Ticket No. 1
1.Mechanical movement is a change in the position of a body in space over time relative to other bodies.
Of all the diverse forms of motion of matter, this type of motion is the simplest.
For example: moving the clock hand around the dial, people walking, tree branches swaying, butterflies fluttering, an airplane flying, etc.
Determining the position of the body at any given time is the main task of mechanics.
The movement of a body in which all points move equally is called translational.
A material point is a physical body, the dimensions of which under given conditions of motion can be neglected, assuming that all its mass is concentrated at one point.
A trajectory is a line that a material point describes during its movement.
Path is the length of the trajectory of a material point.
Displacement is a directed straight line segment (vector) connecting the initial position of the body with its subsequent position.
A reference system is: a reference body, an associated coordinate system, as well as a device for counting time.
An important feature of fur. movement is its relativity.
Relativity of motion– this is the movement and speed of a body relative to different reference systems are different (for example, a person and a train). The speed of a body relative to a fixed coordinate system is equal to the geometric sum of the speed of the body relative to a moving system and the speed of a moving coordinate system relative to a fixed one. (V 1 is the speed of a person on the train, V 0 is the speed of the train, then V = V 1 + V 0).
The classical law of addition of velocities is formulated as follows: the speed of movement of a material point in relation to the reference system, taken as a stationary one, is equal to the vector sum of the speeds of movement of the point in the moving system and the speed of movement of the moving system relative to the stationary one.
The characteristics of mechanical motion are interconnected by basic kinematic equations.
s =v 0 t + at 2 / 2;
v = v 0 + at .
Let us assume that a body is moving without acceleration (an airplane on a route), its speed does not change for a long time, A= 0, then the kinematic equations will look like: v = const, s =vt .
Movement in which the speed of a body does not change, i.e., the body moves by the same amount over any equal periods of time, is called uniform linear movement.
During launch, the speed of the rocket increases rapidly, i.e. acceleration A>Oh, a == const.
In this case, the kinematic equations look like this: v = V 0 + at , s = V 0 t + at 2 / 2.
With such movement, speed and acceleration have the same directions, and the speed changes equally over any equal intervals of time. This type of movement is called uniformly accelerated.
When braking a car, the speed decreases equally over any equal periods of time, the acceleration is less than zero; since the speed decreases, the equations take the form : v = v 0 + at , s = v 0 t - at 2 / 2 . This type of motion is called uniformly slow.
2.Everyone can easily divide bodies into solid and liquid. However, this division will only be based on external signs. In order to find out what properties solids have, we will heat them. Some bodies will begin to burn (wood, coal) - these are organic substances. Others will soften (resin) even at low temperatures - these are amorphous. Still others will change their state when heated as shown in the graph (Fig. 12). These are crystalline bodies. This behavior of crystalline bodies when heated is explained by their internal structure. Crystal bodies- these are bodies whose atoms and molecules are arranged in a certain order, and this order is preserved over a fairly large distance. The spatial periodic arrangement of atoms or ions in a crystal is called crystal lattice. The points of the crystal lattice at which atoms or ions are located are called nodes crystal lattice. Crystalline bodies are either single crystals or polycrystals. Monocrystal has a single crystal lattice throughout its entire volume. Anisotropy single crystals lies in the dependence of their physical properties on direction. Polycrystal It is a combination of small, differently oriented single crystals (grains) and does not have anisotropy of properties. 
Most solids have a polycrystalline structure (minerals, alloys, ceramics).
The main properties of crystalline bodies are: certainty of melting point, elasticity, strength, dependence of properties on the order of arrangement of atoms, i.e., on the type of crystal lattice.
Amorphous are substances that have no order in the arrangement of atoms and molecules throughout the entire volume of this substance. Unlike crystalline substances, amorphous substances isotropic. This means that the properties are the same in all directions. The transition from an amorphous state to a liquid occurs gradually; there is no specific melting point. Amorphous bodies do not have elasticity, they are plastic. Various substances are in an amorphous state: glass, resins, plastics, etc.
Elasticity- the property of bodies to restore their shape and volume after the cessation of external forces or other causes that caused the deformation of bodies. For elastic deformations, Hooke’s law is valid, according to which elastic deformations are directly proportional to the external influences causing them, where is mechanical stress,
- relative elongation, E - Young's modulus (modulus of elasticity). Elasticity is due to the interaction and thermal movement of the particles that make up the substance.
Plastic- the property of solids under the influence of external forces to change their shape and size without collapsing and to retain residual deformations after the action of these forces ceases
Ticket#2
|
Ticket No. 3
The position of a point in space can also be determined by a radius vector drawn from a certain origin to a given point (Fig. 2). In this case, to describe the movement you need to set:
a) origin of the radius vector r;
b) start of time t;
c) law of motion of a point r(t).
Since specifying one vector quantity r is equivalent to specifying its three projections x, y, z on the coordinate axes; it is easy to move from the vector method to the coordinate one. If we introduce unit vectors i, j, k (i= j = k= 1), directed respectively along the x, y and z axes (Fig. 2), then, obviously, the law of motion can be represented in the form *)
r(t) = x(t) i+y(t) j+z(t) k. (1)
The advantage of the vector form of recording over the coordinate form is compactness (instead of three quantities one operates with one) and often greater clarity.
To solve the first part of the problem, we will use the coordinate method, directing the x-axis of the Cartesian system along the rod and choosing its origin at point A. Since the inscribed AMS is a straight line (as based on the diameter),x(t) = AM = 2Rcos = 2Rcost,
where R is the radius of the semicircle. The resulting law of motion is called a harmonic oscillation (this oscillation will obviously continue only until the moment the ring reaches point A).
We will solve the second part of the problem using the natural method. Let us choose the positive direction of counting the distance along the trajectory (semicircle AC) counterclockwise (Fig. 3), and zero coinciding with point C. Then the length of the arc SM as a function of time will give the law of motion of point M
S(t) = R2 = 2Rt,
those. the ring will move uniformly around a circle of radius R with an angular velocity of 2. As is clear from the examination,
the zero of the time count in both cases corresponded to the moment when the ring was at point C.
Ticket No. 4
Coordinate method. We will set the position of the point using coordinates ( Fig.1.7). If a point moves, then its coordinates change over time. Since the coordinates of a point depend on time, we can say that they are functions time.
Mathematically, this is usually written in the form
Equations (1.1) are called kinematic equations of motion of a point, written in coordinate form. If they are known, then for each moment in time we will be able to calculate the coordinates of the point, and therefore its position relative to the selected reference body. The form of equations (1.1) for each specific movement will be quite specific. The line along which a point moves in space is called trajectory . Depending on the shape of the trajectory, all movements of a point are divided into rectilinear and curvilinear. If the trajectory is a straight line, the movement of the point is called straightforward, and if the curve is curvilinear.
Good afternoon Speed is relative because it depends on the chosen frame of reference. Example: a car is driving at a certain speed along the street. There is a house next to it and a cyclist is riding along the sidewalk. So, relative to the house the car moves at the same speed, but if we consider the speed of the car relative to the moving cyclist, then it will be different (because the cyclist is also moving).
Inna
In the simulator, I didn’t understand how to solve the problem: “A long cord moves along a smooth horizontal surface to the left at a speed of 2 m/s. Point A begins to move to the right at a speed of 1 m/s. How long will the part of the cord move to the right after 3 s?” Help with a solution :(
Teacher's answer: Postny Alexey Vitalievich
Consider the movement of one end relative to the other. It turns out that they are approaching at a speed of 3 m/s. Next, calculate how much the distance between the ends of the cord will decrease in 3 seconds. Then make a drawing: at the beginning of the movement and after 3 seconds. This will help you find the correct answer.
User 372914
When you explained the topic, 2 points were missed (1. You did not graphically show why v-banks are taken with a minus sign 2. An experiment with the chalk-ruler-board trajectory (it was not clearly explained why the chalk moves in a straight line relative to the ruler. Because our school is aimed at middle schoolers student, I would like students who are below average to be able to fully understand what you are saying. In general, the resource is very good, and you, as a physics teacher, are the best on this resource. I am not talking about knowledge, but about the methodology of teaching the subject. With great respect!
Teacher's answer: Postny Alexey Vitalievich
Thank you very much for your feedback! As for the comments, indeed, the moment with speed relative to the shore is not graphically highlighted, but it is explained verbally. Therefore, if you look carefully, you can understand why the “-” sign is taken. As for the chalk and ruler, no explanation is provided due to its intuitive understanding: ruler straight, which means the chalk moves along it directly linear.
User 362168
I would like to ask for a solution to the problem: While going up the river, a fisherman dropped a wooden hook from his boat as he passed under a bridge. Half an hour later, he discovered the loss and, turning back, caught up with the gaff at a distance of 2.7 km from the bridge. Find the speed of the river current, assuming the boat's speed relative to the water remains constant.
Teacher's answer: Postny Alexey Vitalievich
To solve the problem, first consider the motion relative to the river. The hook was at rest relative to the water, and the fisherman swam in one direction for half an hour, then returned (accordingly, another half hour passed, because the hook was at rest). That is, just an hour. Next consider the motion relative to the bridge. In the indicated hour, the hook floated 2.7 km.
Lukichev Mikhail
“What is the speed of the ball relative to the Earth after an absolutely elastic impact on the wall? (wall speed U = 2 m/s, ball speed before impact v = 3 m/s).” Tell me why the correct answer is 7 m/s and not 5 m/s, because... Is the impact elastic and the velocities are adding up?..
Teacher's answer: Postny Alexey Vitalievich
When solving the problem, you need to consider the speed of the ball relative to the wall. Then take into account that with an absolutely elastic impact, the modulus of the ball’s velocity will not change, but the direction will change to the opposite. Then again go to the reference system associated with the Earth. How to switch to a reference system associated with a moving body is described in detail in the lesson. Do all the above and you will get the correct answer. And the statement that during an absolutely elastic impact the velocities of the bodies add up is incorrect.
Islamia
Hello! One point is not entirely clear. The notes contain the following words: “So, movement in two reference systems. Look at Fig. 2. It can be noted that the chalk moves along the ruler in a straight line, therefore, the trajectory will be straight. And when we consider the movement - the chalk in the plane of the board, then the trajectory will be a curved line. In this case, it is easiest to talk about the distance traveled, since the distance traveled is the length of the trajectory, therefore, in the reference system associated with the ruler, the distance traveled will be less than the path traveled in the plane of the board. As can be seen from the experiment, both the trajectory of the body’s movement and the distance traveled depend on the choice of reference system.” I can’t understand why the chalk moves along the ruler not curvilinearly, but rectilinearly?
What is Landau's theory of relativity Lev Davidovich
Speed has a limit
Speed has a limit
Before World War II, airplanes flew at speeds slower than the speed of sound, and now “supersonic” airplanes have been built. Radio waves travel at the speed of light. But is it not possible to set ourselves the task of creating “superluminal” telegraphy in order to transmit signals at a speed even greater than the speed of light? This turns out to be impossible.
In fact, if it were possible to transmit signals at an infinite speed, then we would be able to unambiguously establish the simultaneity of two events. We would say that these events occurred simultaneously if the infinitely fast signal about the first event arrived simultaneously with the signal about the second event. Thus, simultaneity would acquire an absolute character, independent of the movement of the laboratory to which this statement refers.
But since the absoluteness of time is refuted by experience, we conclude that the transmission of signals cannot be instantaneous. The speed of transmission of action from one point in space to another cannot be infinite, in other words, it cannot exceed a certain finite value called the maximum speed.
This maximum speed coincides with the speed of light.
In fact, according to the principle of relativity of motion, in all laboratories moving relative to each other (rectilinearly and uniformly) the laws of nature must be the same. The statement that no speed can exceed a given limit is also a law of nature, and therefore the value of the limit speed must be exactly the same in different laboratories. As we know, the speed of light differs in these same properties.
Thus, the speed of light is not just the speed of propagation of some natural phenomenon. It plays the most important role of top speed.
The discovery of the existence of a world of extreme speed is one of the greatest triumphs of human thought and the experimental capabilities of mankind.
A physicist of the last century could not figure out that there is a limiting speed in the world, that the fact of its existence can be proven. Moreover, even if in his experiments he had stumbled upon the presence of a limiting speed in nature, he could not be sure that this was a law of nature, and not a consequence of limited experimental capabilities that could be eliminated in the process of further development of technology.
The principle of relativity shows that the existence of maximum speed lies in the very nature of things. Expecting that the progress of technology will make it possible to achieve speeds exceeding the speed of light is as ridiculous as believing that the absence of points on the earth’s surface separated by a distance of more than 20 thousand kilometers is not a geographical law, but the limitations of our knowledge, and hoping that according to As geography develops, it will be possible to find points on Earth that are even more distant from each other.
The speed of light plays such an exceptional role in nature because it is the maximum speed for the propagation of anything. Light either precedes any other phenomenon, or, in extreme cases, arrives simultaneously with it.
If the Sun were to split into two parts and form a double star, then, of course, the Earth's motion would change.
A physicist of the last century, who did not know about the existence of a limiting speed in nature, would certainly have assumed that the change in the Earth's motion would have occurred instantly following the splitting of the Sun. Meanwhile, it would have taken eight minutes for light to travel from the broken Sun to the Earth.
In reality, however, the change in the Earth's motion will also begin only eight minutes after the Sun breaks apart, and until that moment the Earth will move as if the Sun had not broken apart. And in general, not a single event that happened with the Sun or on the Sun will have any effect on either the Earth or its movement before the expiration of these eight minutes.
The finite speed of signal propagation, of course, does not deprive us of the opportunity to establish the simultaneity of two events. To do this, you just need to take into account the signal delay time, as is usually done.
However, this method of establishing simultaneity is already completely compatible with the relativity of this concept. In fact, to subtract the delay time, we will have to divide the distance between the places where the events occurred by the speed of propagation of the signal. On the other hand, while still discussing the issue of sending letters from the Moscow-Vladivostok express, we saw that the very place in space is also a very relative concept!
From the book The Newest Book of Facts. Volume 3 [Physics, chemistry and technology. History and archaeology. Miscellaneous] author Kondrashov Anatoly Pavlovich From the book What is the Theory of Relativity author Landau Lev Davidovich From the book Evolution of Physics author Einstein Albert From the book Physics at every step author Perelman Yakov Isidorovich From the book Movement. Heat author Kitaygorodsky Alexander Isaakovich From the book Tweets about the Universe by Chaun Marcus From the book The Prevalence of Life and the Uniqueness of Mind? author Mosevitsky Mark IsaakovichDoes every statement have meaning? Obviously not. Even if you take completely meaningful words and combine them in full accordance with the rules of grammar, even then the result can be complete nonsense. For example, the statement “this water is triangular” is difficult to assign any
From the book Hyperspace by Kaku MichioAnd speed is relative! From the principle of relativity of motion it follows that talking about the rectilinear and uniform motion of a body with a certain speed, without indicating which of the resting laboratories the speed is measured against, makes as little sense as saying
From the book The King's New Mind [On computers, thinking and the laws of physics] by Penrose RogerSpeed of light In Galileo's "Conversations on the Two New Sciences" we find a conversation between a teacher and his students about the speed of light: Sagredo: But what kind and what degree of speed should this movement of light be? Should we consider it instantaneous or taking place in time, as
From the book Who the Apple Fell On author Kesselman Vladimir SamuilovichSpeed of sound Have you ever watched a woodcutter cutting down a tree from a distance? Or perhaps you have watched a carpenter working in the distance, hammering in nails? You may have noticed a very strange thing: the blow does not occur when the ax crashes into a tree or
From the author's bookSpeed of sound There is no need to be afraid of thunder after lightning has flashed. You've probably heard about this. Why? The fact is that light travels incomparably faster than sound—almost instantly. Thunder and lightning occur at the same moment, but we see lightning in
From the author's book35. Does the Sun have a surface? The Sun is a giant glowing ball of gas, so it does not have a solid surface like the Earth. But, of course, it seems so at first glance. Why? The solar “surface”, or photosphere, to which the sun’s rays have great difficulty penetrating
From the author's book From the author's bookWarp speed 5 Does this mean that black holes can be used to travel throughout the galaxy, like in Star Trek and other science fiction films? As we saw earlier, the curvature of a particular space is determined by the amount of matter-energy,
From the author's book From the author's book“Interest has no conscience” Voltaire in his “English Letters” reports that in 1726, when he was in England, he happened to be present at a scientific dispute, the participants of which discussed the question: who was the greatest of people - Caesar, Alexander, Timur or Cromwell ?
Questions.
1. What do the following statements mean: speed is relative, trajectory is relative, path is relative?
This means that these quantities (speed, trajectory and path) for movement differ depending on which frame of reference the observation is made from.
2. Show with examples that speed, trajectory and distance traveled are relative quantities.
For example, a person stands motionless on the surface of the Earth (there is no speed, no trajectory, no path), but at this time the Earth rotates around its axis, and therefore the person, relative to, for example, the center of the Earth, moves along a certain trajectory (in a circle), moves and has a certain speed.
3. Briefly formulate what the relativity of motion is.
The movement of a body (speed, path, trajectory) is different in different reference systems.
4. What is the main difference between the heliocentric system and the geocentric one?
In the heliocentric system the body of reference is the Sun, and in the geocentric system it is the Earth.
5. Explain the change of day and night on Earth in the heliocentric system (see Fig. 18).
In the heliocentric system, the cycle of day and night is explained by the rotation of the Earth.
Exercises.
1. Water in a river moves at a speed of 2 m/s relative to the shore. A raft is floating along the river. What is the speed of the raft relative to the shore? regarding the water in the river?
The speed of the raft relative to the shore is 2 m/s, relative to the water in the river - 0 m/s.
2. In some cases, the speed of a body may be the same in different reference systems. For example, a train moves at the same speed in the frame of reference associated with the station building and in the frame of reference associated with a tree growing by the road. Doesn't this contradict the statement that speed is relative? Explain your answer.
If both bodies with which the reference systems of these bodies are associated remain motionless relative to each other, then they are associated with a third reference system - the Earth, relative to which the measurements take place.
3. Under what condition will the speed of a moving body be the same relative to two reference systems?
If these reference systems are stationary relative to each other.
4. Thanks to the daily rotation of the Earth, a person sitting on a chair in his house in Moscow moves relative to the Earth’s axis at a speed of approximately 900 km/h. Compare this speed with the initial speed of the bullet relative to the gun, which is 250 m/s.
5. A torpedo boat moves along the sixtieth parallel of southern latitude at a speed of 90 km/h relative to land. The speed of the Earth's daily rotation at this latitude is 223 m/s. What is the speed of the boat relative to the earth's axis in (SI) and where is it directed if it is moving east? to the west?
