Everyday experience shows that immovable bodies can be set in motion, while movable ones can be stopped. We are constantly doing something, the world is bustling around, the sun is shining ... But where does man, animals, and nature as a whole take strength to do this work? Does mechanical movement disappear without a trace? Will one body begin to move without changing the motion of another? We will talk about all this in our article.
Energy concept
For the operation of engines that give movement to cars, tractors, diesel locomotives, aircraft, you need fuel, which is a source of energy. Electric motors give movement to machines with the help of electricity. Due to the energy of water falling from a height, hydroturbines turn around, connected to electric machines that produce electric current. In order to exist and work, man also needs energy. They say that in order to do some work, energy is needed. What is energy?
- Observation 1. Raise the ball above the ground. While he is in a state of calm, mechanical work is not performed. Let him go. Under the influence of gravity, the ball falls to the ground from a certain height. During the fall of the ball, mechanical work is performed.
- Observation 2. Close the spring, fix it with a thread and put a weight on the spring. Let’s set the thread on fire, the spring will straighten and lift the weight to a certain height. The spring has performed mechanical work.
- Observation 3. On the trolley we fix the rod with the block at the end. Throw a thread through the block, one end of which is wound on the axis of the trolley, and a weight hangs on the other. Let go of the weight. Under the influence of gravity, it will fall down and give the trolley movement. A small weight performed mechanical work.
After analyzing all of the above observations, we can conclude that if a body or several bodies perform mechanical work during interaction, then they are said to have mechanical energy, or energy.
Energy concept
Energy (from the Greek word energy - activity) is a physical quantity that characterizes the ability of bodies to do work. The unit of energy, as well as work in the SI system is one Joule (1 J). In a letter, energy is indicated by the letter E. It can be seen from the above experiments that the body performs work when it passes from one state to another. The energy of the body changes (decreases), and the mechanical work performed by the body is equal to the result of a change in its mechanical energy.
Types of mechanical energy. Concept of potential energy
There are 2 types of mechanical energy: potential and kinetic. Now let's take a closer look at potential energy.
Potential energy (PE) is the energy determined by the relative position of the bodies that interact, or by parts of the body itself. Since any body and earth attract each other, that is, they interact, the PE of the body raised above the ground will depend on the height of rise h . The higher the body is raised, the more its PE. It has been experimentally established that PE depends not only on the height to which it is raised, but also on body weight. If the bodies were raised to the same height, then a body having a large mass will also have a large PE. The formula of this energy is as follows: E p = mgh, where E p is the potential energy, m is the body weight, g = 9.81 N / kg, h is the height.
Potential spring energy
The potential energy of an elastically deformed body is the physical quantity E p, which, when the speed of translational motion under the action of elastic forces changes, decreases exactly as much as the kinetic energy grows. The springs (like other elastically deformed bodies) have such a PE that is equal to half the product of their rigidity k and the square of the deformation: x = kx 2 : 2.
Kinetic energy: formula and definition
Sometimes the value of mechanical work can be considered without using the concepts of force and displacement, focusing on the fact that work characterizes a change in the energy of the body. All that we may need is the mass of a certain body and its initial and final speeds, which will lead us to kinetic energy. Kinetic energy (CE) is energy that belongs to the body due to its own movement.
Kinetic energy has the wind, it is used to give movement to wind engines. Movable air masses exert pressure on the inclined planes of the wings of the wind engines and make them turn around. Rotational movement with the help of transmission systems is transmitted to mechanisms that perform a specific job. Moving water that wraps up the turbines of a power plant loses part of its FE, performing work. In addition to PE, a plane flying high in the sky has FE. If the body is at rest, that is, its velocity relative to the Earth is zero, then its FE relative to the Earth is zero. It was experimentally established that the greater the mass of the body and the speed with which it moves, the greater its FE. The formula for the kinetic energy of translational motion in mathematical expression is as follows:
Where K is kinetic energy, m is body mass, v is speed.
Kinetic energy change
Since the speed of the body is a quantity that depends on the choice of the reference frame, the value of the FE of the body also depends on its choice. The change in the kinetic energy (IKE) of the body occurs due to the action of an external force F on the body. The physical quantity A , which is equal to the ICE ΔE to the body due to the action of the force F on it , is called the work: A = ΔE to . If a force F coinciding with the direction acts on a body that moves at a speed of v 1 , then the speed of the body will increase over a period of time t to a certain value of v 2 . In this case, the IKE is:
Where m is body weight; d is the distance traveled by the body; V f1 = (V 2 - V 1 ); V f2 = (V 2 + V 1 ); a = F: m . It is according to this formula that it calculates how much the kinetic energy changes. The formula can also have the following interpretation: Δ = Flcos ά , where cosά is the angle between the vectors of force F and velocity V.
Average kinetic energy
Kinetic energy is the energy determined by the speed of movement of different points that belong to this system. However, it should be remembered that it is necessary to distinguish between 2 energies characterizing different types of motion: translational and rotational. The average kinetic energy (SCE) in this case is the average difference between the total energy of the whole system and its calm energy, that is, in fact, its value is the average value of potential energy. The formula for the average kinetic energy is as follows:
where k is the Boltzmann constant; T is the temperature. It is this equation that is the basis of the molecular-kinetic theory.
Average kinetic energy of gas molecules
It was established by numerous experiments that the average kinetic energy of gas molecules in translational motion at a given temperature is the same and does not depend on the type of gas. In addition, it was also found that when the gas is heated by 1 ° C, the SCE increases by one and the same value. More precisely, this value is equal to: Δ = 2.07 x 10 -23 J / . In order to calculate what the average kinetic energy of gas molecules in translational motion is equal to, it is necessary, in addition to this relative value, to know at least one more absolute value of the energy of translational motion. In physics, these values are quite accurately determined for a wide range of temperatures. For example, at a temperature t = 500 ° C, the kinetic energy of the translational motion of the molecule is Ek = 1600 x 10 -23 J. Knowing 2 quantities ( Δ and ), we can both calculate the translational energy of molecules at a given temperature and solve the inverse problem is to determine the temperature from the given energy values.
Finally, we can conclude that the average kinetic energy of the molecules, the formula which is given above, depends only on the absolute temperature (and for any state of aggregation of substances).
The law of conservation of total mechanical energy
The study of the motion of bodies under the action of gravity and elastic forces showed that there is a certain physical quantity, which is called the potential energy E p ; it depends on the coordinates of the body, and its change is equal to the IKE, which is taken with the opposite sign: Δ = - Δ . So, the sum of the changes in CE and PE of the body, which interact with gravitational and elastic forces, is 0 : Δ + Δ = 0. Forces that depend only on the coordinates of the body are called conservative. The forces of gravity and elasticity are conservative forces. The sum of the kinetic and potential energies of the body is the total mechanical energy: E p + E k = E.
This fact, which has been proven by the most accurate experiments,
called the law of conservation of mechanical energy . If bodies interact with forces that depend on the speed of relative motion, mechanical energy is not stored in the system of interacting bodies. An example of forces of this type, called non-conservative , are friction forces. If friction forces act on the body, then to overcome them it is necessary to expend energy, that is, part of it is used to perform work against friction forces. However, the violation of the law of conservation of energy here is only imaginary, because it is a separate case of the general law of conservation and conversion of energy. The energy of bodies never disappears or reappears: it only transforms from one species to another. This law of nature is very important; it holds true everywhere. It is also sometimes called the general law of conservation and conversion of energy.
The relationship between the internal energy of the body, kinetic and potential energies
The internal energy (U) of the body is its total energy of the body minus the FE of the body as a whole and its PE in the external field of forces. From this we can conclude that the internal energy consists of the CE of the chaotic motion of molecules, the PE interaction between them and intramolecular energy. Internal energy is an unambiguous function of the state of the system, which indicates the following: if the system is in a given state, its internal energy takes on its inherent values, regardless of what happened earlier.
Relativism
When the speed of the body is close to the speed of light, kinetic energy is found by the following formula:
The kinetic energy of the body, the formula of which was written above, can also be calculated according to this principle:
Examples of tasks for finding kinetic energy
1. Compare the kinetic energy of a ball weighing 9 g, flying at a speed of 300 m / s, and a person weighing 60 kg, running at a speed of 18 km / h.
So, what was given to us: m 1 = 0.009 kg; V 1 = 300 m / s; m 2 = 60 kg, V 2 = 5 m / s.
Decision:
- Kinetic energy (formula): = mv 2 : 2.
- We have all the data for the calculation, and therefore we will find E k for both the person and the ball.
- E k1 = (0.009 kg x (300 m / s) 2 ): 2 = 405 J;
- E k2 = (60 kg x (5 m / s) 2 ): 2 = 750 J.
- E k1 < E k2.
Answer: the kinetic energy of the ball is less than that of man.
2. A body with a mass of 10 kg was raised to a height of 10 m, after which he was released. What FE will it have at a height of 5 m? Air resistance is negligible.
So, what was given to us: m = 10 kg; h = 10 m; h 1 = 5 m; g = 9.81 N / kg. E k1 -?
Decision:
- A body of a certain mass, raised to a certain height, has potential energy: E p = mgh. If the body falls, then it will have sweat at a certain height h 1 . energy E p = mgh 1 and kin. energy E k1. In order for the kinetic energy to be correctly found, the formula that was given above will not help, and therefore we will solve the problem by the following algorithm.
- In this step we use the law of conservation of energy and write: 1 + 1 = .
- Then E k1 = E p - E p1 = mgh - mgh 1 = mg (hh 1 ).
- Substituting our values in the formula, we obtain: E k1 = 10 x 9.81 (10-5) = 490.5 J.
Answer: E k1 = 490.5 J.
3. A flywheel having mass m and radius R is wrapped around an axis passing through its center. The angular velocity of the flywheel wrapping is ω . In order to stop the flywheel, a brake pad is pressed against its rim, acting on it with friction force F. How many revolutions will the flywheel make to a complete stop? Take into account that the mass of the flywheel is concentrated along the rim.
So, what was given to us: m; R; ω; F friction. N -?
Decision:
- When solving the problem, we consider the flywheel revolutions to be similar to those of a thin homogeneous hoop with radius R and mass m, which turns around with an angular velocity ω.
- The kinetic energy of such a body is: E k = (J ω 2 ): 2, where J = m R 2 .
- The flywheel will stop under the condition that all of its FE will be spent on the work to overcome the friction force F friction arising between the brake pad and the rim: = F friction * s, where s is the stopping distance, which is 2 πRN.
- Therefore, F friction * 2 πRN = (m R 2 ω 2 ): 2, whence N = ( m ω 2 R): (4 π F Tr).
Answer: N = (mω 2 R): (4πF tr).
Finally
Energy is the most important component in all aspects of life, because without it no bodies would be able to carry out work, including man. We think that the article made it clear to you what energy is, and a detailed exposition of all aspects of one of its components - kinetic energy - will help you become aware of many processes taking place on our planet. And about how to find kinetic energy, you can learn from the above formulas and examples of problem solving.