The topic of our article today will be the kinematics of the material point. What is this all about? What concepts appear in it and what definition should be given to this term? We will try to answer these and many other questions today.
Definition and Concept
The kinematics of a material point is nothing more than a subsection of physics called “mechanics”. She, in turn, studies the laws of motion of certain bodies. Kinematics of the material point is also engaged in this task, but does not do it in a general way. In fact, this subsection studies methods that allow us to describe the motion of bodies. Moreover, only the so-called idealized bodies are suitable for research. These include: material point, absolutely solid body and ideal gas. Let's consider the concepts in more detail. We all know from school that the material point is usually called the body, the size of which in a given situation can be neglected. By the way, the kinematics of the translational motion of a material point for the first time begins to appear in textbooks of the seventh grade in physics. This is the simplest industry, so it is most convenient to start acquaintance with science with its help. A separate issue is what are the elements of the kinematics of the material point. There are a lot of them, and conditionally they can be divided into several levels having different difficulty for understanding. If we talk, for example, about the radius vector, then, in principle, there is nothing prohibitively difficult in its definition. However, agree that it will be much easier for a student to understand it than a student in secondary or high school. And to be honest, there is no need to explain the features of this term to high school students.
A brief history of the creation of kinematics
Many, many years ago, the great scientist Aristotle devoted the lion's share of his free time to the study and description of physics as a separate science. In particular, he worked on kinematics, trying to present its main theses and concepts, one way or another applied in attempts to solve practical and even everyday problems. Aristotle gave initial ideas about what are the elements of the kinematics of the material point. His works and works are very valuable to all mankind. Nevertheless, he made a considerable number of mistakes in his conclusions, and the reason was certain errors and miscalculations. The work of Aristotle at one time became interested in another scientist - Galileo Galilei. One of the fundamental theses put forward by Aristotle, said that the movement of the body occurs only if it acts on some kind of force, determined by intensity and direction. Galileo proved that this is a mistake. The force will affect the parameter of the speed of movement, but no more. The Italian showed that force is the cause of acceleration, and it can only arise in a mutual relationship with it. Galileo Galilei also paid considerable attention to the study of the free fall process , deriving the corresponding laws. Probably, everyone remembers his famous experiments that he conducted on the Leaning Tower of Pisa. In his work, the physicist Ampère also used the basics of kinematic solutions.
Source concepts
As mentioned earlier, kinematics is exploring ways to describe the motion of idealized objects. Moreover, in practice, the basics of mathematical analysis, ordinary algebra and geometry can be applied. But what concepts (namely concepts, and not definitions and parametric quantities) underlie this subsection of physics? First, everyone should clearly understand that the kinematics of the translational motion of a material point considers motion without taking into account force indicators. That is, to solve the corresponding problems, we do not need formulas related to force. It is not taken into account by kinematics, no matter how many there are - one, two, three, at least several hundred thousand. Nevertheless, the existence of acceleration is still envisaged. In a number of problems, the kinematics of the motion of a material point requires that the magnitude of the acceleration be determined. However, the causes of this phenomenon (that is, the forces and their nature) are not considered, but omitted.
Classification
We found that kinematics explores and applies methods for describing the motion of bodies without regard to the forces acting on them. By the way, another task of mechanics, which is called dynamics, is already engaged in such a task. Newton’s laws are already applied there , which allow in practice to determine quite a few parameters with a small amount of known initial data. The basic concepts of the kinematics of a material point are space and time. And in connection with the development of science both in general and in this field, the question arose of the advisability of using such a combination.
From the very beginning, there was classical kinematics. We can say that it is characteristic not only of the presence of both time and space intervals, but also of their independence from the choice of a particular reference frame. By the way, we will talk about this a little later. Now we’ll just explain what we are talking about. The spatial gap in this case will be considered the interval, the time - the time interval. Everything seems to be clear. So, these gaps in classical kinematics will be considered absolute, invariant, in other words, independent of the transition from one reference frame to another. Whether it is relativistic kinematics. In it, the gaps during the transition between reference systems can vary. It would even be more correct to say that they cannot, but they must, probably. Due to this, the simultaneity of two random events also becomes relative and is subject to special consideration. That is why in relativistic kinematics two concepts - space and time - are combined into one.
Kinematics of the material point: speed, acceleration and other quantities
In order to at least a little understanding of this subsection of physics, it is necessary to navigate in the most basic concepts, to know the definitions and to imagine what this or that quantity is in general terms. There is nothing complicated in this, in fact, everything is very easy and simple. Let's consider, for starters, the basic concepts used in kinematics problems.
Traffic
We consider a mechanical movement a process during which a particular idealized object changes its position in space. Moreover, we can say that the change occurs relative to other bodies. It is necessary to take into account the fact that at the same time the establishment of a certain time interval between two events takes place. For example, it will be possible to distinguish a certain interval formed during the time elapsed between the time when the body arrived from one position to another. We also note that the bodies in this case can and will interact with each other, according to the general laws of mechanics. This is exactly what the kinematics of a material point most often operates on. The reference system is the following concept, which is inextricably linked with it.
Coordinates
They can be called ordinary data, which allow you to determine the position of the body at a given moment in time. Coordinates are inextricably linked with the concept of a reference frame, as well as a coordinate grid. Most often a combination of letters and numbers.
Radius vector
From the name it should already be clear what it is. Nevertheless, we’ll talk more about this in more detail. If a point moves along a certain trajectory, and we know the beginning of a particular reference frame, then we can draw a radius vector at any time. It will connect the initial position of the point with the instantaneous or final.
Trajectory
It will be called a continuous line, which is drawn as a result of the movement of a material point in a particular reference system.
Speed (both linear and angular)
This is a value that can tell about how quickly the body goes through a certain distance interval.
Acceleration (both angular and linear)
Shows according to what law and how intensively the speed parameter of the body changes.
Perhaps they are the basic elements of the kinematics of the material point. It should be noted that both speed and acceleration are vector quantities. And this means that they not only have some indicative value, but also a certain direction. By the way, they can be directed both in one direction or in opposite directions. In the first case, the body will accelerate, in the second - slow down.
Simple tasks
The kinematics of the material point (speed, acceleration and distance at which are almost fundamental concepts) does not even include a huge number of tasks, but many of their various categories. Let's try to solve a rather simple task to determine the distance traveled by the body.
Suppose the conditions that we have on hand are as follows. Racer car is on the starting line. The operator gives the go-ahead with the flag, and the car abruptly breaks off. Determine if she can set a new record in the competition of riders, if the distance equal to one hundred meters, the next leader passed in 7.8 seconds. Acceleration of the car to take equal to 3 meters, divided by the second squared.
So, how to solve a similar problem? It is quite interesting, since we are not required to have a “dry” definition of certain parameters. It is brightened up by turns and a certain situation, which diversifies the process of solving and searching for indicators. But what should we be guided before we approach the task?
1. The kinematics of the material point involves the use in this case of acceleration.
2. A solution is proposed using the distance formula, since its numerical value appears in conditions.
The task is actually solved simply. To do this, we take the distance formula: S = VoT + (-) AT ^ 2/2. What is the point? We need to find out how long the rider will go the designated distance, and then compare the figure with the record to find out if he will beat him or not. To do this, we select the time, we obtain the formula for it: AT ^ 2 + 2VoT - 2S. This is nothing but a quadratic equation. But the car breaks down, which means that the initial speed will be 0. When solving the equation, the discriminant will be equal to 2400. To find the time, you need to extract the root. Make up to the second decimal place: 48.98. Find the root of the equation: 48.98 / 6 = 8.16 seconds. It turns out that the rider will not be able to break the existing record.