§2.6 Kinetic energy. Kinetic energy - the energy of movement of bodies. The physical meaning of work.

The word "energy" is translated from Greek as "action". We call an energetic person 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.

Energy is what makes life possible not only on our planet, but also in the Universe. However, it can be very different. So, heat, sound, light, electricity, microwaves, calories are different types of energy. This substance is necessary for all processes occurring around us. Everything on Earth receives most of its energy from the Sun, but there are other sources. The sun transmits it to our planet as much as 100 million of the most powerful power plants would produce at the same time.

What is energy?

The theory put forward by Albert Einstein examines the relationship between matter and energy. This great scientist was able to prove the ability of one substance to transform into another. It turned out that energy is the most important factor in the existence of bodies, and matter is secondary.

Energy is, by and large, the ability to do some kind of work. It is she who stands behind the concept of force capable of moving a body or giving it new properties. What does the term “energy” mean? Physics is to which many scientists from different eras and countries have dedicated their lives. Aristotle also used the word “energy” to denote human activity. Translated from Greek, “energy” is “activity”, “strength”, “action”, “power”. The first time this word appeared was in the treatise of a Greek scientist called “Physics”.

In the now generally accepted sense, this term was introduced into use by an English physicist. This significant event occurred back in 1807. In the 50s of the XIX century. English mechanic William Thomson first used the concept of “kinetic energy”, and in 1853 Scottish physicist William Rankine introduced the term “potential energy”.

Today this scalar quantity is present in all branches of physics. It is a single measure of various forms of movement and interaction of matter. In other words, it represents a measure of the transformation of one form into another.

Units of measurement and symbols

The amount of energy is measured. This special unit, depending on the type of energy, may have different designations, for example:

• W is the total energy of the system.
• Q - thermal.
• U - potential.

Types of energy

There are many different types of energy in nature. The main ones are:

• mechanical;
• electromagnetic;
• electric;
• chemical;
• thermal;
• nuclear (atomic).

There are other types of energy: light, sound, magnetic. In recent years, an increasing number of physicists are inclined to the hypothesis of the existence of so-called “dark” energy. Each of the previously listed types of this substance has its own characteristics. For example, sound energy can be transmitted using waves. They contribute to the vibration of the eardrums in the ears of people and animals, thanks to which sounds can be heard. During various chemical reactions, the energy necessary for the life of all organisms is released. Any fuel, food, batteries, batteries are a storage of this energy.

Our star gives the Earth energy in the form of electromagnetic waves. This is the only way she can overcome the vastness of Space. Thanks to modern technologies such as solar panels, we can use it to the greatest effect. Excess unused energy is accumulated in special energy storage facilities. Along with the above types of energy, thermal springs, rivers, oceans, and biofuels are often used.

Mechanical energy

This type of energy is studied in the branch of physics called “Mechanics”. It is designated by the letter E. It is measured in joules (J). What is this energy? Mechanical physics studies the movement of bodies and their interaction with each other or with external fields. In this case, the energy due to the movement of bodies is called kinetic (denoted by Ek), and the energy due to or external fields is called potential (Ep). The sum of motion and interaction represents the total mechanical energy of the system.

There is a general rule for calculating both types. To determine the amount of energy, one must calculate the work required to transfer the body from the zero state to the given state. Moreover, the more work, the more energy the body will have in a given state.

Separation of species according to different characteristics

There are several types of energy sharing. According to various criteria, it is divided into: external (kinetic and potential) and internal (mechanical, thermal, electromagnetic, nuclear, gravitational). Electromagnetic energy, in turn, is divided into magnetic and electric, and nuclear energy into the energy of weak and strong interactions.

Kinetic

Any moving body is characterized by the presence of kinetic energy. It is often called the driving force. The energy of a moving body is lost when it slows down. Thus, the faster the speed, the greater the kinetic energy.

When a moving body comes into contact with a stationary object, a kinetic part is transferred to the latter, causing it to move. The formula for kinetic energy is as follows:

• E k = mv 2: 2,
  where m is the mass of the body, v is the speed of movement of the body.

In words, this formula can be expressed as follows: the kinetic energy of an object is equal to half the product of its mass by the square of its speed.

Potential

This type of energy is possessed by bodies that are in some kind of force field. Thus, magnetic occurs when an object is exposed to a magnetic field. All bodies on earth have potential gravitational energy.

Depending on the properties of the objects of study, they can have different types of potential energy. Thus, elastic and elastic bodies that are capable of stretching have potential energy of elasticity or tension. Any falling body that was previously motionless loses potential and acquires kinetic. In this case, the magnitude of these two types will be equivalent. In the gravitational field of our planet, the formula for potential energy will have the following form:

• E p = mhg,
  where m is body weight; h is the height of the center of body mass above the zero level; g is the acceleration of free fall.

In words, this formula can be expressed as follows: the potential energy of an object interacting with the Earth is equal to the product of its mass, the acceleration of gravity and the height at which it is located.

This scalar quantity is a characteristic of the energy reserve of a material point (body) located in a potential force field and used to acquire kinetic energy due to the work of field forces. Sometimes it is called the coordinate function, which is a term in the Langrangian of the system (the Lagrange function of the dynamical system). This system describes their interaction.

Potential energy is equated to zero for a certain configuration of bodies located in space. The choice of configuration is determined by the convenience of further calculations and is called “normalization of potential energy.”

Law of energy conservation

One of the most basic postulates of physics is the Law of Conservation of Energy. According to him, energy does not appear from anywhere and does not disappear anywhere. It constantly changes from one form to another. In other words, only a change in energy occurs. For example, the chemical energy of a flashlight battery is converted into electrical energy, and from it into light and heat. Various household appliances convert electricity into light, heat or sound. Most often the end result of the change is heat and light. After this, the energy goes into the surrounding space.

The law of energy can explain many scientists who claim that the total volume of energy in the universe constantly remains unchanged. No one can create energy again or destroy it. When producing one of its types, people use the energy of fuel, falling water, and an atom. In this case, one type of it turns into another.

In 1918, scientists were able to prove that the law of conservation of energy is a mathematical consequence of the translational symmetry of time - the value of conjugate energy. In other words, energy is conserved because the laws of physics do not differ at different times.

Energy Features

Energy is the body's ability to do work. In closed physical systems, it is preserved throughout the entire time (as long as the system is closed) and represents one of the three additive integrals of motion that retain their value during motion. These include: energy, moment The introduction of the concept of “energy” is appropriate when the physical system is homogeneous in time.

Internal energy of bodies

It is the sum of the energies of molecular interactions and thermal movements of the molecules that make it up. It cannot be measured directly because it is a unique function of the state of the system. Whenever a system finds itself in a given state, its internal energy has an inherent value, regardless of the history of the system's existence. The change in internal energy during the transition from one physical state to another is always equal to the difference between its values ​​in the final and initial states.

Internal energy of gas

In addition to solids, gases also have energy. It represents the kinetic energy of the thermal (chaotic) movement of particles of the system, which include atoms, molecules, electrons, and nuclei. The internal energy of an ideal gas (a mathematical model of a gas) is the sum of the kinetic energies of its particles. In this case, the number of degrees of freedom is taken into account, which is the number of independent variables that determine the position of the molecule in space.

Every year humanity consumes more and more energy resources. Most often, fossil hydrocarbons such as coal, oil and gas are used to obtain the energy necessary for lighting and heating our homes, the operation of vehicles and various mechanisms. They refer to

Unfortunately, only a small portion of our planet's energy comes from renewable resources such as water, wind and the sun. Today their share in the energy sector is only 5%. People receive another 3% in the form of nuclear energy produced at nuclear power plants.

Non-renewable resources have the following reserves (in joules):

• nuclear energy - 2 x 10 24;
• energy of gas and oil - 2 x 10 23;
• the internal heat of the planet is 5 x 10 20.

Annual value of the Earth's renewable resources:

• solar energy - 2 x 10 24;
• wind - 6 x 10 21;
• rivers - 6.5 x 10 19;
• sea ​​tides - 2.5 x 10 23.

Only with a timely transition from the use of non-renewable energy reserves of the Earth to renewable ones does humanity have a chance for a long and happy existence on our planet. To implement advanced developments, scientists around the world continue to carefully study the various properties of energy.

Closely related to the concept of work is another fundamental physical concept – the concept of energy. Since mechanics studies, firstly, the movement of bodies, and secondly, the interaction of bodies with each other, it is customary to distinguish between two types of mechanical energy: kinetic energy, caused by the movement of the body, and potential energy, caused by the interaction of a body with other bodies.

Kinetic energy mechanical system called energydepending on the speed of movement of the points of this system.

An expression for kinetic energy can be found by determining the work of the resultant force applied to a material point. Based on (2.24), we write the formula for the elementary work of the resultant force:

Because
, then dA = mυdυ. (2.25)

To find the work done by the resultant force when the speed of the body changes from υ 1 to υ 2, we integrate expression (2.29):

(2.26)

Since work is a measure of the transfer of energy from one body to another, then

Based on (2.30), we write that the quantity there is kinetic energy

body:
whence instead of (1.44) we get

(2.27)

The theorem expressed by formula (2.30) is usually called kinetic energy theorem . In accordance with it, the work of forces acting on a body (or system of bodies) is equal to the change in the kinetic energy of this body (or system of bodies).

From the kinetic energy theorem it follows physical meaning of kinetic energy : The kinetic energy of a body is equal to the work that it is capable of doing in the process of reducing its speed to zero. The greater the “reserve” of kinetic energy a body has, the more work it can do.

The kinetic energy of a system is equal to the sum of the kinetic energies of the material points of which this system consists:

(2.28)

If the work of all forces acting on the body is positive, then the kinetic energy of the body increases; if the work is negative, then the kinetic energy decreases.

It is obvious that the elementary work of the resultant of all forces applied to the body will be equal to the elementary change in the kinetic energy of the body:

dA = dE k. (2.29)

In conclusion, we note that kinetic energy, like the speed of movement, is relative. For example, the kinetic energy of a passenger sitting on a train will be different if we consider the movement relative to the road surface or relative to the carriage.

§2.7 Potential energy

The second type of mechanical energy is potential energy – energy due to the interaction of bodies.

Potential energy does not characterize any interaction of bodies, but only that which is described by forces that do not depend on speed. Most forces (gravity, elasticity, gravitational forces, etc.) are just that; the only exception is friction forces. The work of the forces under consideration does not depend on the shape of the trajectory, but is determined only by its initial and final positions. The work done by such forces on a closed trajectory is zero.

Forces whose work does not depend on the shape of the trajectory, but depends only on the initial and final position of the material point (body) are called potential or conservative forces .

If a body interacts with its environment through potential forces, then the concept of potential energy can be introduced to characterize this interaction.

Potential is the energy caused by the interaction of bodies and depending on their relative position.

Let's find the potential energy of a body raised above the ground. Let a body of mass m move uniformly in a gravitational field from position 1 to position 2 along a surface whose cross-section by the plane of the drawing is shown in Fig. 2.8. This section is the trajectory of a material point (body). If there is no friction, then three forces act on the point:

1) force N from the surface is normal to the surface, the work of this force is zero;

2) gravity mg, the work of this force A 12;

3) traction force F from some driving body (internal combustion engine, electric motor, person, etc.); Let's denote the work of this force by A T.

Let's consider the work of gravity when moving a body along an inclined plane of length ℓ (Fig. 2.9). As can be seen from this figure, the work is equal to

A" = mgℓ cosα = mgℓ cos(90° + α) = - mgℓ sinα

From triangle ВСD we have ℓ sinα = h, so from the last formula it follows:

The trajectory of a body (see Fig. 2.8) can be schematically represented by small sections of an inclined plane, therefore, for the work of gravity on the entire trajectory 1 -2, the following expression is valid:

A 12 =mg (h 1 -h 2) =-(mg h 2 - mg h 1) (2.30)

So, the work of gravity does not depend on the trajectory of the body, but depends on the difference in the heights of the starting and ending points of the trajectory.

Size

e n = mg h (2.31)

called potential energy a material point (body) of mass m raised above the ground to a height h. Therefore, formula (2.30) can be rewritten as follows:

A 12 = =-(En 2 - En 1) or A 12 = =-ΔEn (2.32)

The work of gravity is equal to the change in the potential energy of bodies taken with the opposite sign, i.e. the difference between its final and initialvalues (potential energy theorem ).

Similar reasoning can be given for an elastically deformed body.

(2.33)

Note that the difference in potential energies has a physical meaning as a quantity that determines the work of conservative forces. In this regard, it does not matter to which position, configuration, zero potential energy should be attributed.

One very important corollary can be obtained from the potential energy theorem: Conservative forces are always directed towards decreasing potential energy. The established pattern is manifested in the fact that any system left to itself always tends to move into a state in which its potential energy has the least value. This is principle of minimum potential energy .

If a system in a given state does not have minimum potential energy, then this state is called energetically unfavorable.

If the ball is at the bottom of a concave bowl (Fig. 2.10, a), where its potential energy is minimal (compared to its values ​​in neighboring positions), then its state is more favorable. The equilibrium of the ball in this case is sustainable: If you move the ball to the side and release it, it will return to its original position.

For example, the position of the ball on the top of a convex surface is energetically unfavorable (Fig. 2.10, b). The sum of the forces acting on the ball is zero, and therefore this ball will be in equilibrium. However, this balance is unstable: the slightest impact is enough for it to roll down and thereby move into a state that is energetically more favorable, i.e. having less

P potential energy.

At indifferent In equilibrium (Fig. 2.10, c), the potential energy of a body is equal to the potential energy of all its possible nearest states.

In Figure 2.11, you can indicate some limited region of space (for example cd), in which the potential energy is less than outside it. This area was named potential well .

>>Physics 10th grade >>Physics: Kinetic energy and its change

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 the position from which 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.

Energy is a scalar quantity. The SI unit of energy is the Joule.

Kinetic and potential energy

There are two types of energy - kinetic and potential.

DEFINITION

Kinetic energy- this is the energy that a body possesses due to its movement:

DEFINITION

Potential energy is energy that is determined by the relative position of bodies, as well as the nature of the interaction forces between these bodies.

Potential energy in the Earth's gravitational field is the energy due to the gravitational interaction of a body with the Earth. It is determined by the position of the body relative to the Earth and is equal to the work of moving the body from a given position to the zero level:

Potential energy is the energy caused by the interaction of body parts with each other. It is equal to the work of external forces in tension (compression) of an undeformed spring by the amount:

A body can simultaneously possess both kinetic and potential energy.

The total mechanical energy of a body or system of bodies is equal to the sum of the kinetic and potential energies of the body (system of bodies):

Law of energy conservation

For a closed system of bodies, the law of conservation of energy is valid:

In the case when a body (or a system of bodies) is acted upon by external forces, for example, the law of conservation of mechanical energy is not satisfied. In this case, the change in the total mechanical energy of the body (system of bodies) is equal to the external forces:

The law of conservation of energy allows us to establish a quantitative connection between various forms of motion of matter. Just like , it is valid not only for, but also for all natural phenomena. The law of conservation of energy says that energy in nature cannot be destroyed just as it cannot be created from nothing.

In its most general form, the law of conservation of energy can be formulated as follows:

• Energy in nature does not disappear and is not created again, but only transforms from one type to another.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2