Kinetic energy. Kinetic energy and its change - Knowledge Hypermarket Internal energy of gas

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Kinetic energy

Kinetic energy is the energy a body has due to its motion.

In simple terms, the concept of kinetic energy should mean only the energy that a body has when moving. If the body is at rest, that is, does not move at all, then the kinetic energy will be zero.

Kinetic energy equals the work that it must expend to bring a body from a state of rest to a state of motion at some speed.

Therefore, kinetic energy is the difference between the total energy of the system and its rest energy. In other words, kinetic energy will be part of the total energy that is due to movement.

Let's try to understand the concept of kinetic energy of a body. For example, let's take the movement of a puck on ice and try to understand the relationship between the amount of kinetic energy and the work that must be done to bring the puck out of rest and set it in motion at a certain speed.

Example

A hockey player playing on the ice, hitting the puck with his stick, imparts speed and kinetic energy to it. Immediately after being hit with the stick, the puck begins to move very quickly, but gradually its speed slows down and finally it stops completely. This means that the decrease in speed was the result of the frictional force occurring between the surface and the puck. Then the friction force will be directed against the movement and the actions of this force are accompanied by movement. The body uses the available mechanical energy, performing work against the force of friction.

From this example we see that kinetic energy will be the energy that a body receives as a result of its movement.

Consequently, the kinetic energy of a body having a certain mass will move at a speed equal to the work that must be done by the force applied to the body at rest in order to impart this speed to it:

Kinetic energy is the energy of a moving body, which is equal to the product of the mass of the body by the square of its speed, divided in half.

Properties of kinetic energy

The properties of kinetic energy include: additivity, invariance with respect to rotation of the reference frame, and conservation.

A property such as additivity is the kinetic energy of a mechanical system, which is composed of material points and will be equal to the sum of the kinetic energies of all material points that are included in this system.

The property of invariance with respect to rotation of the reference system means that kinetic energy does not depend on the position of the point and the direction of its speed. Its dependence extends only from the module or from the square of its speed.

The conservation property means that the kinetic energy does not change at all during interactions that change only the mechanical characteristics of the system.

This property is unchanged with respect to Galilean transformations. The properties of conservation of kinetic energy and Newton's second law will be quite sufficient to derive the mathematical formula for kinetic energy.

Relationship between kinetic and internal energy

But there is such an interesting dilemma as the fact that kinetic energy can depend on from what point of view this system is viewed. If, for example, we take an object that can only be viewed under a microscope, then as a whole, this body is motionless, although internal energy also exists. Under such conditions, kinetic energy appears only when this body moves as a single whole.

The same body, when viewed at the microscopic level, has internal energy due to the movement of the atoms and molecules of which it consists. And the absolute temperature of such a body will be proportional to the average kinetic energy of such movement of atoms and molecules.

What do “conditions for converting one type of energy into another” and “conservation of laws over time” have to do with it?

There is such a theorem of Noether. This is in mathematics, not even in physics, strictly speaking. She says that if a certain system of equations has some kind of symmetry, then there will also be something that does not change during transformations within the framework of this symmetry.

Well, if something doesn’t change, then it is “saved.” All physical “conservation laws” of something are a consequence of one or another symmetry of physical equations.

The law of conservation of energy is just one of many physical conservation laws, some of which you also know (for example, the law of conservation of momentum, the law of conservation of angular momentum, the law of conservation of electric charge). And each of the physical conservation laws reflects one of the symmetries of physical equations.

For example, parallel transport in space does not change the physical laws and the form of physical equations that reflect these laws. A consequence of this fact is the conservation of momentum of any closed system. And if the physical laws and the equations describing them changed during such a transfer, we would not have conserved the total momentum.

The situation is similar with time transfer. Since and as long as physical laws do not change over time, then the total energy of a closed system does not change. Accordingly, the fact of the immutability of physical laws “allows” individual “types of energy” to change only in such a way that the total (total) energy of a closed system is conserved. Accordingly, an increase in one type of energy, willy-nilly, is ALWAYS accompanied by a decrease in another, so that the amount does not change. And if the total energy of a closed system begins to change over time, then physical laws have begun to change. So far, such a phenomenon has not been registered, but who knows what happened, for example, at the time of the emergence of our Universe? Or what will happen over billions of years.

Thus, GLOBALLY conservation of energy is a synonym (consequence, equivalent) of the constancy of physical laws in time. The conservation condition is the universal root cause of the transition of one “type of energy” to another. Since the sum does not change, then the terms can only change at the expense of each other. Well, the more specific physical mechanisms of implementation will be different in different cases.

With conservation of momentum and other conservation laws, it’s exactly the same story.

It is clear that electrons and their components are directly involved in energy conversion, but what exactly happens?

An atom or group of interacting atoms have certain energy levels corresponding to their stable state. More precisely, these levels correspond not so much to the state of the atom or atoms as a whole, but to the state of its/their electrons.

Where do these energy levels and their corresponding states come from? States are stationary solutions to the equations of quantum mechanics, and the energy level is a characteristic number (or, if you like, a parameter of the system) at which a stationary solution can be found. An atom or system of atoms can have any other energy only for a very short time (the state is not stationary) and will certainly go into one of the stationary states.

Now consider a situation where 1) two atoms were far from each other and 2) they were very close. In the second case, the electric fields of charged nuclei will overlap. Electrons in such a joint field will have different stationary states than in the situation of two atoms far from each other. And other states have other (their) energies.

Now we compare the lowest values ​​of stationary energy levels in the first and second cases. If in the second the energy is lower, then it is “beneficial” for the atoms to unite into a molecule and emit the excess energy (then the emitted photon will fly somewhere far away, or, conversely, interact many times, re-emitted with other atoms and its energy will turn into the kinetic energy of the chaotic movement of atoms, that is, into heat). Here you have the formation of a diatomic molecule with the release of energy during a chemical reaction.

In the opposite case, the minimum internal energy of the molecule is higher than the sum of the minimum energies of the two atoms. Can such atoms form a molecule? Yes, if they first get a difference in energy from somewhere. For example, one atom could not have the lowest possible energy, but a higher one. Why? Well, it absorbed a photon, but did not have time to emit it back. Or it collided with another atom and was excited due to the energy of the collision (the kinetic energy of thermal vision turned into the internal energy of the atom and has not yet been emitted). And since the energy of one of the atoms is not minimal, then it may be “profitable” to create a molecule and “fall” on its minimum energy. Here's an example of a chemical reaction with energy absorption: something excites an atom by expending its energy, and only because of this the atom was able to react with its neighbor. And the energy absorbed before the reaction remained inside the molecule. This internal energy will only be released after the destruction of the molecule.

And only electrons are involved in this?

Electrons and electric fields of nuclei with which electrons interact. Any chemical reaction is a change in the state of electronic shells.

Why aren't the nuclei involved? Because nuclei are incomparably heavier than electrons. The sun, too, will hardly react to the approach or distance of the Earth - it is too heavy to twitch any noticeably because of such a trifle. So atomic nuclei do not pay much attention to what happens to their electrons

The nuclei themselves also do not fall apart due to the electric field of the electrons. The internal forces that hold quarks in the nucleus are incomparably more powerful than the electric fields in the atom.

For this reason, quantum mechanics solves the problem of the control of electrons in the field of nuclei, but is not interested in the behavior of nuclei in the field of electrons - this is such a small correction that it cannot be measured. Accordingly, all chemistry is the behavior of electron shells in the fields of one or several nuclei. And when it comes to the behavior of the nucleus itself, there is no time for chemistry.

Potential and kinetic energy make it possible to characterize the state of any body. If the first is used in systems of interacting objects, then the second is associated with their movement. These types of energy are usually considered when the force connecting the bodies is independent of the trajectory of movement. In this case, only their initial and final positions are important.

General Information and Concepts

The kinetic energy of a system is one of its most important characteristics. Physicists distinguish two types of such energy depending on the type of movement:

Progressive;

Rotations.

Kinetic energy (E k) is the difference between the total energy of the system and the rest energy. Based on this, we can say that it is caused by the movement of the system. The body has it only when it moves. When the object is at rest, it is equal to zero. The kinetic energy of any bodies depends solely on the speed of movement and their masses. The total energy of a system is directly dependent on the speed of its objects and the distance between them.

Basic formulas

In the case when any force (F) acts on a body at rest so that it comes into motion, we can talk about doing work dA. In this case, the value of this energy dE will be higher, the more work is done. In this case, the following equality is true: dA = dE.

Taking into account the path traveled by the body (dR) and its speed (dU), we can use Newton’s 2nd law, based on which: F = (dU/dE)*m.

The above law is used only when there is an inertial frame of reference. There is another important nuance taken into account in the calculations. The energy value is affected by the choice of system. So, according to the SI system, it is measured in joules (J). The kinetic energy of a body is characterized by mass m, as well as speed of movement υ. In this case, it will be: E k = ((υ*υ)*m)/2.

Based on the above formula, we can conclude that kinetic energy is determined by mass and speed. In other words, it represents a function of body movement.

Energy in a mechanical system

Kinetic energy represents mechanical energy systems. It depends on the speed of movement of its points. This energy of any material point is represented by the following formula: E = 1/2mυ 2, where m is the mass of the point, and υ is its speed.

The kinetic energy of a mechanical system is the arithmetic sum of the same energies of all its points. It can also be expressed by the following formula: E k = 1/2Mυ c2 + Ec, where υc is the speed of the center of mass, M is the mass of the system, Ec is the kinetic energy of the system when moving around the center of mass.

Solid body energy

The kinetic energy of a body that moves translationally is defined as the same energy of a point with a mass equal to the mass of the entire body. To calculate indicators when moving, more complex formulas are used. The change in this energy of the system at the moment of its movement from one position to another occurs under the influence of applied internal and external forces. It is equal to the sum of the work Aue and A"u of these forces during this movement: E2 - E1 = ∑u Aue + ∑u A"u.

This equality reflects a theorem concerning the change in kinetic energy. With its help, a variety of mechanical problems are solved. Without this formula it is impossible to solve a number of important problems.

Kinetic energy at high speeds

If the speed of the body is close to the speed of light, the kinetic energy of the material point can be calculated using the following formula:

E = m0c2/√1-υ2/c2 - m0c2,

where c is the speed of light in vacuum, m0 is the mass of the point, m0с2 is the energy of the point. At low speed (υ

Energy during rotation of the system

During the rotation of a body around an axis, each of its elementary volumes with mass (mi) describes a circle with radius ri. At this moment the volume has a linear velocity υi. Since we are considering a solid body, angular velocity rotation of all volumes will be the same: ω = υ1/r1 = υ2/r2 = … = υn/rn (1).

The kinetic energy of rotation of a solid body is the sum of all the same energies of its elementary volumes: E = m1υ1 2/2 + miυi 2/2 + … + mnυn 2/2 (2).

Using expression (1), we obtain the formula: E = Jz ω 2/2, where Jz is the moment of inertia of the body around the Z axis.

When comparing all formulas, it becomes clear that the moment of inertia is a measure of the inertia of a body during rotational movement. Formula (2) is suitable for objects rotating about a fixed axis.

Flat body movement

The kinetic energy of a body moving down a plane is the sum of the rotational energy and forward movement: E = mυc2/2 + Jz ω 2/2, where m is the mass of a moving body, Jz is the moment of inertia of the body around the axis, υc is the speed of the center of mass, ω is the angular velocity.

Energy change in a mechanical system

The change in the value of kinetic energy is closely related to potential energy. The essence of this phenomenon can be understood thanks to the law of conservation of energy in the system. The sum of E + dP during the movement of the body will always be the same. A change in the value of E always occurs simultaneously with a change in dP. Thus, they transform, as if flowing into each other. This phenomenon can be found in almost all mechanical systems.

Interrelation of energies

Potential and kinetic energies are closely related. Their sum can be represented as the total energy of the system. At the molecular level it is internal energy bodies. It is constantly present as long as there is at least some interaction between bodies and thermal movement.

Selecting a reference system

To calculate the energy value, an arbitrary moment is selected (it is considered the initial moment) and a reference system. It is possible to determine the exact value of potential energy only in the zone of influence of forces that do not depend on the trajectory of the body when performing work. In physics, these forces are called conservative. They have a constant connection with the law of conservation of energy.

The difference between potential and kinetic energy

If the external influence is minimal or reduced to zero, the system under study will always gravitate towards a state in which its potential energy will also tend to zero. For example, a ball thrown up will reach the limit of this energy at the top point of its trajectory and at the same moment begin to fall down. At this time, the energy accumulated during the flight is converted into movement (work performed). For potential energy, in any case, there is an interaction of at least two bodies (in the example with the ball, the gravity of the planet affects it). Kinetic energy can be calculated individually for any moving body.

Interrelation of different energies

Potential and kinetic energy change exclusively during the interaction of bodies, when the force acting on the bodies does work, the value of which is different from zero. In a closed system, the work done by the force of gravity or elasticity is equal to the change in the potential energy of objects with the sign “-”: A = - (Ep2 - Ep1).

The work done by the force of gravity or elasticity is equal to the change in energy: A = Ek2 - Ek1.

From a comparison of both equalities, it is clear that the change in the energy of objects in a closed system is equal to the change in potential energy and is opposite in sign: Ek2 - Ek1 = - (Ep2 - Ep1), or otherwise: Ek1 + Ep1 = Ek2 + Ep2.

From this equality it is clear that the sum of these two energies of bodies in a closed mechanical system and the interacting forces of elasticity and gravity always remains constant. Based on the above, we can conclude that in the process of studying a mechanical system, the interaction of potential and kinetic energies should be considered.

The word "energy" is translated from Greek as "action". We call a person energetic who moves actively, performing many different actions.

Energy in physics

And if in life we ​​can evaluate a person’s energy mainly by the consequences of his activities, then in physics energy can be measured and studied in many different ways. Your cheerful friend or neighbor will most likely refuse to repeat the same action thirty to fifty times when it suddenly occurs to you to investigate the phenomenon of his energy.

But in physics, you can repeat almost any experiment as many times as you like, doing the research you need. So it is with the study of energy. Research scientists have studied and labeled many types of energy in physics. These are electrical, magnetic, atomic energy and so on. But now we will talk about mechanical energy. And more specifically about kinetic and potential energy.

Kinetic and potential energy

Mechanics studies the movement and interaction of bodies with each other. Therefore, it is customary to distinguish between two types of mechanical energy: energy due to the movement of bodies, or kinetic energy, and energy due to the interaction of bodies, or potential energy.

In physics, there is a general rule connecting energy and work. To find the energy of a body, it is necessary to find the work that is necessary to transfer the body to a given state from zero, that is, one at which its energy is zero.

Potential energy

In physics, potential energy is the energy that is determined by the relative position of interacting bodies or parts of the same body. That is, if a body is raised above the ground, then it has the ability to do some work while falling.

And the possible value of this work will be equal to the potential energy of the body at height h. For potential energy, the formula is determined according to the following scheme:

A=Fs=Ft*h=mgh, or Ep=mgh,

where Ep is the potential energy of the body,
m body weight,
h is the height of the body above the ground,
g acceleration of free fall.

Moreover, any position convenient for us can be taken as the zero position of the body, depending on the conditions of the experiments and measurements being carried out, not only the surface of the Earth. This could be the surface of the floor, table, and so on.

Kinetic energy

In the case when a body moves under the influence of force, it not only can, but also does some work. In physics, kinetic energy is the energy possessed by a body due to its motion. When a body moves, it expends energy and does work. For kinetic energy the formula is calculated as follows:

A = Fs = mas = m * v / t * vt / 2 = (mv^2) / 2, or Eк = (mv^2) / 2,

where Ek is the kinetic energy of the body,
m body weight,
v body speed.

From the formula it is clear that the greater the mass and speed of a body, the higher its kinetic energy.

Every body has either kinetic or potential energy, or both at once, like, for example, a flying airplane.