Examples of uniform motion. Uniform and uneven movement. Speed. Definition of mechanical movement

Topic: Interaction of bodies

Lesson:Uniform and uneven movement. Speed

Consider two examples of the motion of two bodies. The first body is a car moving along a straight deserted street. The second is a sled that, accelerating, rolls down a snowy hill. The trajectory of both bodies is a straight line. From the last lesson, you know that such a movement is called rectilinear. But there is a difference in the movements of the car and the sled. A car travels equal distances in equal intervals of time. And the sled for equal periods of time passes more and more, that is, different segments of the path. The first kind of motion (car motion in our example) is called uniform motion. The second type of movement (the movement of the sled in our example) is called non-uniform movement.

Uniform movement is such a movement in which for any equal intervals of time the body passes the same segments of the path.

Uneven movement is such a movement in which the body passes different segments of the path in equal intervals of time.

Note the words "any equal intervals of time" in the first definition. The fact is that sometimes you can specifically select such time intervals for which the body travels equal paths, but the movement will not be uniform. For example, the end of the second hand of an electronic clock travels the same path every second. But this will not be a uniform movement, since the arrow moves in leaps and bounds.

Rice. 1. An example of uniform motion. This car travels 50 meters every second.

Rice. 2. An example of uneven movement. Accelerating, every second the sledge passes more and more segments of the path

In our examples, the bodies moved in a straight line. But the concepts of uniform and non-uniform motion are equally applicable to the motion of bodies along curvilinear trajectories.

We come across the concept of speed quite often. From the course of mathematics, you are perfectly familiar with this concept, and it is easy for you to calculate the speed of a pedestrian who walked 5 kilometers in 1.5 hours. To do this, it is enough to divide the path traveled by the pedestrian by the time spent on the passage of this path. Of course, this assumes that the pedestrian was moving uniformly.

The speed of uniform motion is called a physical quantity, numerically equal to the ratio of the path traveled by the body to the time spent on passing this path.

The speed is indicated by the letter . Thus, the formula for calculating the speed is:

In the International System of Units, the path, like any length, is measured in meters, and time is measured in seconds. Consequently, speed is measured in meters per second.

In physics, off-system units for measuring speed are also very often used. For example, a car is moving at 72 kilometers per hour (km/h), the speed of light in a vacuum is 300,000 kilometers per second (km/s), a pedestrian is moving at 80 meters per minute (m/min), but the speed of a snail is only 0.006 centimeters per second (cm/s).

Rice. 3. Speed can be measured in various off-system units

It is customary to convert non-systemic units of measurement into the SI system. Let's see how it's done. For example, to convert kilometers per hour to meters per second, you need to remember that 1 km = 1000 m, 1 hour = 3600 s. Then

A similar translation can be carried out with any other off-system unit of measurement.

Is it possible to tell where the car will be if it was moving at a speed of 72 km/h for, say, two hours? It turns out not. Indeed, in order to determine the position of the body in space, it is necessary to know not only the path traveled by the body, but also the direction of its movement. The car in our example could move at a speed of 72 km/h in any direction.

A way out of the situation can be found if the speed is assigned not only a numerical value (72 km/h), but also a direction (north, southwest, along a given X axis, etc.).

Quantities for which not only the numerical value is important, but also the direction are called vector.

Consequently, speed is a vector quantity (vector).

Consider an example. Two bodies are moving towards each other, one with a speed of 10 m/s, the other with a speed of 30 m/s. To depict this movement in the figure, we need to choose the direction of the coordinate axis along which these bodies move (the X axis). You can depict bodies conditionally, for example, in the form of squares. The directions of the speed of bodies are indicated by arrows. The arrows allow you to indicate that the bodies are moving in opposite directions. In addition, the scale is observed in the figure: the arrow depicting the speed of the second body is three times longer than the arrow depicting the speed of the first body, since the numerical value of the speed of the second body is three times greater by the condition.

Rice. 4. Image of the velocity vectors of two bodies

Please note that when we depict the speed symbol next to the arrow that indicates its direction, then a small arrow is placed above the letter: . This arrow indicates that this is a velocity vector (i.e. both the numerical value and the direction of the velocity are indicated). Next to the numbers 10 m/s and 30 m/s, arrows are not shown above the speed symbols. A symbol without an arrow indicates the numerical value of the vector.

So, mechanical movement can be uniform and uneven. The characteristic of movement is speed. In the case of uniform motion, to find the numerical value of the speed, it is enough to divide the path traveled by the body by the time it takes to travel this path. In the SI system, speed is measured in meters per second, but there are many non-SI units of speed. In addition to the numerical value, the speed is also characterized by the direction. That is, speed is a vector quantity. To indicate the speed vector, a small arrow is placed above the speed symbol. To indicate the numerical value of the speed, such an arrow is not placed.

Bibliography

1. Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. – M.: Bustard, 2010.

2. Peryshkin A.V. Collection of problems in physics, grades 7 - 9: 5th ed., stereotype. - M: Publishing house "Exam", 2010.

3. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7 - 9 educational institutions. – 17th ed. - M .: Education, 2004.

1. A single collection of Digital Educational Resources ().

2. A single collection of Digital Educational Resources ().

Homework

Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7 - 9

95. Give examples of uniform motion.
It is very rare, for example, the movement of the Earth around the Sun.

96. Give examples of uneven movement.
The movement of the car, aircraft.

97. A boy slides down a mountain on a sleigh. Can this movement be considered uniform?
No.

98. Sitting in the car of a moving passenger train and watching the movement of an oncoming freight train, it seems to us that the freight train is going much faster than our passenger train was going before the meeting. Why is this happening?
Relative to the passenger train, the freight train moves with the total speed of the passenger and freight trains.

99. The driver of a moving car is in motion or at rest in relation to:
a) roads
b) car seats;
c) gas stations;
d) the sun;
e) trees along the road?
In motion: a, c, d, e
At rest: b

100. Sitting in the car of a moving train, we watch in the window a car that goes forward, then seems to be stationary, and finally moves back. How can we explain what we see?
Initially, the speed of the car is higher than the speed of the train. Then the speed of the car becomes equal to the speed of the train. After that, the speed of the car decreases compared to the speed of the train.

101. The plane performs a "dead loop". What is the trajectory of movement seen by observers from the ground?
ring trajectory.

102. Give examples of the movement of bodies along curved paths relative to the earth.
The movement of the planets around the sun; the movement of the boat on the river; Flight of bird.

103. Give examples of the movement of bodies that have a rectilinear trajectory relative to the earth.
moving train; person walking straight.

104. What types of movement do we observe when writing with a ballpoint pen? Chalk?
Equal and uneven.

105. What parts of the bike with it rectilinear motion describe rectilinear trajectories relative to the ground, and which ones are curvilinear?
Rectilinear: handlebar, saddle, frame.
Curvilinear: pedals, wheels.

106. Why is it said that the Sun rises and sets? What in this case is the reference body?
The reference body is the Earth.

107. Two cars are moving along the highway so that some distance between them does not change. Indicate with respect to which bodies each of them is at rest and with respect to which bodies they move during this period of time.
Relative to each other, the cars are at rest. Vehicles move relative to surrounding objects.

108. Sledges roll down the mountain; the ball rolls down the inclined chute; the stone released from the hand falls. Which of these bodies move forward?
The sled is moving forward from the mountain and the stone released from the hands.

109. A book placed on a table in a vertical position (Fig. 11, position I) falls from the shock and takes position II. Two points A and B on the cover of the book described the trajectories AA1 and BB1. Can we say that the book moved forward? Why?

Do you think you are moving or not when you read this text? Almost every one of you will immediately answer: no, I'm not moving. And it will be wrong. Some might say I'm moving. And they are wrong too. Because in physics, some things are not quite what they seem at first glance.

For example, the concept mechanical movement in physics it always depends on the reference point (or body). So a person flying in an airplane moves relative to the relatives left at home, but is at rest relative to a friend sitting next to him. So, bored relatives or a friend sleeping on his shoulder are, in this case, reference bodies for determining whether our aforementioned person is moving or not.

Definition of mechanical movement

In physics, the definition of mechanical motion studied in the seventh grade is as follows: a change in the position of a body relative to other bodies over time is called mechanical motion. Examples of mechanical movement in everyday life would be the movement of cars, people and ships. Comets and cats. Air bubbles in a boiling kettle and textbooks in a schoolboy's heavy backpack. And every time a statement about the movement or rest of one of these objects (bodies) will be meaningless without indicating the body of reference. Therefore, in life we most often, when we talk about movement, we mean movement relative to the Earth or static objects - houses, roads, and so on.

Trajectory of mechanical movement

It is also impossible not to mention such a characteristic of mechanical movement as a trajectory. A trajectory is a line along which a body moves. For example, footprints in the snow, the footprint of an airplane in the sky, and the footprint of a tear on a cheek are all trajectories. They can be straight, curved or broken. But the length of the trajectory, or the sum of the lengths, is the path traveled by the body. The path is marked with the letter s. And it is measured in meters, centimeters and kilometers, or in inches, yards and feet, depending on what units of measurement are accepted in this country.

Types of mechanical movement: uniform and uneven movement

What are the types of mechanical movement? For example, during a trip by car, the driver moves at different speeds when driving around the city and at almost the same speed when entering the highway outside the city. That is, it moves either unevenly or evenly. So the movement, depending on the distance traveled for equal periods of time, is called uniform or uneven.

Examples of uniform and non-uniform motion

There are very few examples of uniform motion in nature. The Earth moves almost evenly around the Sun, raindrops drip, bubbles pop up in soda. Even a bullet fired from a pistol moves in a straight line and evenly only at first glance. From friction against the air and the attraction of the Earth, its flight gradually becomes slower, and the trajectory decreases. Here in space, a bullet can move really straight and evenly until it collides with some other body. And with uneven movement, things are much better - there are many examples. The flight of a football during a football game, the movement of a lion hunting its prey, the travel of a chewing gum in the mouth of a seventh grader, and a butterfly fluttering over a flower are all examples of uneven mechanical movement of bodies.

Uniform movement- movement along a straight line with a constant (both modulo and direction) speed. With uniform motion, the paths that the body travels in equal intervals of time are also equal.

For a kinematic description of motion, let's place the OX axis along the direction of motion. To determine the displacement of a body during uniform rectilinear motion, one coordinate X is sufficient. The projections of displacement and velocity on the coordinate axis can be considered as algebraic quantities.

Let at time t 1 the body was at a point with coordinate x 1 , and at time t 2 - at a point with coordinate x 2 . Then the projection of the point displacement on the OX axis will be written as:

∆ s \u003d x 2 - x 1.

Depending on the direction of the axis and the direction of movement of the body, this value can be either positive or negative. With rectilinear and uniform motion, the modulus of displacement of the body coincides with the distance traveled. The speed of uniform rectilinear motion is determined by the formula:

v = ∆ s ∆ t = x 2 - x 1 t 2 - t 1

If v > 0 , the body moves along the OX axis in a positive direction. Otherwise - in the negative.

The law of motion of a body in uniform rectilinear motion is described by a linear algebraic equation.

Equation of motion of a body with uniform rectilinear motion

x (t) \u003d x 0 + v t

v = c o n s t ; x 0 - coordinate of the body (point) at time t = 0.

An example of a uniform motion graph is in the figure below.

Here are two graphs describing the movement of bodies 1 and 2. As you can see, body 1 at time t = 0 was at the point x = - 3 .

From point x 1 to point x 2 the body moved in two seconds. The movement of the body was three meters.

∆ t \u003d t 2 - t 1 \u003d 6 - 4 \u003d 2 s

∆s = 6 - 3 = 3 m.

Knowing this, you can find the speed of the body.

v = ∆ s ∆ t = 1.5 m s 2

There is another way to determine the speed: from the graph it can be found as the ratio of the sides BC and AC of the triangle ABC.

v = ∆ s ∆ t = B C A C .

Moreover, the greater the angle that the graph forms with the time axis, the greater the speed. They also say that the speed is equal to the tangent of the angle α.

Similarly, calculations are carried out for the second case of motion. Consider now a new graph depicting movement using line segments. This is the so-called piecewise line graph.

The movement depicted on it is uneven. The speed of the body changes instantly at the breakpoints of the graph, and each segment of the path to new point At the break, the body moves uniformly with a new speed.

From the graph, we see that the speed changed at times t = 4 s, t = 7 s, t = 9 s. Velocity values are also easily found from the graph.

Note that the path and displacement do not coincide for the motion described by the piecewise linear graph. For example, in the time interval from zero to seven seconds, the body traveled a distance equal to 8 meters. The displacement of the body is then zero.

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For example, the concept of mechanical motion in physics always depends on the reference point (or body). So a person flying in an airplane moves relative to the relatives left at home, but is at rest relative to a friend sitting next to him. So, bored relatives or a friend sleeping on his shoulder are, in this case, reference bodies for determining whether our aforementioned person is moving or not.

Definition of mechanical movement

Trajectory of mechanical movement

It is also impossible not to mention such a characteristic of mechanical movement as a trajectory. A trajectory is a line along which a body moves. For example, footprints in the snow, the footprint of an airplane in the sky, and the footprint of a tear on a cheek are all trajectories. They can be straight, curved or broken. But the length of the trajectory, or the sum of the lengths, is the path traveled by the body. The path is marked with the letter s. And it is measured in meters, centimeters and kilometers, or in inches, yards and feet, depending on which units of measurement are accepted in this country.

Types of mechanical movement: uniform and uneven movement

Examples of uniform and non-uniform motion