Energy abstract on technology, essays from materials science and materials technology. Kinetic and potential energy

• In mechanics, the energy of a system of bodies is determined by the position of the bodies and their velocities. First, let's find how the energy of bodies depends on their velocities.

Let us calculate the work of the force acting on a body (material point) with mass m, in the simple case, when the body moves in a straight line, the force is constant and its direction coincides with the direction of speed.

When a body moves by Δ, its speed changes from value 1 to value 2. We choose the coordinate axis X so that the vectors , 1 , 2 and Δ are co-directed with this axis (Fig. 6.8). Then the work of the force

Rice. 6.8

According to the kinematic formula (1.20.8), the displacement of the body when moving with constant acceleration is

In our case v 1 = v 2 , v 0x = v 1 , a x = a.

Therefore, the expression for work (6.5.1) will take the form

According to Newton's second law = m. Consequently,

A value equal to half the product of the mass of the body and the adrat of its speed is called kinetic (1) energy.

Let us denote the kinetic energy by E k:

Any moving body has an energy proportional to its mass and the square of its speed.

Given the definition of kinetic energy (6.5.4), expression (6.5.3) for work can be rewritten as:

Equality (6.5.5) expresses the theorem on the change in kinetic energy: the change in the kinetic energy of a body (more precisely, a material point) over a certain period of time is equal to the work done during this time by the force acting on the body.

Kinetic energy increases when work is positive and decreases when work is negative.

It can be proved that Theorem (6.5.5) is also valid in those cases when a variable force acts on the body and it moves along a curvilinear trajectory.

Kinetic energy is expressed in the same units as work, that is, in joules.

Since the kinetic energy of an individual body is determined by its mass and speed, it does not depend on whether this body interacts with other bodies or not. The value of kinetic energy depends on the frame of reference, as does the value of velocity. The kinetic energy of a system of bodies is equal to the sum of the kinetic energies of the individual bodies included in this system.

It is significant that in proving the theorem on the change in kinetic energy, we used only the definition of work and Newton's second law. No assumptions about the nature of the forces of interaction between bodies have been made. These could be gravitational forces, elastic forces or friction forces.

A moving body has kinetic energy. This energy is equal to the work that must be done to increase the speed of the body from zero to v.

(1) From the Greek word kinema, movement.

Are you familiar with conservation laws? // Quantum. - 1987. - No. 5. - S. 32-33.

By special agreement with the editorial board and the editors of the journal "Kvant"

Things cannot be created from nothing, nor,
once having arisen, again turn into nothing...
Lucretius Kar. "On the Nature of Things"

The development of physics was accompanied by the establishment of a variety of conservation laws, stating that in isolated systems certain quantities cannot arise or disappear. The idea that such laws exist dates back to the mists of time: the saying of Lucretius given in the epigraph reflects ancient views. Today, physicists know quite a lot of such laws, some of them are familiar to you too - these are the laws of conservation of momentum, energy, charge. Further study of physics will reveal that there are very unusual conservation laws, such as strangeness, parity and charm. But first - let's work with those that you should know well.

Questions and tasks

1. Can the kinetic energy of a body change if there are no forces acting on the body?
2. Can the kinetic energy of a body remain unchanged if the resultant of the forces applied to the body is nonzero?
3. When is the transfer of electric charge from one point of the electric field to another not accompanied by a change in energy?
4. What type of energy is converted by the photoelectric effect from the energy of light falling on a substance?
5. How can an astronaut who is not associated with the ship return to the ship?
6. Does the total momentum of a well-centered flywheel depend on its rotational speed?
7. A massive homogeneous cylinder, which can rotate without friction around a horizontal axis, is hit by a bullet flying horizontally at a speed υ , and after hitting the cylinder falls onto the trolley. Does the speed of the cart, which it acquires after the impact of the bullet, depend on which part of the cylinder the bullet hits?

   

8. By emitting a photon, a gas atom changes its momentum. Why is this change inevitable?
9. In the process of annihilation of an electron and a positron, one gamma-quantum never occurs. Which of the conservation laws manifests itself in this fact?
10. The metal plate was charged by the action of X-rays. What is the charge sign?
11. When an electron annihilates with a positron, gamma quanta are formed; however, this does not happen when two electrons or two positrons meet. What is the conservation law here?

Microexperience

Walk from the stern of the initially motionless boat to its bow. Why will the boat move in the opposite direction?

It is curious that…

Often, some conservation laws turn out to be valid only when describing a limited range of phenomena. Thus, in the study of chemical reactions, it can be assumed that the mass is conserved, but in nuclear reactions the application of such a law was erroneous, since, for example, the mass of the final fission products of uranium is less than the mass of the initial amount of uranium.

If the charge conservation law were not a completely accurate law of nature, then the electron could decay, for example, into a neutrino and a photon. The search for such decays, however, was not crowned with success and showed that the lifetime of an electron is at least not less than 1021 years. (The age of the Universe is estimated today by scientists at 10 10 years.)

It was the law of conservation of charge that suggested to J. Maxwell the idea of ​​the possible occurrence of a magnetic field as a result of a change in the electric field. The development of this idea led Maxwell to the prediction of periodic electromagnetic processes propagating in space. The calculated value of the propagation velocity turned out to be exactly equal to the previously measured speed of light.

Law of energy conservation.

The increment of potential energies thrown up

body occurs due to the decrease in its kinetic energy;

when a body falls, the increment of kinetic energy

occurs due to the loss of potential energy, so that

the total mechanical energy of the body does not change1.

Similarly, if a compressed spring acts on the body, then

it can impart some speed to the body, i.e.

kinetic energy, but the spring will

straighten up and its potential energy will come true

decrease accordingly. the amount of potential and

kinetic energy will remain constant. If on the body

in addition to the spring, the force of gravity also acts, although at

movement of the body, the energy of each type will change, but

the sum of the potential energy of gravity, potential

the energy of the spring and the kinetic energy of the body again

will remain constant.

Energy can change from one form to another

can pass from one body to another, but the general

1 Landsberg G.S. Elementary textbook of physics. Volume 1. M.; 1995 2 Butikov E.I. Physics for university students. 1982

the supply of mechanical energy remains unchanged. Experiences

and theoretical calculations show that in the absence of

friction forces and under the influence of only the forces of elasticity and traction

tensile total potential and kinetic energy

body or system of bodies remains constant in all cases

This is the law of conservation of mechanical

Let us illustrate the law of conservation of energy on

next experience. A steel ball dropped from some

height on a steel or glass plate and hit

about it, jumps almost to the same height from which

fell. During the movement of the ball, a series of

energy transformations. When falling, the potential energy

is converted into kinetic energy of the ball. When the ball

touches the stove, and he and the stove start

deform. Kinetic energy is converted into

potential energy of elastic deformation of the ball and

plates, and this process continues until

the ball will not stop, i.e. until all of its kinetic

energy will not be transferred to the potential energy of the elastic

deformations. Then, under the action of elastic forces

deformed plate, the ball acquires speed,

upward: the elastic deformation energy of the plate

and the ball terminates in, the kinetic energy of the ball.

On further upward movement, the speed of the ball under

the force of gravity also decreases the kinetic

energy is converted into potential energy

gravity, At the highest point, the ball has again

only potential gravitational energy.

the height from which it began to fall, the potential energy

ball at the beginning and at the end of the described process is the same

same. Moreover, at any moment in time for all

energy transformations the amount of potential energy

gravity, potential energy of elastic deformation, and

kinetic energy remains the same all the time.

For the process of potential energy conversion,

due to gravity, to kinetic and vice versa

during the fall and rise of the ball, this was shown by a simple

calculation. It could be verified that

converting kinetic energy into potential

energy of elastic deformation of the plate and ball and then at

the reverse process of converting this energy into

the kinetic energy of the bouncing ball is the sum

potential energy of gravity, elastic energy

strain and kinetic energy also remains

unchanged, i.e. the law of conservation of mechanical energy

completed.

Now we can explain why the law was broken

saving work in a simple machine that

deformed during the transfer of work: the fact is that

work expended at one end of the machine, partially or

was completely spent on the deformation of the simplest

machine (lever, rope, etc.), creating in it some

potential energy of deformation, and only the remainder

work was transferred to the other end of the machine. In total

transferred work together with strain energy

turns out to be equal to the work expended. In the case of absolute

noy rigidity of the lever, inextensibility of the rope and

etc. a simple machine cannot accumulate energy in itself, and

all the work done at one end of it is completely

sent to the other end.

Friction forces and conservation law, mechanical

energy. Watching the movement of the ball,

bouncing on the stove, you will find that after

each hit the ball rises by a slightly smaller

height than before, i.e. the total energy does not remain in

accuracy is constant, but gradually decreases; it means that

the law of conservation of energy in the form we

formulated, observed in this case only

approximately.2 The reason is that in this experiment

those friction forces arise; air resistance in which

ohm the ball moves, and the internal friction in the

ball and plate material. In general, in the presence of friction

conservation of mechanical energy is always violated and

the total energy of the bodies decreases. Due to this loss

energy and work is done against the forces of friction. For example

ep, when a body falls from a great height, the speed,

due to the action of increasing resistance forces

environment, soon becomes constant; kinetic

the energy of the body stops changing, but its potential

energy is decreasing. Work against the force of resistance

air makes the force of gravity due to the potential,

body energy. Although some kina is reported

static energy to the surrounding air, but it is less

than the decrease in the potential energy of the body, and, therefore, the total

th mechanical energy decreases.

The work against the forces of friction can also be performed due to

kinetic energy. For example, when a boat is moving,

who was pushed away from the shore of the pond, the potential overthrew

th boat remains constant, but due to resistance

water flow decreases the speed of the boat, i.e. her

kinetic energy, i increment kinetic energy

water observed in this case is less than the loss

the kinetic energy of the boat.

Similarly, friction forces between solids also act.

smoke bodies. For example, the speed acquired

a load sliding down an inclined plane

hence its kinetic energy is less than that

which he acquired being the absence of friction. Can it be like this

pick up the angle of inclination of the plane that the load will be

slide evenly. However, its potential

energy will decrease, and kinetic energy will remain

constant, and the work against the forces of friction will be done

through potential energy.

In nature, all movements (with the exception of movements in

vacuum, for example, movements of celestial bodies) sop

generated by friction. Therefore, with such movements, the law

conservation of mechanical energy is violated, and this

violation always occurs in one direction - in the direction

decrease in total energy.

The transformation of mechanical energy into

internal energy. The characteristic of friction forces is

as we have seen, in that the work done against the forces

friction, does not completely transform into kinetic or

potential energy of bodies; as a result, the total

the mechanical energy of the bodies decreases. However, work

against the forces of friction does not disappear without a trace. First of all, d

the movement of bodies in the presence of friction leads to their heating.

We can easily detect this by rubbing our hands hard or

stretching a metal strip between those who are squeezing it

two pieces of wood; the strip is even noticeable to the touch

warms up. Primitive people are known to have mined

fire by rapidly rubbing dry pieces of wood against each other.

Heating also occurs during work.

against forces. internal friction, for example when

repeated bending of the wire. Heating at

movement associated with overcoming frictional forces, often

gets very strong. For example, when a train brakes

the brake pads get very hot. When descending

ship from stocks to water to reduce friction

the slipways are abundantly lubricated, and yet the heating

Iko that the grease smokes, and sometimes even catches fire.

When moving bodies in the air at low speeds,

e.g. when moving a thrown stone, resistance

air is small, to overcome the forces of friction

little work is spent, and the stone is practically not

warms up. But the fast-flying bullet is heating up

much stronger. At high jet speeds

aircraft already have to take special measures

to reduce the heating of the aircraft skin. small

meteorites flying in at high speeds (tens of

kilometers per second) into the Earth's atmosphere, experience

such a large resistance force of the medium that completely

burn up in the atmosphere. Heating in the atmosphere of art

this satellite of the Earth returning to Earth, so

large that it has to install a special

thermal protection.

In addition to heating, rubbing bodies can also experience

other Changes. For example, they can be crushed

grind into dust, melting can occur, i.e.

transition of bodies from a solid to a liquid state: a piece of ice

may melt as a result of friction against another piece

ice or any other body.

So, if the movement of bodies is connected with the overcoming of forces

friction, then it is accompanied by two phenomena: a) the sum

kinetic and potential energies of all involved

decreases in the movement of bodies; b) there is a change

state of bodies, in particular, heating can occur.

This change in the state of bodies always occurs in this way

in such a way that in the new state of the body can produce

more work than the original. So, for example, if

pour into a metal tube closed at one end

a little ether and, plugging the tube with a cork, clamp it between

two plates and bring into rapid rotation, then

the ether will evaporate and push the cork out. So, as a result

work to overcome the forces of friction of the tube on the plates

the tube with ether came to a new state in which it

was able to do the work required to push

plugs, i.e. work against friction forces holding

cork in the tube, and work going to the message cork

kinetic energy. In its original state, the tube

ether could not do this work.

Thus, the heating of bodies, as well as other

changes in their state, accompanied by a change

"reserve" of the ability of these bodies to do work. We

we see that the “working capacity margin” depends, in addition to

positions of bodies relative to the earth, in addition to their

deformations and their speeds, also on the state of the bodies. Means,

in addition to the potential energy of gravity and elasticity and

kinetic energy The body also has energy,

depending on his state "We will call her

internal energy. The internal energy of a body depends on

its temperature, whether the body is solid,

liquid or gaseous, how large is its surface,

whether it is solid or finely divided, etc.

e. In particular, the higher the body temperature, the more it

internal energy.

Thus, although during movements associated with pre-

overcoming friction forces, mechanical energy of systems]

moving bodies decreases, but their

internal energy. For example, when a train brakes at

a decrease in its kinetic energy is accompanied by

an increase in the internal energy of the brake pads,

tires, rails, ambient air, etc. in

the result of heating these bodies.

All of the above also applies to cases where

friction forces arise inside the body, for example, when stretching

on a piece of wax, with an inelastic impact of lead balls

when bending a piece of wire, etc.

The universal nature of the law of conservation of energy.

Friction forces occupy a special position in the question of

the law of its storage of mechanical energy. If the friction forces

no, then the law of conservation of mechanical energy obeys

Xia: the total mechanical energy of the system remains

constant If friction forces act, then the energy

no longer remains constant, but decreases with movement. But

at the same time, the internal energy always increases. With development

physicists discovered all new types of energy: there was

detected light energy, electromagnetic energy

waves, chemical energy manifested in chemical

reactions (it suffices to indicate at least

on the chemical energy stored in explosives

substances and transforming into mechanical and thermal

energy in an explosion), finally, nuclear

energy. It turned out that the work done on the body

equal to the increment of the sum of all types of body energy; Job

same, performed by some body on, by other bodies,

is equal to the decrease in the total energy of the given body. For all

types of energy, it turned out that it is possible to transfer energy from

one type to another, the transfer of energy from one body to

another, but what with all such transition; total energy

of all kinds remain strictly constant all the time. In that

is the universality of the law of conservation of energy.

Although the total amount of energy remains constant

the amount of energy useful to us may decrease

and in fact is constantly decreasing. Transition

energy into another form may mean its transition into

useless form. In mechanics, this is usually

heating of the environment, rubbing surfaces and

etc. Such losses are not only disadvantageous, but also harmful.

are found on the mechanisms themselves; yes, to avoid

overheating, it is necessary to specially cool the rubbing

parts of mechanisms.

At the beginning of this section, we noted that energy, like momentum, is a conserved quantity. However, in the previous lessons, we were convinced that the work of all forces acting on the body leads to a change in the kinetic and potential energy of the body, but we did not receive the law of conservation of energy. In this lesson, we will derive the law of conservation of total mechanical energy, and also talk about the conditions under which it is valid.

2. Using the law of conservation of energy, calculate the speed of a body freely falling from a certain height near the surface of the Earth. Compare the result obtained with the one obtained from the kinematic formulas.

3. Consider the following questions and their answers:

List of questions - answers:

Question: Where does the energy of the system go when the bodies interact with dissipative forces? Why is it impossible to use the law of conservation of total mechanical energy?

Answer: Basically, energy under the action of dissipative forces is converted into heat. In general, we can say that energy is transformed into another, non-mechanical energy. Thus, we cannot use the law of total mechanical energy, since mechanics is not able to describe thermal or any other phenomena occurring in this system.

Question: Does the law of conservation of energy hold true if both the force of gravity and the elastic force act on the body at the same time?

Answer: Yes, of course, if a system of bodies interacts with several conservative forces, and it is closed, then the law of conservation of total mechanical energy is fulfilled.

Question: How does the action of an external force affect the energy of a system of bodies? Is the total mechanical energy conserved in this case?

Answer: The fact that an external force acts on a system of bodies indicates that the system ceases to be closed, therefore, the law of conservation of total mechanical energy does not work in it. However, if a body is included in this system, the measure of interaction of which is this external force, then this new extended system will already be closed, and, therefore, the energy conservation law will be valid.

Question: The satellite is in orbit around the earth. With the help of a rocket engine, he was transferred to another orbit. Has its mechanical energy changed?

Answer: Yes, the energy has changed due to the fact that the system is no longer closed during the operation of the rocket engine.

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

Kinetic and potential energy

There are two types of energy - kinetic and potential.

DEFINITION

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

DEFINITION

Potential energy- this is the energy, which is determined by the mutual arrangement of bodies, as well as the nature of the forces of interaction between these bodies.

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

Potential energy is the energy due to 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 value:

A body can have both kinetic and potential energy at the same time.

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 external forces act on a body (or system of bodies), for example, the law of conservation of mechanical energy is not fulfilled. 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 makes it possible to establish a quantitative relationship between various forms of motion of matter. Just like , it is valid not only for , but for all natural phenomena. The law of conservation of energy says that energy in nature cannot be destroyed in the same way 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 form to another.

Examples of problem solving

EXAMPLE 1

EXAMPLE 2