Physics table path and displacement. Differences between movement and path. Kinematics of rotary motion

Class: 9

Lesson Objectives:

• Educational:
  – introduce the concepts of “displacement”, “path”, “trajectory”.
• Developing:
  - develop logical thinking, correct physical speech, use the appropriate terminology.
• Educational:
  - achieve high class activity, attention, concentration of students.

Equipment:

• plastic bottle with a capacity of 0.33 l with water and a scale;
• medical vial with a capacity of 10 ml (or a small test tube) with a scale.

Demos: Determination of displacement and distance travelled.

During the classes

1. Actualization of knowledge.

- Hello guys! Sit down! Today we will continue to study the topic “Laws of interaction and motion of bodies” and in the lesson we will get acquainted with three new concepts (terms) related to this topic. In the meantime, check your homework for this lesson.

2. Checking homework.

Before class, one student writes the solution to the following homework assignment on the board:

Two students are given cards with individual tasks that are performed during the oral test of exercise. 1 page 9 of the textbook.

1. What coordinate system (one-dimensional, two-dimensional, three-dimensional) should be chosen to determine the position of bodies:

a) a tractor in the field;
b) a helicopter in the sky;
c) train
d) a chess piece on the board.

2. An expression is given: S \u003d υ 0 t + (a t 2) / 2, express: a, υ 0

1. What coordinate system (one-dimensional, two-dimensional, three-dimensional) should be chosen to determine the position of such bodies:

a) a chandelier in the room;
b) an elevator;
c) a submarine;
d) the plane is on the runway.

2. An expression is given: S \u003d (υ 2 - υ 0 2) / 2 a, express: υ 2, υ 0 2.

3. The study of new theoretical material.

The value introduced to describe the motion is associated with changes in body coordinates, – MOVING.

The displacement of a body (material point) is a vector connecting the initial position of the body with its subsequent position.

The movement is usually denoted by the letter . In SI, displacement is measured in meters (m).

- [ m ] - meter.

Displacement - magnitude vector, those. in addition to the numerical value, it also has a direction. The vector quantity is represented as segment, which starts at some point and ends with a point that indicates the direction. Such an arrow segment is called vector.

Knowing the displacement vector means knowing its direction and module. The modulus of a vector is a scalar, i.e. numerical value. Knowing the initial position and the displacement vector of the body, it is possible to determine where the body is located.

In the process of motion, the material point occupies different positions in space relative to the chosen reference system. In this case, the moving point “describes” some line in space. Sometimes this line is visible - for example, a high-flying aircraft can leave a trail in the sky. A more familiar example is the mark of a piece of chalk on a blackboard.

An imaginary line in space along which a body moves is called TRAJECTORY body movements.

The trajectory of a body's motion is a continuous line, which is described by a moving body (considered as a material point) with respect to the chosen frame of reference.

The movement in which all points body moving along the same trajectories, is called progressive.

Very often the trajectory is an invisible line. Trajectory moving point can be straight or crooked line. According to the shape of the trajectory motion it happens straightforward and curvilinear.

The path length is WAY. The path is a scalar value and is denoted by the letter l. The path increases if the body moves. And remains unchanged if the body is at rest. Thus, path cannot decrease over time.

The modulus of displacement and the path can have the same value only if the body moves along a straight line in the same direction.

What is the difference between travel and movement? These two concepts are often confused, although in fact they are very different from each other. Let's take a look at these differences: Annex 3) (distributed in the form of cards to each student)

1. The path is a scalar value and is characterized only by a numeric value.
2. Displacement is a vector quantity and is characterized by both a numerical value (modulus) and a direction.
3. When the body moves, the path can only increase, and the displacement modulus can both increase and decrease.
4. If the body has returned to the starting point, its displacement is zero, and the path is not equal to zero.

4. Demonstration of experience (students perform independently in their places at their desks, the teacher, together with the students, performs a demonstration of this experience)

1. Fill a plastic bottle with a scale up to the neck with water.
2. Fill the bottle with a scale with water to 1/5 of its volume.
3. Tilt the bottle so that the water comes up to the neck, but does not flow out of the bottle.
4. Quickly lower the bottle of water into the bottle (without capping it) so that the neck of the bottle enters the water of the bottle. The vial floats on the surface of the water in the bottle. Some of the water will spill out of the bottle.
5. Screw on the bottle cap.
6. While squeezing the sides of the bottle, lower the float to the bottom of the bottle.

1. By releasing the pressure on the walls of the bottle, achieve the ascent of the float. Determine the path and movement of the float: ______________________________________________________________
2. Lower the float to the bottom of the bottle. Determine the path and movement of the float:______________________________________________________________________________
3. Make the float float and sink. What is the path and movement of the float in this case?

5. Exercises and questions for repetition.

1. Do we pay for the journey or transportation when traveling in a taxi? (Way)
2. The ball fell from a height of 3 m, bounced off the floor and was caught at a height of 1 m. Find the path and move the ball. (Path - 4 m, movement - 2 m.)

6. The result of the lesson.

Repetition of the concepts of the lesson:

– movement;
– trajectory;
- way.

7. Homework.

§ 2 of the textbook, questions after the paragraph, exercise 2 (p. 12) of the textbook, repeat the experience of the lesson at home.

Bibliography

1. Peryshkin A.V., Gutnik E.M.. Physics. Grade 9: textbook for educational institutions - 9th ed., stereotype. – M.: Bustard, 2005.

Separate physical terms, mixed with everyday ideas about the world, look very similar. In the usual sense, the path and movement are one and the same, only one concept describes the process, and the second describes the result. But if we turn to encyclopedic definitions, it becomes clear how serious the difference between them is.

Definition

Way- this is a movement that leads to a change in the location of an object in space. This is a scalar value that has no direction and indicates the total distance covered. The path may be in a straight line, curved path, in a circle or in another way.

moving is a vector denoting the difference between the starting and ending location of a point in space after a certain path has been traveled. The vector quantity is always positive and also has a definite direction. The path coincides with the movement only if it is carried out in a straight line, and the direction does not change.

Comparison

Thus, the path is primary, the movement is secondary. For the first value, the beginning of the movement matters, the second can do without it. The main difference between these concepts is that the path has no direction, but the movement does. Hence other features that characterize the terms. Thus, the length of the path includes the entire distance traveled by an object in a certain time. Displacement is a vector quantity that characterizes a relative change in space.

If an entrepreneur decides to drive around four retail outlets, each of which is located at a distance of 10 kilometers from each other, and then return home, then his path will be 80 kilometers. However, the displacement will be equal to zero, since the position in space has not changed as a result of following. The path is always positive, since one can speak about it only after the movement has begun. For this value, the speed that affects the total distance matters.

Findings site

1. Type. The path is a scalar quantity, the displacement is a vector.
2. Measurement method. The path is calculated by the total segment traveled, the movement - by changing the location of the object in space.
3. Expression. The displacement may be equal to zero (if the movement was carried out along a closed trajectory), but the path cannot be.

At first glance, movement and path are concepts that are close in meaning. However, in physics there are key differences between movement and path, although both concepts are associated with a change in the position of the body in space and are often (usually in rectilinear motion) numerically equal to each other.

To understand the differences between movement and path, let us first give them the definitions that physics gives them.

body movement- This directed line segment (vector), whose beginning coincides with the initial position of the body, and whose end coincides with the final position of the body.

body path- This distance passed by the body in a certain period of time.

Let's imagine that you stood at your entrance to a certain point. We walked around the house and returned to the starting point. So: your displacement will be equal to zero, but the path will not. The path will be equal to the length of the curve (for example, 150 m) that you walked around the house.

But back to the coordinate system. Let a point body move rectilinearly from point A with coordinate x 0 \u003d 0 m to point B with coordinate x 1 \u003d 10 m. The movement of the body in this case will be 10 m. body way.

If the body moved in a straight line from the initial (A) point with coordinate x 0 = 5 m, to the final (B) point with coordinate x 1 = 0, then its displacement will be -5 m, and the path will be 5 m.

The displacement is found as a difference, where the initial coordinate is subtracted from the final one. If the end coordinate is less than the start coordinate, i.e. the body moved in the opposite direction with respect to the positive direction of the X axis, then the displacement will be a negative value.

Since displacement can be both positive and negative, displacement is a vector quantity. In contrast, the path is always a positive or zero value (the path is a scalar value), since the distance cannot be negative in principle.

Let's consider one more example. The body moved in a straight line from point A (x 0 \u003d 2 m) to point B (x 1 \u003d 8 m), then it also moved straight from B to point C with coordinate x 2 \u003d 5 m. What are the common path (A →B→C) done by this body and its total displacement?

Initially, the body was at a point with a coordinate of 2 m, at the end of its movement it ended up at a point with a coordinate of 5 m. Thus, the movement of the body was 5 - 2 = 3 (m). It is also possible to calculate the total displacement as the sum of two displacements (vectors). The displacement from A to B was 8 - 2 = 6 (m). The displacement from point B to C was 5 - 8 = -3 (m). Adding both displacements we get 6 + (-3) = 3 (m).

The total path is calculated by adding the two distances traveled by the body. The distance from point A to B is 6 m, and from B to C the body has traveled 3 m. In total, we get 9 m.

Thus, in this problem, the path and displacement of the body differ from each other.

The considered problem is not entirely correct, since it is necessary to indicate the moments of time at which the body is at certain points. If x 0 corresponds to the time t 0 = 0 (the start of observations), then let x 1 correspond to t 1 = 3 s, and x 2 corresponds to t 2 = 5 s. That is, the time interval between t 0 and t 1 is 3 s, and between t 0 and t 2 is 5 s. In this case, it turns out that the path of the body for a period of time of 3 seconds was 6 meters, and for a period of 5 seconds - 9 meters.

Time is involved in determining the path. In contrast, for movement, time does not really matter.

Displacement, shift, movement, migration, movement, permutation, regrouping, transfer, transportation, transition, relocation, transfer, travel; shifting, moving, telekinesis, epeirophoresis, rebasing, rolling, waddling, ... ... Synonym dictionary

MOVEMENT, displacement, cf. (book). 1. Action according to Ch. move move. Service movement. 2. Action and status according to Ch. move move. Movement of layers of the earth's crust. Explanatory Dictionary of Ushakov. D.N. Ushakov. 1935 1940 ... Explanatory Dictionary of Ushakov

In mechanics, a vector connecting the positions of a moving point at the beginning and end of a certain period of time; vector P. is directed along the chord of the trajectory of the point. Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A. M. ... ... Physical Encyclopedia

MOVE, eat, eat; still (yon, ena); owls, whom what. Place, transfer to another place. P. scenery. P. brigade to another site. Displaced persons (persons forcibly displaced from their country). Explanatory dictionary of Ozhegov. S.I.… … Explanatory dictionary of Ozhegov

- (relocation) Relocation of an office, enterprise, etc. to another place. Often it is caused by a merger or acquisition. Sometimes employees receive a relocation allowance, which should encourage them to stay in the service in this ... ... Glossary of business terms

moving- - Telecommunication topics, basic concepts of EN redeployment ... Technical Translator's Handbook

moving,- Displacement, mm, the amount of change in the position of any point of the element of the window block (usually, the impost of the frame or vertical bars of the sashes) in the direction of the normal to the plane of the product under the influence of wind load. Source: GOST ... ...

moving- Migration of material in the form of a solution or suspension from one soil horizon to another ... Geography Dictionary

moving- 3.14 transfer (in relation to storage location): A change in the storage location of a document. Source: GOST R ISO 15489-1 2007: System of standards for information ... Dictionary-reference book of terms of normative and technical documentation

moving- ▲ change position, in space motionless movement change in position in space; a shape transformation that preserves the distances between the points of the shape; movement to another place. movement. progressive movement ... ... Ideographic Dictionary of the Russian Language

Books

• GESNm 81-03-40-2001. Part 40. Additional movement of equipment and material resources,. State budget standards. The state elemental estimated norms for the installation of equipment (hereinafter referred to as GESNm) are designed to determine the need for resources (labor costs of workers, ...
• Movement of people and goods in near-Earth space by means of technical ferrographitization, R. A. Sizov. This publication is the second applied edition to the books by R. A. Sizov "Matter, Antimatter and Energy Environment - the Physical Triad of the Real World", in which, based on the discovered…