Do you think you are moving or not when you read this text? Almost each of you will immediately answer: no, I’m not moving. And he will be wrong. Some might say: moving. And they will also be wrong. Because in physics, some things are not quite what they seem at first glance.
For example, the concept of mechanical motion in physics always depends on a reference point (or body). Thus, a person flying on an airplane moves relative to his relatives remaining at home, but is at rest relative to his friend sitting next to him. So, bored relatives or a friend sleeping on a shoulder are, in in this case, reference bodies to determine 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: the change in the position of a body relative to other bodies over time is called mechanical motion. Examples of mechanical motion in everyday life include the movement of cars, people and ships. Comets and cats. Air bubbles in a boiling kettle and textbooks in a heavy schoolboy’s 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, most often, when we talk about movement, we mean movement relative to the Earth or static objects - houses, roads, and so on.
Mechanical motion path
It is also impossible not to mention such a characteristic of mechanical movement as trajectory. A trajectory is a line along which a body moves. For example, boot prints in the snow, the footprint of an airplane in the sky, and the trace 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 designated by 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, when driving a car, the driver moves at different speeds when driving around the city and at almost the same speed when driving on the highway outside the city. That is, it moves either unevenly or evenly. So the movement, depending on the distance traveled in equal periods of time, is called uniform or uneven.
Examples of uniform and uneven movement
There are very few examples of uniform motion in nature. The Earth moves almost uniformly around the Sun, raindrops drip, bubbles float in the soda. Even a bullet fired from a pistol moves straight and evenly only at first glance. Due to friction with the air and the gravity of the Earth, its flight gradually becomes slower and its trajectory decreases. In space, a bullet can move really straight and evenly until it collides with some other body. But with uneven movement the situation is much better - there are many examples. The flight of a ball while playing football, the movement of a lion hunting prey, the travel of 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.
Topic: Interaction of bodies
Lesson:Uniform and uneven movement. Speed
Let's 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 a car and a sled. A car covers equal distances in equal periods of time. And the sleds cover larger and larger distances at equal intervals of time, that is, different sections of the path. The first type 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 uneven movement.
Uniform motion is a motion in which, in any equal intervals of time, the body covers equal distances.
Uneven motion is a motion in which a body passes through different segments of a path in equal intervals of time.
Notice the words “any equal periods of time” in the first definition. The fact is that sometimes you can specially select such periods of time during which the body travels equal distances, but the movement will not be uniform. For example, the end of the second hand of a digital watch travels the same path every second. But this will not be a uniform movement, since the arrow moves spasmodically, with stops.
Rice. 1. An example of uniform motion. Every second this car travels 50 meters
Rice. 2. An example of uneven movement. As the sled accelerates, it travels longer and longer distances every second.
In our examples, the bodies moved in a straight line. But the concepts of uniform and non-uniform motion are equally applicable to the movement of bodies along curved trajectories.
We come across the concept of speed quite often. From your mathematics course, you are very 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 walking this path. Of course, this assumes that the pedestrian moved 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 traveling this path.
Speed is indicated by the letter . Thus, the formula for calculating speed is:
IN International system units, the path, like any length, is measured in meters, and time - in seconds. Hence, speed is measured in meters per second.
In physics, non-systemic units of measurement of speed are also very often used. For example, a car moves at a speed of 72 kilometers per hour (km/h), the speed of light in a vacuum is 300,000 kilometers per second (km/s), the speed of a pedestrian is 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 non-system units
Non-system units of measurement are usually converted to the SI system. Let's look at how this is 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 non-systemic unit of measurement.
Is it possible to tell where a car will be if it was moving at a speed of 72 km/h for, for example, two hours? It turns out not. Indeed, in order to determine the position of a 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 travel at a speed of 72 km/h in any direction.
A way out of the situation can be found if we assign the speed not only a numerical value (72 km/h), but also a direction (to the north, to the southwest, along a given X axis, etc.).
Quantities for which not only the numerical value, but also the direction are important are called vector quantities.
Hence, speed – vector quantity (vector).
Let's look at 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 select the direction of the coordinate axis along which these bodies move (X axis). Bodies can be depicted conventionally, for example, in the form of squares. The directions of speed of bodies are indicated using arrows. Arrows allow you to indicate that bodies are moving in opposite directions. In addition, the figure is scaled: 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.
Rice. 4. Image of the velocity vectors of two bodies
Please note that when we draw a speed symbol next to an arrow indicating its direction, a small arrow is placed above the letter: . This arrow indicates that we are talking about the velocity vector (i.e., both the numerical value and the direction of the velocity are indicated). There are no arrows shown next to the numbers 10 m/s and 30 m/s above the speed symbols. The 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 sufficient 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-system units of speed. In addition to its numerical value, speed is also characterized by direction. That is, speed is a vector quantity. To indicate the velocity vector, a small arrow is placed above the velocity symbol. To indicate the numerical value of speed, such an arrow is not placed.
Bibliography
1. Peryshkin A.V. Physics. 7th grade – 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 problems in physics for grades 7 – 9 of general education institutions. – 17th ed. – M.: Education, 2004.
1. Unified collection of Digital Educational Resources ().
2. Unified collection of Digital Educational Resources ().
Homework
Lukashik V.I., Ivanova E.V. Collection of physics problems for grades 7 – 9
95. Give examples of uniform motion.
It occurs very rarely, for example, the movement of the Earth around the Sun.
96. Give examples of uneven movement.
Movement of a car, plane.
97. A boy slides down a mountain on a sled. Can this movement be considered uniform?
No.
98. Sitting in the carriage of a moving passenger train and observing 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 it met. Why is this happening?
Relative passenger train, freight train moves with the total speed of passenger and freight trains.
99. The driver of a moving car is in motion or at rest relative to:
a) roads;
b) car seats;
c) gas stations;
d) the Sun;
e) trees along the road?
In motion: a, c, d, d
At rest: b
100. Sitting in the carriage of a moving train, we watch through the window a car that goes forward, then seems motionless, and finally moves backward. How to 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 this, the speed of the car decreases compared to the speed of the train.
101. The plane performs a “dead loop”. What trajectory do observers on the ground see?
A circular path.
102. Give examples of the movement of bodies along curved trajectories relative to the ground.
The movement of planets around the Sun; boat movement on the river; Flight of bird.
103. Give examples of the motion of bodies that have a rectilinear trajectory relative to the ground.
Moving train; man walking straight.
104. What types of movement do we observe when writing with a ballpoint pen? Chalk?
Uniform and uneven.
105. Which parts of a bicycle, when moving in a straight line, describe rectilinear trajectories relative to the ground, and which parts – curved ones?
Straight-line: handlebar, saddle, frame.
Curvilinear: pedals, wheels.
106. Why do they say that the Sun rises and sets? What is the reference body in this case?
The reference body is considered to be the Earth.
107. Two cars are moving along a highway so that some distance between them does not change. Indicate relative to which bodies each of them is at rest and relative to which bodies they are moving during this period of time.
The cars are at rest relative to each other. Cars move relative to surrounding objects.
108. The sled is rolling down the mountain; the ball rolls down an inclined chute; The stone released from the hands falls. Which of these bodies are moving forward?
A sled moving forward from the mountain and a stone released from the hands.
109. A book placed on a table in a vertical position (Fig. 11, position I) falls from a push and takes position II. Two points A and B on the binding 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 each of you will immediately answer: no, I’m not moving. And he will be wrong. Some might say: moving. And they will also be wrong. Because in physics, some things are not quite what they seem at first glance.
For example, the concept of mechanical motion in physics always depends on a reference point (or body). Thus, a person flying on an airplane moves relative to his relatives remaining at home, but is at rest relative to his friend sitting next to him. So, bored relatives or a friend sleeping on a shoulder are, in this case, bodies of reference 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: the change in the position of a body relative to other bodies over time is called mechanical motion. Examples of mechanical motion in everyday life include the movement of cars, people and ships. Comets and cats. Air bubbles in a boiling kettle and textbooks in a heavy schoolboy’s 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, most often, when we talk about movement, we mean movement relative to the Earth or static objects - houses, roads, and so on.
Mechanical motion path
It is also impossible not to mention such a characteristic of mechanical movement as trajectory. A trajectory is a line along which a body moves. For example, boot prints in the snow, the footprint of an airplane in the sky, and the trace 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 designated by 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, when driving a car, the driver moves at different speeds when driving around the city and at almost the same speed when driving on the highway outside the city. That is, it moves either unevenly or evenly. So the movement, depending on the distance traveled in equal periods of time, is called uniform or uneven.
Examples of uniform and uneven movement
There are very few examples of uniform motion in nature. The Earth moves almost uniformly around the Sun, raindrops drip, bubbles float in the soda. Even a bullet fired from a pistol moves straight and evenly only at first glance. Due to friction with the air and the gravity of the Earth, its flight gradually becomes slower and its trajectory decreases. In space, a bullet can move really straight and evenly until it collides with some other body. But with uneven movement the situation is much better - there are many examples. The flight of a ball while playing football, the movement of a lion hunting prey, the travel of 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 motion is motion along a straight line with a constant (both in magnitude and in direction) speed. With uniform motion, the paths that the body travels in equal periods of time are also equal.
For a kinematic description of the movement, we place the OX axis along the direction of movement. To determine the displacement of a body during uniform rectilinear motion, one X coordinate is sufficient. Projections of displacement and velocity onto the coordinate axis can be considered as algebraic quantities.
Let at the moment of time t 1 the body be at a point with coordinate x 1 , and at the moment of time t 2 - at a point with coordinate x 2 . Then the projection of the point’s movement on the OX axis will be written in the form:
∆ s = 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 module of movement 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 the positive direction. Otherwise - in the negative.
The law of motion of a body during uniform rectilinear motion is described by a linear algebraic equation.
Equation of body motion for uniform rectilinear motion
x (t) = 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 graph of uniform motion is shown in the figure below.
Here are two graphs describing the movement of bodies 1 and 2. As we can see, body 1 at time t = 0 was at point x = - 3.
The body moved from point x 1 to point x 2 in two seconds. The movement of the body was three meters.
∆ t = t 2 - t 1 = 6 - 4 = 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 speed: from the graph it can be found as the ratio of sides BC and AC of 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. It is also said that the speed is equal to the tangent of the angle α.
The calculations are carried out similarly for the second case of motion. Let us now consider a new graph depicting motion using line segments. This is the so-called piecewise linear graph.
The movement depicted on it is uneven. The speed of the body changes instantly at the break points of the graph, and each segment of the path to a new break point 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. The speed values are also easy to find from the graph.
Note that path and displacement are not the same for motion described by a piecewise linear graph. For example, in the time interval from zero to seven seconds the body traveled a distance of 8 meters. The displacement of the body in this case is zero.
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