Loss of mechanical energy. Law of energy conservation

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One of the most important laws, according to which a physical quantity - energy is conserved in an isolated system. All known processes in nature, without exception, obey this law. In an isolated system, energy can only change from one form to another, but its amount remains constant.

In order to understand what the law is and where it comes from, let's take a body of mass m, which we drop to the Earth. At point 1, the body is at a height h and is at rest (velocity is 0). At point 2, the body has a certain speed v and is at a distance h-h1. At point 3, the body has a maximum speed and it almost lies on our Earth, that is, h=0

At point 1, the body has only potential energy, since the speed of the body is 0, so the total mechanical energy is equal.

After we released the body, it began to fall. When falling, the potential energy of the body decreases, as the height of the body above the Earth decreases, and its kinetic energy increases, as the speed of the body increases. In the section 1-2 equal to h1, the potential energy will be equal to

And the kinetic energy will be equal at that moment ( - the speed of the body at point 2):

The closer the body becomes to the Earth, the less its potential energy, but at the same moment the speed of the body increases, and because of this, the kinetic energy. That is, at point 2, the law of conservation of energy works: potential energy decreases, kinetic energy increases.

At point 3 (on the surface of the Earth), the potential energy is zero (since h = 0), and the kinetic energy is maximum (where v3 is the speed of the body at the moment of falling to the Earth). Since , then the kinetic energy at point 3 will be equal to Wk=mgh. Therefore, at point 3 the total energy of the body is W3=mgh and is equal to the potential energy at height h. The final formula for the law of conservation of mechanical energy will be:

The formula expresses the law of conservation of energy in a closed system in which only conservative forces act: the total mechanical energy of a closed system of bodies interacting with each other only by conservative forces does not change with any movements of these bodies. There are only mutual transformations of the potential energy of bodies into their kinetic energy and vice versa.

In the formula we used.

1. Consider a free fall of a body from a certain height h relative to the surface of the Earth (Fig. 77). At the point A the body is motionless, therefore it has only potential energy. At the point B on high h 1 the body has both potential energy and kinetic energy, since the body at this point has a certain speed v one . At the moment of touching the Earth's surface, the potential energy of the body is zero, it has only kinetic energy.

Thus, during the fall of the body, its potential energy decreases, and its kinetic energy increases.

full mechanical energy E called the sum of potential and kinetic energies.

E = E n+ E to.

2. Let us show that the total mechanical energy of the system of bodies is conserved. Consider once again the fall of a body onto the surface of the Earth from a point A exactly C(see fig. 78). We will assume that the body and the Earth are a closed system of bodies, in which only conservative forces act, in this case gravity.

At the point A the total mechanical energy of a body is equal to its potential energy

E = E n = mgh.

At the point B the total mechanical energy of the body is

E = E n1 + E k1 .
E n1 = mgh 1 , E k1 = .

Then

E = mgh 1 + .

body speed v 1 can be found using the kinematics formula. Since the movement of the body from the point A exactly B equals

s = h – h 1 = , then= 2 g(h – h 1).

Substituting this expression into the formula for the total mechanical energy, we obtain

E = mgh 1 + mg(h – h 1) = mgh.

Thus, at the point B

E = mgh.

At the moment of touching the Earth's surface (point C) the body has only kinetic energy, therefore, its total mechanical energy

E = E k2 = .

The speed of the body at this point can be found by the formula = 2 gh, given that the initial velocity of the body is zero. After substituting the expression for the velocity into the formula for the total mechanical energy, we obtain E = mgh.

Thus, we have obtained that at the three considered points of the trajectory, the total mechanical energy of the body is equal to the same value: E = mgh. We will arrive at the same result by considering other points of the body's trajectory.

The total mechanical energy of a closed system of bodies, in which only conservative forces act, remains unchanged for any interactions of the bodies of the system.

This statement is the law of conservation of mechanical energy.

3. Friction forces act in real systems. So, with a free fall of a body in the considered example (see Fig. 78), the force of air resistance acts, therefore, the potential energy at the point A more total mechanical energy at a point B and at the point C by the amount of work done by the force of air resistance: D E = A. In this case, the energy does not disappear, part of the mechanical energy is converted into the internal energy of the body and air.

4. As you already know from the 7th grade physics course, various machines and mechanisms are used to facilitate human labor, which, having energy, perform mechanical work. Such mechanisms include, for example, levers, blocks, cranes, etc. When work is performed, energy is converted.

Thus, any machine is characterized by a value showing what part of the energy transferred to it is used usefully or what part of the perfect (total) work is useful. This value is called efficiency(efficiency).

The efficiency h is called the value equal to the ratio of useful work A n to full work A.

The efficiency is usually expressed as a percentage.

h = 100%.

5. Problem solution example

A parachutist weighing 70 kg separated from a stationary helicopter and, having flown 150 m before opening the parachute, acquired a speed of 40 m/s. What is the work done by the air resistance force?

Given:

Solution

m= 70 kg

v0 = 0

v= 40 m/s

sh= 150 m

For the zero level of potential energy, we choose the level at which the skydiver acquired speed v. Then, when separated from the helicopter in the initial position at a height h the total mechanical energy of a parachutist is equal to his potential energy E=E n = mgh, since its kineti-

The thermal energy at a given altitude is zero. Flying distance s= h, the skydiver acquired kinetic energy, and his potential energy at this level became equal to zero. Thus, in the second position, the total mechanical energy of the parachutist is equal to his kinetic energy:

E = E k = .

Potential energy of a skydiver E n when separated from the helicopter is not equal to the kinetic E k, since the force of air resistance does work. Consequently,

A = E to - E P;

A =– mgh.

A\u003d - 70 kg 10 m / s 2 150 m \u003d -16 100 J.

The work has a minus sign, since it is equal to the loss of total mechanical energy.

Answer: A= -16 100 J.

Questions for self-examination

1. What is total mechanical energy?

2. Formulate the law of conservation of mechanical energy.

3. Does the law of conservation of mechanical energy hold true if a friction force acts on the bodies of the system? Explain the answer.

4. What does the efficiency ratio show?

Task 21

1. A ball of mass 0.5 kg is thrown vertically upwards with a speed of 10 m/s. What is the potential energy of the ball at its highest point?

2. An athlete weighing 60 kg jumps from a 10-meter tower into the water. What are equal to: the potential energy of the athlete relative to the surface of the water before the jump; its kinetic energy when entering the water; its potential and kinetic energy at a height of 5 m relative to the surface of the water? Ignore air resistance.

3. Determine the efficiency of an inclined plane 1 m high and 2 m long when a load of 4 kg is moved along it under the action of a force of 40 N.

Chapter 1 Highlights

1. Types of mechanical movement.

2. Basic kinematic quantities (Table 2).

table 2

Name	Designation	What characterizes	Unit of measurement	Measurement method	Vector or scalar	Relative or absolute
Coordinate a	x, y, z	body position	m	Ruler	Scalar	Relative
Way	l	change in body position	m	Ruler	Scalar	Relative
moving	s	change in body position	m	Ruler	Vector	Relative
Time	t	process duration	from	Stopwatch	Scalar	Absolute
Speed	v	speed of change of position	m/s	Speedometer	Vector	Relative
Acceleration	a	rate of change of speed	m/s2	Accelerometer	Vector	Absolute

3. Basic equations of motion (Table 3).

Table 3

	rectilinear		Uniform around the circumference
	Uniform	Uniformly accelerated
Acceleration	a = 0	a= const; a =	a = ; a= w2 R
Speed	v = ; vx =	v = v 0 + at; vx = v 0x + axt	v= ; w =
moving	s = vt; sx=vxt	s = v 0t + ; sx=vxt+
Coordinate	x = x 0 + vxt	x = x 0 + v 0xt +

4. Basic traffic charts.

Table 4

Type of movement	Modulus and projection of acceleration	Velocity modulus and projection	Modulus and projection of displacement	Coordinate*	Way*
Uniform
Equally accelerated e

5. Basic dynamic quantities.

Table 5

Name	Designation	Unit of measurement	What characterizes	Measurement method	Vector or scalar	Relative or absolute
Weight	m	kg	inertia	Interaction, weighing on a balance scale	Scalar	Absolute
Strength	F	H	Interaction	Weighing on spring scales	Vector	Absolute
body momentum	p = m v	kgm/s	body condition	Indirect	Vector	relative i
Impulse of force	Ft	Ns	Change in body state (change in body momentum)	Indirect	Vector	Absolute

6. Basic laws of mechanics

Table 6

Name	Formula	Note	Limits and conditions of applicability
Newton's first law		Establishes the existence of inertial frames of reference	Valid: in inertial frames of reference; for material points; for bodies moving at speeds much less than the speed of light
Newton's second law	a =	Allows you to determine the force acting on each of the interacting bodies
Newton's third law	F 1 = F 2	Applies to both interacting bodies
Newton's second law (other wording)	mvm v 0 = Ft	Sets the change in momentum of a body when an external force acts on it
Law of conservation of momentum	m 1 v 1 + m 2 v 2 = = m 1 v 01 + m 2 v 02	Valid for closed systems
Law of conservation of mechanical energy	E = E to + E P	Valid for closed systems in which conservative forces act
The law of change of mechanical energy	A=D E = E to + E P	Valid for non-closed systems in which non-conservative forces act

7. Forces in mechanics.

8. Basic energy quantities.

Table 7

Name	Designation	Unit of measurement	What characterizes	Relationship with other quantities	Vector or scalar	Relative or absolute
Work	A	J	Energy measurement	A =fs	Scalar	Absolute
Power	N	Tue	The speed of doing work	N =	Scalar	Absolute
mechanical energy	E	J	Ability to do work	E = E n+ E to	Scalar	Relative
Potential energy	E P	J	Position	E n = mgh E n =	Scalar	Relative
Kinetic energy	E to	J	Position	E k =	Scalar	Relative
Efficiency			What part of the perfect work is useful

This video tutorial is intended for self-acquaintance with the topic "The Law of Conservation of Mechanical Energy". Let us first define the total energy and the closed system. Then we formulate the Law of conservation of mechanical energy and consider in which areas of physics it can be applied. We will also define work and learn how to define it by looking at the formulas associated with it.

The topic of the lesson is one of the fundamental laws of nature - law of conservation of mechanical energy.

We talked earlier about potential and kinetic energy, and also about the fact that a body can have both potential and kinetic energy together. Before talking about the law of conservation of mechanical energy, let's remember what total energy is. full mechanical energy called the sum of the potential and kinetic energies of the body.

Also remember what is called a closed system. closed system- this is such a system in which there is a strictly defined number of bodies interacting with each other and no other bodies from the outside act on this system.

When we have decided on the concept of total energy and a closed system, we can talk about the law of conservation of mechanical energy. So, the total mechanical energy in a closed system of bodies interacting with each other through gravitational forces or elastic forces (conservative forces) remains unchanged during any movement of these bodies.

We have already studied the Law of Conservation of Momentum (FSI):

Very often it happens that the tasks can be solved only with the help of the laws of conservation of energy and momentum.

It is convenient to consider the conservation of energy using the free fall of a body from a certain height as an example. If a body is at rest at a certain height relative to the earth, then this body has potential energy. As soon as the body begins its movement, the height of the body decreases, and the potential energy also decreases. At the same time, the speed begins to increase, kinetic energy appears. When the body approaches the ground, the height of the body is 0, the potential energy is also 0, and the maximum will be the kinetic energy of the body. This is where the transformation of potential energy into kinetic energy is seen (Fig. 1). The same can be said about the movement of the body in reverse, from the bottom up, when the body is thrown vertically upwards.

Rice. 1. Free fall of a body from a certain height

Additional problem 1. "On the fall of a body from a certain height"

Task 1

Condition

The body is at a height from the surface of the Earth and begins to fall freely. Determine the speed of the body at the moment of contact with the ground.

Solution 1:

initial speed of the body. Need to find .

Consider the law of conservation of energy.

Rice. 2. Body movement (task 1)

At the top point, the body has only potential energy: . When the body approaches the ground, the height of the body above the ground will be equal to 0, which means that the potential energy of the body has disappeared, it has turned into kinetic:

According to the law of conservation of energy, we can write:

Body weight is reduced. Transforming the indicated equation, we obtain: .

The final answer will be: . Plugging in the whole value, we get: .

Answer: .

An example of a problem solution:

Rice. 3. An example of designing a solution to problem No. 1

This problem can be solved in another way, as a vertical movement with free fall acceleration.

Solution 2 :

Let's write the equation of motion of the body in projection onto the axis:

When the body approaches the Earth's surface, its coordinate will be 0:

Gravitational acceleration is preceded by a "-" sign, since it is directed against the selected axis.

Substituting the known values, we get that the body fell over time . Now let's write the equation for the speed:

Assuming the free fall acceleration to be equal, we get:

The minus sign means that the body is moving against the direction of the selected axis.

Answer: .

An example of designing a solution to problem No. 1 in the second way.

Rice. 4. An example of designing a solution to problem No. 1 (method 2)

Also, to solve this problem, it was possible to use a formula that does not depend on time:

Of course, it should be noted that we considered this example taking into account the absence of friction forces, which in reality act in any system. Let us turn to the formulas and see how the law of conservation of mechanical energy is written:

Additional task 2

A body falls freely from a height. Determine at what height the kinetic energy is equal to a third of the potential ().

Rice. 5. Illustration for problem number 2

Solution:

When a body is at a height, it has potential energy, and only potential energy. This energy is determined by the formula: . This will be the total energy of the body.

When the body begins to move down, the potential energy decreases, but at the same time, the kinetic energy increases. At the height to be determined, the body will already have some speed V. For the point corresponding to the height h, the kinetic energy has the form:

The potential energy at this height will be denoted as follows: .

According to the law of conservation of energy, our total energy is conserved. This energy remains constant. For a point, we can write the following relationship: (according to Z.S.E.).

Recalling that the kinetic energy according to the condition of the problem is , we can write the following: .

Please note: the mass and acceleration of free fall is reduced, after simple transformations, we get that the height at which this ratio is satisfied is .

Answer:

An example of task 2.

Rice. 6. Formulation of the solution of problem No. 2

Imagine that a body in some frame of reference has kinetic and potential energy. If the system is closed, then with any change, a redistribution occurs, the transformation of one type of energy into another, but the total energy remains the same in its value (Fig. 7).

Rice. 7. Law of conservation of energy

Imagine a situation where a car is moving along a horizontal road. The driver turns off the engine and continues driving with the engine turned off. What happens in this case (Fig. 8)?

Rice. 8. Vehicle movement

In this case, the car has kinetic energy. But you know perfectly well that over time the car will stop. Where did the energy go in this case? After all, the potential energy of the body in this case also did not change, it was some kind of constant relative to the Earth. How did the energy change happen? In this case, the energy went to overcome the forces of friction. If friction occurs in the system, then it also affects the energy of this system. Let's see how the energy change is written in this case.

Energy changes, and this change in energy is determined by the work against the friction force. We can determine the work of the friction force using the formula, which is known from class 7 (force and displacement are directed oppositely):

So, when we talk about energy and work, we must understand that every time we must take into account the fact that part of the energy is spent on overcoming the forces of friction. Work is being done to overcome the forces of friction. Work is a quantity that characterizes the change in the energy of a body.

In conclusion of the lesson, I would like to say that work and energy are inherently related quantities through acting forces.

Additional task 3

Two bodies - a bar with mass and a plasticine ball with mass - move towards each other with the same speeds (). After the collision, the plasticine ball stuck to the bar, the two bodies continue to move together. Determine what part of the mechanical energy has turned into the internal energy of these bodies, taking into account the fact that the mass of the bar is 3 times the mass of the plasticine ball ().

Solution:

The change in internal energy can be denoted by . As you know, there are several types of energy. In addition to mechanical, there is also thermal, internal energy.

The law of conservation of energy states that the energy of the body never disappears and does not reappear, it can only turn from one form to another. This law is universal. It has its own formulation in various branches of physics. Classical mechanics considers the law of conservation of mechanical energy.

The total mechanical energy of a closed system of physical bodies, between which conservative forces act, is a constant value. This is how the law of conservation of energy in Newtonian mechanics is formulated.

A closed or isolated system is considered to be a physical system that is not affected by external forces. It does not exchange energy with the surrounding space, and its own energy, which it possesses, remains unchanged, that is, it is preserved. In such a system, only internal forces act, and the bodies interact with each other. It can only convert potential energy into kinetic energy and vice versa.

The simplest example of a closed system is a sniper rifle and a bullet.

Types of mechanical forces

The forces that act inside a mechanical system are usually divided into conservative and non-conservative.

conservative forces are considered whose work does not depend on the trajectory of the body to which they are applied, but is determined only by the initial and final position of this body. The conservative forces are also called potential. The work of such forces in a closed loop is zero. Examples of conservative forces − gravity force, elastic force.

All other forces are called non-conservative. These include friction force and drag force. They are also called dissipative forces. These forces perform negative work during any motions in a closed mechanical system, and under their action the total mechanical energy of the system decreases (dissipates). It passes into other, non-mechanical types of energy, for example, into heat. Therefore, the law of conservation of energy in a closed mechanical system can be fulfilled only if there are no non-conservative forces in it.

The total energy of a mechanical system consists of kinetic and potential energy and is their sum. These types of energies can transform into each other.

Potential energy

Potential energy is called the energy of interaction of physical bodies or their parts with each other. It is determined by their mutual arrangement, that is, the distance between them, and is equal to the work that needs to be done to move the body from the reference point to another point in the field of conservative forces.

Potential energy has any motionless physical body, raised to some height, since it is affected by gravity, which is a conservative force. Such energy is possessed by water at the edge of a waterfall, a sled at the top of a mountain.

Where did this energy come from? While the physical body was being raised to a height, work was done and energy was expended. It is this energy that was stored in the raised body. And now this energy is ready to do work.

The value of the potential energy of the body is determined by the height at which the body is located relative to some initial level. We can take any point we choose as a starting point.

If we consider the position of the body relative to the Earth, then the potential energy of the body on the surface of the Earth is zero. And on top h it is calculated by the formula:

E p = mɡ h ,

where m - body mass

ɡ - acceleration of gravity

h – height of the center of mass of the body relative to the Earth

ɡ \u003d 9.8 m / s 2

When a body falls from a height h1 up to height h2 gravity does work. This work is equal to the change in potential energy and has a negative value, since the magnitude of potential energy decreases as the body falls.

A = - ( E p2 - E p1) = - ∆ E p ,

where E p1 is the potential energy of the body at height h1 ,

E p2 - potential energy of a body at a height h2 .

If the body is raised to a certain height, then work is done against the forces of gravity. In this case, it has a positive value. And the value of the potential energy of the body increases.

An elastically deformed body (compressed or stretched spring) also has potential energy. Its value depends on the stiffness of the spring and on how long it was compressed or stretched, and is determined by the formula:

E p \u003d k (∆x) 2 / 2 ,

where k - stiffness coefficient,

∆x - lengthening or contraction of the body.

The potential energy of the spring can do work.

Kinetic energy

Translated from the Greek "kinema" means "movement". The energy that a physical body receives as a result of its movement is called kinetic. Its value depends on the speed of movement.

A soccer ball rolling across the field, a sledge rolling down a mountain and continuing to move, an arrow fired from a bow - they all have kinetic energy.

If a body is at rest, its kinetic energy is zero. As soon as a force or several forces act on the body, it will begin to move. And since the body is moving, the force acting on it does work. The work of the force, under the influence of which the body from rest will go into motion and change its speed from zero to ν , is called kinetic energy body mass m .

If, at the initial moment of time, the body was already in motion, and its speed had the value v 1 , and at the end it was equal to v 2 , then the work done by the force or forces acting on the body will be equal to the increment in the kinetic energy of the body.

∆ E k = E k 2 - E k 1

If the direction of the force coincides with the direction of motion, then positive work is done, and the kinetic energy of the body increases. And if the force is directed in the direction opposite to the direction of motion, then negative work is done, and the body gives off kinetic energy.

Law of conservation of mechanical energy

Ek 1 + E p1= E k 2 + E p2

Any physical body located at some height has potential energy. But when falling, it begins to lose this energy. Where does she go? It turns out that it does not disappear anywhere, but turns into the kinetic energy of the same body.

Suppose , at some height, a load is motionlessly fixed. Its potential energy at this point is equal to the maximum value. If we let it go, it will start falling at a certain speed. Therefore, it will begin to acquire kinetic energy. But at the same time, its potential energy will begin to decrease. At the point of impact, the kinetic energy of the body will reach a maximum, and the potential energy will decrease to zero.

The potential energy of a ball thrown from a height decreases, while the kinetic energy increases. Sledges at rest on top of a mountain have potential energy. Their kinetic energy at this moment is zero. But when they start to roll down, the kinetic energy will increase, and the potential energy will decrease by the same amount. And the sum of their values will remain unchanged. The potential energy of an apple hanging on a tree is converted into its kinetic energy when it falls.

These examples clearly confirm the law of conservation of energy, which says that the total energy of a mechanical system is a constant value . The value of the total energy of the system does not change, and the potential energy is converted into kinetic energy and vice versa.

By what amount the potential energy decreases, the kinetic energy will increase by the same amount. Their amount will not change.

For a closed system of physical bodies, the equality
E k1 + E p1 = E k2 + E p2,
where E k1 , E p1 - kinetic and potential energies of the system before any interaction, E k2 , E p2 - corresponding energies after it.

The process of converting kinetic energy into potential energy and vice versa can be seen by watching a swinging pendulum.

Click on the picture

Being in the extreme right position, the pendulum seems to freeze. At this moment, its height above the reference point is maximum. Therefore, the potential energy is also maximum. And the kinetic is zero, since it does not move. But the next moment the pendulum starts moving down. Its speed increases, and, therefore, its kinetic energy increases. But as the height decreases, so does the potential energy. At the bottom point, it will become equal to zero, and the kinetic energy will reach its maximum value. The pendulum will pass this point and begin to rise up to the left. Its potential energy will begin to increase, and its kinetic energy will decrease. Etc.

To demonstrate the transformation of energy, Isaac Newton came up with a mechanical system, which is called Newton's cradle or Newton's balls .

Click on the picture

If the first ball is deflected and then released, its energy and momentum will be transferred to the last one through three intermediate balls, which will remain motionless. And the last ball will deflect with the same speed and rise to the same height as the first one. Then the last ball will transfer its energy and momentum through the intermediate balls to the first one, and so on.

A ball laid aside has the maximum potential energy. Its kinetic energy at this moment is zero. Having started moving, it loses potential energy and acquires kinetic energy, which reaches its maximum at the moment of collision with the second ball, and potential energy becomes equal to zero. Further, the kinetic energy is transferred to the second, then the third, fourth and fifth balls. The latter, having received kinetic energy, begins to move and rises to the same height at which the first ball was at the beginning of the movement. Its kinetic energy at this moment is equal to zero, and the potential energy is equal to the maximum value. Then it starts to fall and in the same way transfers energy to the balls in reverse order.

This continues for quite a long time and could continue indefinitely if there were no non-conservative forces. But in reality, dissipative forces act in the system, under the influence of which the balls lose their energy. Their speed and amplitude gradually decrease. And eventually they stop. This confirms that the law of conservation of energy is satisfied only in the absence of non-conservative forces.

4.1. Losses of mechanical energy and work of nonpotential forces. K.P.D. Cars

If the law of conservation of mechanical energy were fulfilled in real installations (such as the Oberbeck machine), then many calculations could be done based on the equation:

T about + P about = T(t) + P(t) , (8)

where: T about + P about = E about- mechanical energy at the initial moment of time;

T(t) + P(t) = E(t)- mechanical energy at some subsequent point in time t.

We apply formula (8) to the Oberbeck machine, where it is possible to change the height of the load on the threads (the center of mass of the rod part of the installation does not change its position). Let's lift the load h from the lower level (where we consider P=0). Let the system with the lifted load first be at rest, i.e. T about = 0, P about = mgh(m is the mass of the load on the thread). After the release of the load, the system begins to move and its kinetic energy is equal to the sum of the energy of the translational movement of the load and the rotational movement of the rod part of the machine:

T= + , (9)

where - the speed of forward movement of the load;

, J- angular velocity of rotation and moment of inertia of the rod part

For the moment of time when the load falls to the zero level, from formulas (4), (8) and (9) we obtain:

m gh=
, (10)

where
,  0k - linear and angular speeds at the end of the descent.

Formula (10) is an equation from which (depending on the conditions of the experiment) it is possible to determine the speed And , mass m, moment of inertia J, or the height h.

However, formula (10) describes the ideal type of installation, with the movement of parts of which there are no forces of friction and resistance. If the work of such forces is not equal to zero, then the mechanical energy of the system is not conserved. Instead of equation (8), in this case, one should write:

T about +P about = T(t) + P(t) + A s , (11)

where BUT s- the total work of non-potential forces for the entire time of movement.

For the Oberbeck machine we get:

m gh =
, (12)

where ,  k - linear and angular speeds at the end of the descent in the presence of energy losses.

In the installation under study, friction forces act on the axis of the pulley and the additional block, as well as atmospheric resistance forces during the movement of the load and the rotation of the rods. The work of these non-potential forces significantly reduces the speed of movement of machine parts.

As a result of the action of non-potential forces, part of the mechanical energy is converted into other forms of energy: internal energy and radiation energy. At the same time, work As exactly equal to the sum of these other forms of energy, i.e. the fundamental, general physical law of conservation of energy is always fulfilled.

However, in installations where macroscopic bodies move, there are observed mechanical energy loss determined by the amount of work As. This phenomenon exists in all real machines. For this reason, a special concept is introduced: efficiency factor - efficiency. This coefficient determines the ratio of useful work to the stored (consumed) energy.

In the Oberbeck machine, the useful work is equal to the total kinetic energy at the end of the descent of the load on the thread, and the efficiency is is determined by the formula:

efficiency.= (13)

Here P about = mgh- stored energy expended (converted) into the kinetic energy of the machine and into energy losses equal to As, T to- total kinetic energy at the end of the descent of the load (formula (9)).