What is kinematics? This is a subsection of mechanics that studies mathematical and geometric methods for describing the motion of idealized objects. They fall into several categories. The topic of today's article will be aspects that are somehow related to the concept of “kinematics of a point”. We will analyze many issues, but we will start with the most fundamental concepts and explanations of their application in this area.
What objects are considered?
If kinematics is a branch of physics that studies methods for describing the motion of bodies in different-sized spaces, then you need to operate with the bodies themselves, right? To quickly understand what is at stake, you can find a multimedia lesson designed for students. Kinematics is generally easy to understand if you look at its basics. When familiarizing yourself with them, you will notice that in theory there is information that this section of physics studies the laws of motion of material points. Notice how the general definition of objects is given. On the other hand, material points are not the only objects considered by kinematics. This branch of physics studies the principles of motion of absolutely solid bodies as well as ideal fluids. Very often all these three concepts are combined into one, saying simply “idealized objects”. In this case, idealization is necessary for the conventions of calculations and the departure from possible systematic errors. If you look at the definition of a material point, you will notice that the following is written about it: it is a body whose dimensions in the corresponding situation can be neglected. This can be understood as follows: in comparison with the distance traveled, the linear dimensions of the object are negligible.
What is used to describe?
As mentioned earlier, kinematics is a subsection of mechanics that studies how to describe the motion of a point. But if this is so, then to perform such operations some fundamental concepts and principles, like axiomatic, are needed? Yes. And in our case, they are there. First, in kinematics it is a rule to solve problems without looking back at the forces acting on a material point. We all know perfectly well that the body will accelerate or slow down if a certain force acts on it. And kinematics is that subsection that allows you to operate with acceleration. However, the nature of the emerging forces is not considered here. To describe the motion, methods of mathematical analysis, linear and spatial geometry, and algebra are used. Also a certain role is played by coordinate grids and the coordinates themselves. But we will talk about this a little later.
History of creation
The first works on kinematics were compiled by the great scientist Aristotle. It was he who formed some of the fundamental principles of this industry. And even though his work and conclusions contained a certain amount of erroneous opinions and reflections, his works are still of great value to modern physics. The work of Aristotle was subsequently studied by Galileo Galilei. He conducted the famous experiments with the Leaning Tower of Pisa, when he investigated the laws of the free fall of the body. Having studied everything up and down, Galileo subjected Aristotle's thoughts and conclusions to harsh criticism. For example, if the latter wrote that force is the cause of motion, Galileo proved that force is the cause of acceleration, but not that the body will take and will move and will move. According to Aristotle, the body could gain speed only when exposed to a certain force. But we know that this opinion is erroneous, because there is a uniform forward movement. This is once again proved by the kinematics formulas. And we will move on to the next question.
Kinematics. Physics. Basic concepts
This section contains a number of fundamental principles and definitions. Let's start with the main one.
Mechanical movement
Probably, from school, we are trying to lay the idea of what can be considered a mechanical movement. We encounter him daily, hourly, every second. We will consider a mechanical movement a process that occurs in space over time, namely a change in the position of a body. Moreover, relativity is often applied to the process, that is, they say that the position of, say, the first body has changed with respect to the position of the second. Let's imagine that we have two cars on the starting line. The operator's go-ahead or the lights come on - and the cars break off. At the very beginning, a change in position is already taking place. And you can talk about it for a long and tedious: relative to the competitor, relative to the start line, relative to the fixed viewer. But, probably, the idea is clear. The same can be said about two people who go either in one direction or in different directions. The position of each of them relative to another changes at each moment in time.
Reference system
Kinematics, physics - all these sciences use such a fundamental concept as reference systems. In fact, it has a very important role and is almost universally applied in practical problems. Two other important components can be associated with the frame of reference.
Coordinate grid and coordinates
The latter are nothing more than a set of numbers and letters. Using certain logical settings, we can compose our one-dimensional or two-dimensional coordinate grid, which will allow us to solve the simplest problems of changing the position of a material point in a given time interval. Usually in practice a two-dimensional coordinate grid is used with the axes X ("X") and Y ("game"). In three-dimensional space , the Z axis (“zet”) is added, and in one- dimensional space only X is present. Often, gunners and scouts work with coordinates. And for the first time we encounter them even in elementary school, when we begin to draw segments of a certain length. After all, graduation is nothing but the use of coordinates to indicate the beginning and end.
Kinematics grade 10. Quantities
The main quantities that are used in solving problems on the kinematics of a material point are distance, time, speed and acceleration. Let's talk about the last two in more detail. Both of these quantities are vectorial. In other words, they have not only a numerical indicator, but also a certain given direction. The body will move in the direction that the velocity vector is directed. Moreover, one should not forget about the acceleration vector, if we have a case of uneven motion. Acceleration can be directed in the same direction, or in the opposite. If they are aligned, then the body will begin to move faster and faster. If multidirectional, then the object will slow down until it stops. After this, in the presence of acceleration, the body will acquire the opposite speed, that is, it will move in the opposite direction. In practice, all this is very, very clearly shown by kinematics. Grade 10 is precisely the period when this branch of physics is revealed sufficiently.
Formulas
The kinematics formulas are simple enough for both inference and memorization. For example, the formula of the distance traveled over a given time by the object has the following form: S = VoT + aT ^ 2/2. As we see, on the left side we have exactly the same distance. On the right side you can find the initial speed, time and acceleration. The plus sign is only conditional, since acceleration can take a negative scalar value during the process of braking an object. In general, the kinematics of motion implies the existence of one kind of speed, we constantly say “initial”, “final”, “instant”. Instantaneous speed appears at a certain point in time. But if you think so, then the final or initial components are nothing more than its particular manifestations, right? The topic "Kinematics" is probably a favorite among schoolchildren, because it is simple and interesting.
Examples of tasks
In the simplest kinematics, there are whole categories of various problems. All of them are somehow connected with the movement of the material point. For example, in some it is necessary to determine the distance traveled by the body in a certain time. Parameters such as initial velocity and acceleration may be known. Or maybe the task will be set for the student, which will just be the need to express and calculate the acceleration of the body. Let's take an example. The car starts from a static position. What path does he have time to go in 5 seconds if his acceleration is equal to three meters divided by a second squared?
To solve this problem, we need the formula S = VoT + at ^ 2/2. We simply substitute the available data into it. This is acceleration and time. It should be noted that the term Vot goes to zero, since the initial velocity is zero. Thus, we get a numerical answer of 75 meters. That's all, the problem is solved.
Summary
Thus, we figured out the fundamental principles and definitions, gave an example of a formula and talked about the history of the creation of this subsection. Kinematics, the concept of which is introduced in the seventh grade in physics lessons, continues to be constantly improved in the framework of the relativistic (non-classical) section.