Give a definition of mechanical motion and its types. Motion of a material point

Themes Unified State Exam codifier: mechanical motion and its types, relativity of mechanical motion, speed, acceleration.

The concept of motion is extremely general and covers a wide range of phenomena. They study in physics different kinds movements. The simplest of these is mechanical movement. It is studied in mechanics.
Mechanical movement - this is a change in the position of a body (or its parts) in space relative to other bodies over time.

If body A changes its position relative to body B, then body B changes its position relative to body A. In other words, if body A moves relative to body B, then body B moves relative to body A. Mechanical motion is relative- to describe a movement, it is necessary to indicate in relation to which body it is being considered.

So, for example, we can talk about the movement of a train relative to the ground, a passenger relative to a train, a fly relative to a passenger, etc. Concepts absolute motion and absolute rest do not make sense: a passenger at rest relative to the train will move with it relative to the pole on the road, perform a daily rotation with the Earth and move around the Sun.
The body relative to which motion is considered is called body of reference.

The main task of mechanics is to determine the position of a moving body at any time. To solve this problem, it is convenient to imagine the movement of a body as a change in the coordinates of its points over time. To measure coordinates, you need a coordinate system. To measure time you need a watch. All this together forms a frame of reference.

Frame of reference- this is a reference body together with a coordinate system and a clock rigidly connected to it (“frozen” into it).
The reference system is shown in Fig. 1. The movement of a point is considered in a coordinate system. The origin of coordinates is a body of reference.

Picture 1.

The vector is called radius vector dots The coordinates of a point are at the same time the coordinates of its radius vector.
The solution to the main problem of mechanics for a point is to find its coordinates as functions of time: .
In some cases, you can ignore the shape and size of the object being studied and consider it simply as a moving point.

Material point - this is a body whose dimensions can be neglected in the conditions of this problem.
Thus, a train can be considered a material point when it moves from Moscow to Saratov, but not when passengers board it. The Earth can be considered a material point when describing its movement around the Sun, but not its daily rotation around its own axis.

The characteristics of mechanical motion include trajectory, path, displacement, speed and acceleration.

Trajectory, path, movement.

In what follows, when speaking about a moving (or at rest) body, we always assume that the body can be taken as a material point. Cases when idealization of a material point cannot be used will be specially discussed.

Trajectory - this is the line along which the body moves. In Fig. 1, the trajectory of a point is a blue arc, which the end of the radius vector describes in space.
Path - this is the length of the trajectory section traversed by the body in a given period of time.
Moving is a vector connecting the initial and final position of the body.
Let us assume that the body began to move at a point and ended its movement at a point (Fig. 2). Then the path traveled by the body is the trajectory length. The displacement of a body is a vector.

Figure 2.

Speed ​​and acceleration.

Consider the movement of a body in rectangular system coordinates with the basis (Fig. 3).

Figure 3.

Let at the moment of time the body be at a point with the radius vector

After a short period of time the body found itself at a point with
radius vector

Body movement:

(1)

Instantaneous speed at a moment in time - this is the limit of the ratio of movement to the time interval, when the value of this interval tends to zero; in other words, the speed of a point is the derivative of its radius vector:

From (2) and (1) we obtain:

The coefficients of the basis vectors in the limit give the derivatives:

(The derivative with respect to time is traditionally denoted by a dot above the letter.) So,

We see that the projections of the velocity vector onto the coordinate axes are derivatives of the coordinates of the point:

When it approaches zero, the point approaches the point and the displacement vector turns in the direction of the tangent. It turns out that in the limit the vector is directed exactly tangent to the trajectory at point . This is shown in Fig. 3.

The concept of acceleration is introduced in a similar way. Let the speed of the body be equal at the moment of time, and after a short interval the speed becomes equal.
Acceleration - this is the limit of the ratio of the change in speed to the interval when this interval tends to zero; in other words, acceleration is the derivative of speed:

Acceleration is thus the “rate of change of velocity.” We have:

Consequently, acceleration projections are derivatives of velocity projections (and, therefore, second derivatives of coordinates):

The law of addition of speeds.

Let there be two reference systems. One of them is associated with a stationary reference body. We will denote this reference system and call it motionless.
The second reference system, denoted by , is associated with a reference body that moves relative to the body with a speed of . We call this frame of reference moving . Additionally, we assume that the coordinate axes of the system move parallel to themselves (there is no rotation of the coordinate system), so that the vector can be considered the speed of the moving system relative to the stationary one.

A fixed frame of reference is usually associated with the earth. If a train moves smoothly along the rails at speed , this frame of reference associated with the train car will be a moving frame of reference.

Note that the speed any points of the car (except for the rotating wheels!) is equal to . If a fly sits motionless at some point in the carriage, then relative to the ground the fly moves at a speed of . The fly is carried by the carriage, and therefore the speed of the moving system relative to the stationary one is called portable speed .

Now suppose that a fly crawled along the carriage. The speed of the fly relative to the car (that is, in a moving system) is designated and called relative speed. The speed of a fly relative to the ground (that is, in a stationary frame) is denoted and called absolute speed .

Let's find out how these three speeds are related to each other - absolute, relative and portable.
In Fig. 4 fly is indicated by a dot. Next:
- radius vector of a point in a fixed system;
- radius vector of a point in a moving system;
- radius vector of the body of reference in a stationary system.

Figure 4.

As can be seen from the figure,

Differentiating this equality, we get:

(3)

(the derivative of a sum is equal to the sum of derivatives not only for the case scalar functions, but also for vectors).
The derivative is the speed of a point in the system, that is, the absolute speed:

Similarly, the derivative is the speed of a point in the system, that is, the relative speed:

What is it? This is the speed of a point in a stationary system, that is, the portable speed of a moving system relative to a stationary one:

As a result, from (3) we obtain:

Law of addition of speeds. The speed of a point relative to a stationary reference frame is equal to the vector sum of the speed of the moving system and the speed of the point relative to the moving system. In other words, absolute speed is the sum of portable and relative speeds.

Thus, if a fly crawls along a moving carriage, then the speed of the fly relative to the ground is equal to the vector sum of the speed of the carriage and the speed of the fly relative to the carriage. Intuitively obvious result!

Types of mechanical movement.

The simplest types of mechanical motion of a material point are uniform and rectilinear motion.
The movement is called uniform, if the magnitude of the velocity vector remains constant (the direction of the velocity may change).

The movement is called straightforward , if the direction of the velocity vector remains constant (and the magnitude of the velocity may change). The trajectory of rectilinear motion is a straight line on which the velocity vector lies.
For example, a car that is traveling with constant speed By winding road, makes a uniform (but not rectilinear) movement. A car accelerating on a straight section of highway moves in a straight line (but not uniformly).

But if, when moving a body, both the velocity module and its direction remain constant, then the movement is called uniform rectilinear.

In terms of the velocity vector, we can give shorter definitions for these types of motion:

The most important special case uneven movement is uniformly accelerated motion, at which the magnitude and direction of the acceleration vector remain constant:

Along with the material point, mechanics considers another idealization - a rigid body.
Solid - This is a system of material points, the distances between which do not change over time. Model solid used in cases where we cannot neglect the size of the body, but can not take into account change size and shape of the body during movement.

The simplest types of mechanical motion of a solid body are translational and rotational motion.
The movement of the body is called progressive, if any straight line connecting any two points of the body moves parallel to its original direction. During translational motion, the trajectories of all points of the body are identical: they are obtained from each other by a parallel shift (Fig. 5).

Figure 5.

The movement of the body is called rotational , if all its points describe circles lying in parallel planes. In this case, the centers of these circles lie on one straight line, which is perpendicular to all these planes and is called axis of rotation.

In Fig. 6 shows a ball rotating around vertical axis. This is how they usually draw Earth in corresponding problems of dynamics.

Figure 6.

Mechanical movement

Mechanical movement of a body is the change in its position in space relative to other bodies over time. In this case, the bodies interact according to the laws of mechanics.

Section of mechanics describing geometric properties movement without taking into account the reasons that cause it is called kinematics.

In more general meaning movement called change of state physical system over time. For example, we can talk about the movement of a wave in a medium.

Types of mechanical movement

Mechanical motion can be considered for different mechanical objects:

• Motion of a material point is completely determined by the change in its coordinates in time (for example, two on a plane). This is studied by the kinematics of a point. In particular, important characteristics movements are the trajectory of a material point, displacement, speed and acceleration.
  • Straightforward motion of a point (when it is always on a straight line, the speed is parallel to this straight line)
  • Curvilinear movement� - movement of a point along a trajectory that is not a straight line, with arbitrary acceleration and arbitrary speed at any time (for example, movement in a circle).
• Rigid body motion consists of the movement of any of its points (for example, the center of mass) and rotational movement around this point. Studied by rigid body kinematics.
  • If there is no rotation, then the movement is called progressive and is completely determined by the movement of the selected point. The movement is not necessarily linear.
  • For description rotational movement�- body movements relative to a selected point, for example, fixed at a point�- use Euler Angles. Their number in case three-dimensional space equals three.
  • Also for a solid body there is flat movement� is a movement in which the trajectories of all points lie in parallel planes, while it is completely determined by one of the sections of the body, and the section of the body is determined by the position of any two points.
• Continuum motion. Here it is assumed that the movement of individual particles of the medium is quite independent of each other (usually limited only by the conditions of continuity of velocity fields), therefore the number of defining coordinates is infinite (functions become unknown).

Geometry of movement

Relativity of motion

Relativity is the dependence of the mechanical movement of a body on the reference system. Without specifying the reference system, it makes no sense to talk about motion.

Mechanics concept. Mechanics is a part of physics that studies the movement of bodies, the interaction of bodies, or the movement of bodies under some kind of interaction.

the main task mechanics- this is the determination of the location of the body at any time.

Sections of mechanics: kinematics and dynamics. Kinematics is a branch of mechanics that studies the geometric properties of movements without taking into account their masses and the forces acting on them. Dynamics is a branch of mechanics that studies the movement of bodies under the influence of forces applied to them.

Movement. Motion characteristics. Movement is a change in the position of a body in space over time relative to other bodies. Movement characteristics: distance traveled, movement, speed, acceleration.

Mechanical movement – This is a change in the position of a body (or its parts) in space relative to other bodies over time.

Forward movement

Uniform body movement. Demonstrated via video with explanations.

Uneven mechanical movement- this is a movement in which the body makes unequal movements at equal intervals of time.

Relativity of mechanical motion. Demonstrated via video with explanations.

Reference point and reference system in mechanical motion. The body relative to which the movement is considered is called the reference point. The reference system in mechanical motion is the reference point and the coordinate system of the clock.

Reference system. Characteristics of mechanical movement. The reference system is demonstrated by a video with explanations. Mechanical movement has the following characteristics: Trajectory; Path; Speed; Time.

Straight-line trajectory- This is the line along which the body moves.

Curvilinear movement. Demonstrated via video with explanations.

Path and the concept of scalar quantity. Demonstrated via video with explanations.

Physical formulas and units of measurement of the characteristics of mechanical movement:

Quantity designation	Units of measurement	Formula for determining the value
Path-s	m, km	S= vt
Time- t	s, hour	T = s/v
Speed ​​-v	m/s, km/h	V = s/ t

P concept of acceleration. Revealed with a video demonstration, with explanations.

Formula for determining the magnitude of acceleration:

3. Newton's laws of dynamics.

The great physicist I. Newton. I. Newton debunked the ancient ideas that the laws of motion of earthly and celestial bodies completely different. The entire Universe is subject to uniform laws that can be formulated mathematically.

Two fundamental problems solved by I. Newton's physics:

1. Creation of an axiomatic basis for mechanics, which transferred this science to the category of strict mathematical theories.

2. Creation of dynamics that connects the behavior of the body with the characteristics of external influences (forces) on it.

1. Every body continues to be maintained in a state of rest or uniform and rectilinear motion until and unless it is forced by applied forces to change this state.

2. The change in momentum is proportional to the applied force and occurs in the direction of the straight line along which this force acts.

3. An action always has an equal and opposite reaction, otherwise, the interactions of two bodies on each other are equal and directed in opposite directions.

I. Newton's first law of dynamics. Every body continues to be maintained in a state of rest or uniform and rectilinear motion until and unless it is forced by applied forces to change this state.

Concepts of inertia and inertia of a body. Inertia is a phenomenon in which a body strives to maintain its original state. Inertia is the property of a body to maintain a state of motion. The property of inertia is characterized by body mass.

Newton's development of Galileo's theory of mechanics. For a long time it was believed that in order to maintain any movement it was necessary to carry out uncompensated external influence from other bodies. Newton shattered these beliefs derived by Galileo.

Inertial system countdown. Frames of reference, relative to which free body moves uniformly and in a straight line, are called inertial.

Newton's first law - the law of inertial systems. Newton's first law is a postulate about the existence of inertial frames of reference. In inertial reference systems mechanical phenomena are described most simply.

I. Newton's second law of dynamics. In an inertial reference frame, rectilinear and uniform motion can occur only if other forces do not act on the body or their action is compensated, i.e. balanced. Demonstrated via video with explanations.

The principle of superposition of forces. Demonstrated via video with explanations.

Body weight concept. Mass is one of the most fundamental physical quantities. Mass characterizes several properties of the body at once and has a number of important properties.

Force is a central concept of Newton's second law. Newton's second law determines that a body will then move with acceleration when a force acts on it. Force is a measure of the interaction of two (or more) bodies.

Two conclusions of classical mechanics from I. Newton’s second law:

1. The acceleration of a body is directly related to the force applied to the body.

2. The acceleration of a body is directly related to its mass.

Demonstration of the direct dependence of the acceleration of a body on its mass

I. Newton's third law of dynamics. Demonstrated via video with explanations.

The importance of the laws of classical mechanics for modern physics . Mechanics based on Newton's laws is called classical mechanics. Within the framework of classical mechanics, the movement of not very small bodies with not very high speeds is well described.

Demos:

Physical fields around elementary particles.

Planetary model of the atom by Rutherford and Bohr.

Movement as a physical phenomenon.

Forward movement.

Uniform rectilinear movement

Uneven relative mechanical movement.

Video animation of the reference system.

Curvilinear movement.

Path and trajectory.

Acceleration.

Inertia of rest.

Superposition principle.

Newton's 2nd law.

Dynamometer.

Direct dependence of the acceleration of a body on its mass.

Newton's 3rd law.

Control questions:.

Formulate a definition and scientific subject physics.

Formulate physical properties, common to all natural phenomena.

Formulate the main stages in the evolution of the physical picture of the world.

Name 2 basic principles of modern science.

Name the features of the mechanistic model of the world.

What is the essence of molecular kinetic theory.

Formulate the main features of the electromagnetic picture of the world.

Explain the concept of a physical field.

Identify the characteristics and differences between electric and magnetic fields.

Explain the concepts of electromagnetic and gravitational fields.

Explain the concept of “Planetary Model of the Atom”

Formulate the features of the modern physical picture of the world.

Formulate the main provisions of the modern physical picture of the world.

Explain the meaning of A. Einstein's theory of relativity.

Explain the concept: “Mechanics”.

Name the main sections of mechanics and give them definitions.

Name the main ones physical characteristics movements.

Formulate the signs of forward mechanical movement.

Formulate the signs of uniform and uneven mechanical movement.

Formulate the signs of the relativity of mechanical motion.

Explain the meaning of physical concepts: “Reference point and reference system in mechanical motion.”

Name the main characteristics of mechanical motion in the reference system.

Name the main characteristics of the trajectory of rectilinear motion.

Name the main characteristics of curvilinear motion.

Define physical concept: "Path".

Define the physical concept: “Scalar quantity”.

Reproduce physical formulas and units of measurement of the characteristics of mechanical movement.

Formulate physical meaning concept: "Acceleration".

Play physical formula to determine the magnitude of acceleration.

Name two fundamental problems solved by I. Newton’s physics.

Reproduce the main meanings and content of I. Newton’s first law of dynamics.

Formulate the physical meaning of the concept of inertia and inertia of a body.

How did Newton develop Galileo's theory of mechanics?

Formulate the physical meaning of the concept: “Inertial frame of reference.”

Why is Newton's first law the law of inertial systems?

Reproduce the main meanings and content of I. Newton’s second law of dynamics.

Formulate the physical meaning of the principle of superposition of forces, derived by I. Newton.

Formulate the physical meaning of the concept of body mass.

Justify that strength is central concept Newton's second law.

Formulate two conclusions of classical mechanics based on I. Newton’s second law.

Reproduce the main meanings and content of I. Newton’s third law of dynamics.

Explain the significance of the laws of classical mechanics for modern physics.

Literature:

1. Akhmedova T.I., Mosyagina O.V. Science: Tutorial/ T.I. Akhmedova, O.V. Mosyagina. – M.: RAP, 2012. – P. 34-37.

What is a reference point? What is mechanical movement?

Andreus-dad-ndrey

The mechanical movement of a body is the change in its position in space relative to other bodies over time. In this case, the bodies interact according to the laws of mechanics. The branch of mechanics that describes the geometric properties of motion without taking into account the reasons that cause it is called kinematics

In a more general sense, motion is any spatial or temporal change in the state of a physical system. For example, we can talk about the movement of a wave in a medium.

* The movement of a material point is completely determined by the change in its coordinates in time (for example, two on a plane). This is studied by the kinematics of a point.
o Rectilinear motion of a point (when it is always on a straight line, the speed is parallel to this straight line)
o Curvilinear motion is the movement of a point along a trajectory that is not a straight line, with arbitrary acceleration and arbitrary speed at any time (for example, movement in a circle).
* The motion of a rigid body consists of the motion of any of its points (for example, the center of mass) and rotational motion around this point. Studied by rigid body kinematics.
o If there is no rotation, then the movement is called translational and is completely determined by the movement of the selected point. Note that it is not necessarily linear.
o To describe rotational motion - the movement of a body relative to a selected point, for example, fixed at a point, Euler Angles are used. Their number in the case of three-dimensional space is three.
o Also for a rigid body, plane motion is distinguished - a motion in which the trajectories of all points lie in parallel planes, while it is completely determined by one of the sections of the body, and the section of the body is determined by the position of any two points.
* Continuum movement. Here it is assumed that the movement of individual particles of the medium is quite independent of each other (usually limited only by the conditions of continuity of velocity fields), therefore the number of defining coordinates is infinite (functions become unknown).
Relativity - the dependence of the mechanical movement of a body on a reference system, without specifying the reference system - it makes no sense to talk about movement.

Daniil Yuriev

Types of mechanical movement [edit | edit wiki text]
Mechanical motion can be considered for different mechanical objects:
The movement of a material point is completely determined by a change in its coordinates in time (for example, for a plane - by a change in the abscissa and ordinate). This is studied by the kinematics of a point. In particular, important characteristics of motion are the trajectory of a material point, displacement, speed and acceleration.
Rectilinear motion of a point (when it is always on a straight line, the speed is parallel to this straight line)
Curvilinear motion is the movement of a point along a trajectory that is not a straight line, with arbitrary acceleration and arbitrary speed at any time (for example, movement in a circle).
The motion of a rigid body consists of the motion of any of its points (for example, the center of mass) and rotational motion around this point. Studied by rigid body kinematics.
If there is no rotation, then the movement is called translational and is completely determined by the movement of the selected point. The movement is not necessarily linear.
To describe rotational motion - the movement of a body relative to a selected point, for example, fixed at a point - Euler Angles are used. Their number in the case of three-dimensional space is three.
Also, for a rigid body, plane motion is distinguished - a motion in which the trajectories of all points lie in parallel planes, while it is completely determined by one of the sections of the body, and the section of the body is determined by the position of any two points.
Movement of a continuous medium. Here it is assumed that the movement of individual particles of the medium is quite independent of each other (usually limited only by the conditions of continuity of velocity fields), therefore the number of defining coordinates is infinite (functions become unknown).

Mechanical movement. Path. Speed. Acceleration

Lara

Mechanical movement is a change in the position of a body (or its parts) relative to other bodies.
The position of the body is specified by the coordinate.
The line along which a material point moves is called a trajectory. The length of the trajectory is called the path. The unit of path is meter.
Path = speed * time. S=v*t.

Mechanical movement is characterized by three physical quantities: movement, speed and acceleration.

A directed line segment drawn from the initial position of a moving point to its final position is called displacement (s). Displacement is a vector quantity. The unit of movement is meter.

Speed ​​is a vector physical quantity that characterizes the speed of movement of a body, numerically equal to the ratio of movement over a short period of time to the value of this period of time.
The speed formula is v = s/t. The unit of speed is m/s. In practice, the speed unit used is km/h (36 km/h = 10 m/s).

Acceleration is a vector physical quantity that characterizes the rate of change in speed, numerically equal to the ratio of the change in speed to the period of time during which this change occurred. Formula for calculating acceleration: a=(v-v0)/t; The unit of acceleration is meter/(squared second).

Mechanical movement A body is called a change in its position in space relative to other bodies over time. For example, a person riding an escalator in the subway is at rest relative to the escalator itself and is moving relative to the walls of the tunnel

Types of mechanical movement:

• rectilinear and curvilinear - according to the shape of the trajectory;
• uniform and uneven - according to the law of motion.

Mechanical movement relatively. This is manifested in the fact that the shape of the trajectory, displacement, speed and other characteristics of the body’s movement depend on the choice of the reference system.

The body relative to which motion is considered is called reference body. The coordinate system, the reference body with which it is associated, and the device for counting time form reference system , relative to which the movement of the body is considered.

Sometimes the size of the body compared to the distance to it can be neglected. In these cases, the body is considered material point.

Determining the position of the body at any time is the main task of mechanics.

Important characteristics of movement are trajectory of a material point, displacement, speed and acceleration. The line along which a material point moves is called trajectory . The length of the trajectory is called path (L). The unit of measurement for the path is 1m. The vector connecting the starting and ending points of the trajectory is called displacement (). Displacement unit-1 m.

The simplest type of motion is uniform linear motion. A movement in which a body makes the same movements at any equal intervals of time is called rectilinear uniform movement. Speed() is a vector physical quantity characterizing the speed of movement of a body, numerically equal to the ratio of movement over a short period of time to the value of this interval. The defining formula for speed has the form v = s/t. Speed ​​unit - m/s. Speed ​​is measured with a speedometer.

The movement of a body in which its speed changes equally over any period of time is called uniformly accelerated or equally variable.

— a physical quantity that characterizes the rate of change in speed and is numerically equal to the ratio of the vector of change in speed per unit time. SI unit of acceleration — m/s 2 .

uniformly accelerated, if the velocity modulus increases, the condition of uniformly accelerated motion. For example, accelerating vehicles - cars, trains and free fall bodies near the Earth's surface ( = ).

Equally alternating motion called equally slow, if the speed module decreases. — condition of uniformly slow motion.

Instantaneous speed uniformly accelerated linear motion

Mechanics - branch of physics that studies mechanical motion.

Mechanics is divided into kinematics, dynamics and statics.

Kinematics is a branch of mechanics in which the movement of bodies is considered without identifying the causes of this movement. Kinematics studies ways to describe movement and the relationship between quantities characterizing these movements.

Kinematics problem: definition kinematic characteristics movement (trajectories of movement, displacement, distance traveled, coordinates, speed and acceleration of the body), as well as obtaining equations for the dependence of these characteristics on time.

Mechanical body movement call the change in its position in space relative to other bodies over time.

Mechanical movement relatively, the expression “a body moves” is meaningless until it is determined in relation to what the movement is being considered. Motion of the same body relative to different bodies turns out to be different. To describe the movement of a body, it is necessary to indicate in relation to which body the movement is being considered. This body is called reference body. Rest is also relative (examples: a passenger in a train at rest looks at the train passing by)

The main task of mechanics – be able to calculate the coordinates of body points at any time.

To solve this, you need to have a body from which coordinates are measured, associate a coordinate system with it, and have a device for measuring time intervals.

The coordinate system, the reference body with which it is associated, and the device for counting time form reference system, relative to which the movement of the body is considered.

Coordinate systems there are:

1. one-dimensional– the position of the body on a straight line is determined by one coordinate x.

2. two-dimensional– the position of a point on the plane is determined by two coordinates x and y.

3. three-dimensional– the position of a point in space is determined by three coordinates x, y and z.

Every body has certain dimensions. Different parts of the body are in different places in space. However, in many mechanics problems there is no need to indicate the positions of individual parts of the body. If the dimensions of a body are small compared to the distances to other bodies, then this body can be considered its material point. This can be done, for example, when studying the movement of planets around the Sun.

If all parts of the body move equally, then such movement is called translational.

For example, cabins in the “Giant Wheel” attraction, a car on a straight section of track, etc. move translationally. When a body moves forward, it can also be considered as a material point.

Material point is a body whose dimensions can be neglected under given conditions.

The concept of a material point plays important role in mechanics. A body can be considered a material point if its dimensions are small compared to the distance it travels, or compared to the distance from it to other bodies.

Example. Dimensions orbital station, located in orbit near the Earth, can be ignored, and when calculating the trajectory of movement spaceship When docking with a station, you cannot do without taking its size into account.

Characteristics of mechanical motion: movement, speed, acceleration.

Mechanical motion is characterized by three physical quantities: movement, speed and acceleration.

Moving over time from one point to another, a body (material point) describes a certain line, which is called the trajectory of the body.

The line along which a point on the body moves is called trajectory of movement.

The length of the trajectory is called the distance traveled way.

Designated l, measured in meters. (trajectory – trace, path – distance)

Distance traveledl equal to length arc of the trajectory traversed by the body over some time t. Path– scalar quantity.

By moving the body called a directed straight line segment connecting the initial position of a body with its subsequent position. Displacement is a vector quantity.

The vector connecting the starting and ending points of a trajectory is called moving.

Designated S, measured in meters. (displacement is a vector, displacement module is a scalar)

Speed ​​- a vector physical quantity characterizing the speed of movement of a body, numerically equal to the ratio of movement over a short period of time to the value of this interval.

Designated v

Speed ​​formula: or

SI unit of measurement – m/s.

In practice, the speed unit used is km/h (36 km/h = 10 m/s).

Measure speed speedometer.

Acceleration- vector physical quantity characterizing the rate of change in speed, numerically equal to the ratio of the change in speed to the period of time during which this change occurred.

If the speed changes equally throughout the entire movement, then the acceleration can be calculated using the formula:

Acceleration is measured accelerometer

SI unit m/s 2

Thus, the main physical quantities in the kinematics of a material point are the distance traveled l, movement, speed and acceleration. Path l is scalar quantity. Displacement, speed and acceleration are vector quantities. To set a vector quantity, you need to set its magnitude and indicate the direction. Vector quantities obey certain mathematical rules. Vectors can be projected onto coordinate axes, they can be added, subtracted, etc.

What is mechanical movement and how is it characterized? What parameters are introduced to understand this type of movement? What terms are most often used in this case? In this article we will answer these questions, consider mechanical movement with different points view, we will give examples and deal with solving problems from physics on the relevant topic.

Basic Concepts

Ever since school, we have been taught that mechanical motion is a change in the position of a body at any moment in time relative to other bodies in the system. In fact, that's how it is. Let's take the ordinary house we are in as the zero of the coordinate system. Visually imagine that the house will be the origin of coordinates, and the abscissa and ordinate axis will emerge from it in any direction.

In this case, our movement within the house, as well as outside it, will clearly demonstrate the mechanical movement of the body in the reference frame. Imagine that a point is moving along a coordinate system, at each moment of time changing its coordinate relative to both the abscissa and ordinate axis. Everything will be simple and clear.

Characteristics of mechanical movement

What kind of movement could this be? We will not delve too deeply into the jungle of physics. Let us consider the simplest cases when a material point moves. It is divided into linear motion, as well as curvilinear movement. In principle, everything should already be clear from the title, but let’s talk about this more specifically, just in case.

The rectilinear motion of a material point will be called such a motion that occurs along a trajectory in the form of a straight line. Well, for example, a car drives directly under a road that has no turns. Or along a section of a similar road. This will be a linear movement. In this case, it can be uniform or uniformly accelerated.

Curvilinear motion of a material point will be called such motion that is carried out along a trajectory that does not have the form of a straight line. The trajectory can be a broken line, as well as closed line. That is, a circular trajectory, an ellipsoidal one, and so on.

Mechanical movement of population

This type of movement has almost absolutely nothing to do with physics. Although, depending on what point of view we perceive it from. What, in general, is called the mechanical movement of the population? It refers to the relocation of individuals, which occurs as a result of migration processes. This can be both external and internal migration. Based on duration, mechanical movement of the population is divided into permanent and temporary (plus pendulum and seasonal).

If we consider this process from a physical point of view, then only one thing can be said: this movement will perfectly demonstrate the movement of material points in the reference system associated with our planet - the Earth.

Uniform mechanical movement

As the name implies, this is a type of movement in which the speed of the body has specific value, kept constant modulo. In other words, the speed of a body that moves uniformly does not change. IN real life we can hardly notice ideal examples uniform mechanical movement. You can quite reasonably object that you can drive a car at a speed of 60 kilometers per hour. Yes, definitely a speedometer vehicle may demonstrate a similar value, but this does not mean that in fact the car’s speed will be exactly sixty kilometers per hour.

What is it about? As we know, firstly, all measuring instruments have a certain error. Rulers, scales, mechanical and electronic instruments - they all have a certain error, inaccuracy. You can see this for yourself by taking a dozen rulers and attaching them to one another. After this, you may notice some discrepancies between the millimeter marks and their application.

The same goes for the speedometer. It has a certain error. For instruments, the inaccuracy is numerically equal to half the division value. In cars, the speedometer will be inaccurate by 10 kilometers per hour. That is why at a certain moment it is impossible to say for sure that we are moving at one speed or another. The second factor that will introduce inaccuracy will be the forces acting on the car. But forces are inextricably linked with acceleration, so we will talk about this topic a little later.

Very often, uniform motion occurs in problems of a mathematical nature rather than physical ones. There, motorcyclists, trucks and cars move at the same speed, equal in magnitude at different points in time.

Uniformly accelerated motion

In physics, this type of motion occurs quite often. Even in the problems of part “A” of both the 9th and 11th grades there are tasks in which you need to be able to perform operations with acceleration. For example, “A-1”, where a graph of body movement is drawn in coordinate axes and you need to calculate how far the car has traveled in a given period of time. Moreover, one of the intervals can demonstrate uniform motion, while in the second it is necessary to first calculate the acceleration and only then calculate the distance traveled.

How do you know that the motion is uniformly accelerated? Typically, tasks provide information about this directly. That is, there is either a numerical indication of the acceleration, or parameters are given (time, change in speed, distance) that allow us to determine the acceleration. It should be noted that acceleration is a vector quantity. This means it can be not only positive, but also negative. In the first case, we will observe the acceleration of the body, in the second - its deceleration.

But it happens that information about the type of movement is taught to the student in a somewhat secretive, if you can call it that, form. For example, it is said that nothing acts on the body or the sum of all forces is zero. Well, in this case you need to clearly understand that we're talking about O uniform motion or about the rest of the body in specific system coordinates If you remember Newton's second law (which states that the sum of all forces is nothing more than the product of the mass of a body and the acceleration imparted under the action of the corresponding forces), you will easily notice one interesting thing: if the sum of forces is zero, then the product of mass and acceleration will also be zero.

Conclusion

But mass is a constant quantity for us, and a priori it cannot be zero. In this case, the logical conclusion would be that in the absence of action external forces(or with their compensated action) the body has no acceleration. This means that it is either at rest or moving at a constant speed.

Formula for uniformly accelerated motion

Sometimes found in scientific literature an approach according to which simple formulas are first given, and then, taking into account certain factors, they become more complicated. We will do the opposite, namely, we will first consider uniformly accelerated motion. The formula according to which the distance traveled is calculated is as follows: S = V0t + at^2/2. Here V0 is starting speed of the body, a is the acceleration (can be negative, then the + sign in the formula will change to -), and t is the time elapsed from the beginning of the movement until the body stops.

Uniform motion formula

If we talk about uniform motion, we remember that in this case the acceleration is zero (a = 0). Substitute zero into the formula and get: S = V0t. But the speed along the entire route is constant, roughly speaking, that is, we will have to neglect the forces acting on the body. Which, by the way, is practiced everywhere in kinematics, since kinematics does not study the causes of movement; dynamics deals with this. So, if the speed along the entire section of the route is constant, then its initial value coincides with any intermediate, as well as final. Therefore, the distance formula will look like this: S = Vt. That's all.