min 58.39 s	6,42	14 min 37.33 s	5,70
10000 m	27 min 13.81 s	6,12	30 min 13.75 s	5,51
Marathon (42 km 195 m)	2 h 6 min 50 s	5,5	2 hours 21 minutes 0.6 s	5,0
Ice skating
500 m	36.45 s	13,72	39.10 s	12,78
1500 m	1 min 52.06 s	13,39	1 min 59.30 s	12,57
5000 m	6 min 43.59 s	12,38	7 min 14.13 s	11,35
10000 m	13 min 48.20 s	12,07

100 m (freestyle)	48.74 s	2,05	54.79 s	1,83
200 m (v/s)	1 min 47.25 s	1,86	1 min 57.79 s	1,70
400 m (v/s)	3 min 46.95 s	1,76	4 min 3.85 s	1,64

For convenience of calculations, the average speed can also be written through a change in the coordinates of the body. When moving in a straight line, the distance traveled is equal to the difference between the coordinates of the end and start points. So, if at time t0 the body was at a point with coordinate X0, and at time t1 - at a point with coordinate X1, then the distance traveled ∆Х = X1 - X0, and the time of movement ∆t = t1 - t0 (the symbol ∆ denotes difference of values of the same type or to designate very small intervals). In this case:

The dimension of speed in SI is m/s. When covering long distances, speed is determined in km/h. If necessary, such values can be converted to SI. For example, 54 km/h = 54000 m/3600 s = 15 m/s.

Average speeds on different sections of the path differ significantly even with a relatively uniform distance: starting acceleration, covering a distance with intra-cycle speed fluctuations (during take-off the speed increases, during free gliding in skating or the flight phase in speed skating it decreases) , finishing. As the interval over which the speed is calculated decreases, the speed at a given point on the trajectory can be determined, which is called instantaneous speed.

Or the speed at a given point of the trajectory is the limit to which the movement of a body in the vicinity of this point tends in time with an unlimited decrease in the interval:

Instantaneous speed is a vector quantity.

If the magnitude of the velocity (or the magnitude of the velocity vector) does not change, the movement is uniform; when the magnitude of the velocity changes, it is uneven.

Uniform called movement in which a body travels the same paths over any equal intervals of time. In this case, the magnitude of the speed remains unchanged (in the direction the speed can change if the movement is curvilinear).

Straightforward called movement in which the trajectory is a straight line. In this case, the direction of the speed remains unchanged (the magnitude of the speed can change if the movement is not uniform).

Uniform straight called movement that is both uniform and rectilinear. In this case, both magnitude and direction remain unchanged.

In the general case, when a body moves, both the magnitude and direction of the velocity vector change. In order to characterize how quickly these changes occur, a special quantity is used - acceleration.

Acceleration – this is a quantity equal to the ratio of the change in the speed of movement of a body to the duration of the period of time during which this change in speed occurred. The average acceleration based on this definition is, m/s²:

Instant acceleration called physical quantity equal to the limit to which the average acceleration tends over an interval∆t → 0, m/s²:

Since the speed can change both in magnitude and direction along the trajectory, the acceleration vector has two components.

The component of the acceleration vector a, directed along the tangent to the trajectory at a given point, is called tangential acceleration, which characterizes the change in the velocity vector in magnitude.

The component of the acceleration vector a, directed along the normal to the tangent at a given point on the trajectory, is called normal acceleration. It characterizes the change in the velocity vector in direction in the case of curvilinear motion. Naturally, when a body moves along a trajectory that is a straight line, the normal acceleration is zero.

Rectilinear motion is called uniformly variable if, over any period of time, the speed of the body changes by the same amount. In this case the relation

∆V/ ∆t is the same for any time interval. Therefore, the magnitude and direction of acceleration remain unchanged: a = const.

For rectilinear motion, the acceleration vector is directed along the line of motion. If the direction of acceleration coincides with the direction of the velocity vector, then the magnitude of the velocity will increase. In this case, the movement is called uniformly accelerated. If the direction of acceleration is opposite to the direction of the velocity vector, then the magnitude of the velocity will decrease. In this case, the movement is called uniformly slow. In nature there is a natural uniformly accelerated movement - this is free fall.

Free fall- called the fall of a body if the only force acting on it is gravity. Experiments carried out by Galileo showed that during free fall, all bodies move with the same acceleration of gravity and are denoted by the letter ĝ. Near the Earth's surface ĝ = 9.8 m/s². The acceleration of free fall is caused by gravity from the Earth and is directed vertically downward. Strictly speaking, such movement is only possible in a vacuum. A fall in the air can be considered approximately free.

The trajectory of a freely falling body depends on the direction of the vector initial speed. If a body is thrown vertically downwards, then the trajectory is a vertical segment, and the motion is called uniformly variable. If a body is thrown vertically upward, then the trajectory consists of two vertical segments. First, the body rises, moving equally slow. At the point of maximum ascent, the speed becomes zero, after which the body descends, moving uniformly accelerated.

If the initial velocity vector is directed at an angle to the horizon, then the movement occurs along a parabola. This is how a thrown ball, a disk, an athlete performing a long jump, a flying bullet, etc. move.

Depending on the form of representation of kinematic parameters, there are various types laws of motion.

Law of motion is one of the forms of determining the position of a body in space, which can be expressed:

Analytically, that is, using formulas. This type of law of motion is specified using the equations of motion: x = x(t), y = y(t), z = z(t);

Graphically, that is, using graphs of changes in the coordinates of a point depending on time;

Tabular, that is, in the form of a data vector, when numerical time counts are entered in one column of the table, and in another, in comparison with the first, the coordinates of a point or points of the body.

1. The concept of uniformly accelerated motion. Its characteristics.

2. The concept of a reference system. Examples of different reference systems. Equally slow motion, its characteristics.
3. Concept material point. Uniform linear motion, its characteristics
4. The concept of a reference system. Examples of different reference systems. Uniformly accelerated motion, its characteristics.
5. The concept of a material point. Description of the laws of body motion along a parabola.
6. Description of the movement of a body in a circle. Its characteristics.
7. The concept of uniformly accelerated motion. Its characteristics.
8. Description of the movement of a body in a plane at an angle to the horizontal. Its characteristics.
9. Newton's first law, its application in life and natural phenomena.
10. Newton's second law. Using it to calculate acceleration.
11. Newton's third law. Types of forces. Graphic representation of forces applied to a body.
12. Statics. Static equilibrium condition, with examples.
13. The law of conservation of momentum with examples.
14. Concept of energy, classification. Kinetic energy.
15. Concept of energy, classification. Potential energy spring stretching.
16. Concept of energy, classification. Potential energy of gravity.
17. The concept of total mechanical energy. Law of conservation of energy.
18. MKT – postulates. Characteristics of three states of matter.
19. Gas - movement of molecules. Stern experiment, distribution of molecules by speed.
20. Concept ideal gas. Clayperon-Mendeleev equation. Isoprocesses - isobars.
21. Ideal gas equation, conditions for fulfillment. Isoprocesses - isotherm.
22. The concept of an ideal gas. Clayperon-Mendeleev equation. Isoprocesses – isochores.
23. MKT. The concept of a real gas, comparing it with an ideal one.
24. The first law of thermodynamics, the concept of heat transfer.
25. The first law of thermodynamics for an isochoric process.
26.The first law of thermodynamics for an isobaric process.
27.The first law of thermodynamics for an isothermal process.
28. Concept internal energy ideal gas for isoprocesses.
29. Second law of thermodynamics. Its application to cyclic processes using the example of a steam engine.
30. Second law of thermodynamics. Its application to cyclic processes using the example of an internal combustion engine.
31. The concept of heat engines. Jet engines.
32. The concept of heat engines. Refrigeration machines.
33. Third law of thermodynamics.
34.Adiobate process. The concept of heat capacity.