How is the effective efficiency determined? The concept of efficiency: definition, formula and application in physics

Content:

Each system or device has a certain coefficient useful action(efficiency). This indicator characterizes the efficiency of their work in releasing or converting any type of energy. In terms of its value, efficiency is an immeasurable quantity, represented in the form numerical value ranging from 0 to 1, or as a percentage. This characteristic in to the fullest also applies to all types of electric motors.

Efficiency characteristics in electric motors

Electric motors belong to the category of devices that convert electrical energy into mechanical energy. The efficiency of these devices determines their effectiveness in performing the main function.

How to find engine efficiency? The formula for electric motor efficiency looks like this: ƞ = P2/P1. In this formula, P1 is the electrical power supplied and P2 is the useful mechanical power produced by the engine. The value of electrical power (P) is determined by the formula P = UI, and mechanical power - P = A/t, as the ratio of work per unit time.

The efficiency factor must be taken into account when choosing an electric motor. Great value have efficiency losses associated with reactive currents, power reduction, engine heating and other negative factors.

The conversion of electrical energy into mechanical energy is accompanied by a gradual loss of power. Loss of efficiency is most often associated with heat release when the electric motor heats up during operation. The causes of losses can be magnetic, electrical and mechanical, arising under the influence of friction. Therefore, as an example, the best situation is when electrical energy was consumed for 1000 rubles, and useful work produced for only 700-800 rubles. Thus, the efficiency in in this case will be 70-80%, and the whole difference turns into thermal energy, which heats the engine.

To cool electric motors, fans are used to drive air through special gaps. In accordance with established standards, A-class engines can heat up to 85-90 0 C, B-class - up to 110 0 C. If the engine temperature exceeds established standards, this indicates a possible soon.

Depending on the load, the efficiency of the electric motor can change its value:

• For idle speed - 0;
• At 25% load - 0.83;
• At 50% load - 0.87;
• At 75% load - 0.88;
• At full 100% load, the efficiency is 0.87.

One of the reasons for a decrease in the efficiency of an electric motor may be current asymmetry, when a different voltage appears on each of the three phases. For example, if in the 1st phase there is 410 V, in the 2nd - 402 V, in the 3rd - 288 V, then the average voltage value will be (410 + 402 + 388) / 3 = 400 V. Voltage asymmetry will have value: 410 - 388 = 22 volts. Thus, the efficiency loss for this reason will be 22/400 x 100 = 5%.

Decrease in efficiency and total losses in the electric motor

There are many negative factors, under the influence of which the quantity is formed total losses V electric motors. There are special techniques, allowing them to be determined in advance. For example, you can determine the presence of a gap through which power is partially supplied from the network to the stator, and then to the rotor.

The power losses that occur in the starter itself consist of several components. First of all, these are losses associated with partial magnetization reversal of the stator core. Steel elements have a negligible impact and are practically not taken into account. This is due to the stator rotation speed, which significantly exceeds the speed magnetic flux. In this case, the rotor must rotate in strict accordance with the declared technical characteristics.

The mechanical power value of the rotor shaft is lower than the electromagnetic power. The difference is the amount of losses occurring in the winding. Mechanical losses include friction in bearings and brushes, as well as the effect of air barriers on rotating parts.

Asynchronous electric motors are characterized by the presence of additional losses due to the presence of teeth in the stator and rotor. In addition, vortex flows may appear in individual engine components. All these factors together reduce the efficiency by approximately 0.5% of the rated power of the unit.

When calculating possible losses, the formula is used Engine efficiency, which allows you to calculate the decrease in this parameter. First of all, the total power losses, which are directly related to the engine load, are taken into account. As the load increases, losses proportionally increase and efficiency decreases.

The designs of asynchronous electric motors take into account all possible losses if available maximum loads. Therefore, the efficiency range of these devices is quite wide and ranges from 80 to 90%. In high-power engines this figure can reach 90-96%.

Energy supplied to the mechanism in the form of work by driving forces A dv.s. and moments per cycle of steady motion, is spent on performing useful work And p.s.. , as well as for performing work A Ftr associated with overcoming friction forces in kinematic pairs and environmental resistance forces.

Let's consider steady motion. The increment of kinetic energy is zero, i.e.

In this case, the work done by the forces of inertia and gravity is equal to zero A Ri = 0, A G = 0. Then for steady motion the work of the driving forces is equal to

And the engine =A p.s. + A Ftr.

Consequently, for a full cycle of steady motion, the work of all driving forces is equal to the sum of the work of the forces of production resistance and non-production resistance (friction forces).

Mechanical efficiency η (efficiency)– the ratio of the work of production resistance forces to the work of all driving forces during steady motion:

η = . (3.61)

As can be seen from formula (3.61), efficiency shows what fraction of the mechanical energy supplied to the machine is usefully spent on performing the work for which the machine was created.

The ratio of the work of non-productive resistance forces to the work of driving forces is called loss factor :

ψ = . (3.62)

The mechanical loss coefficient shows what proportion of the mechanical energy supplied to the machine ultimately turns into heat and is uselessly lost in the surrounding space.

Hence we have a relationship between efficiency and loss factor

η =1- ψ.

It follows from this formula that in no mechanism can the work of non-productive resistance forces be equal to zero, therefore the efficiency is always less than one ( η <1 ). From the same formula it follows that efficiency can be zero if A dv.s = A Ftr. The movement in which A dv.s = A Ftr is called single . The efficiency cannot be less than zero, because for this it is necessary that A dv.s<А Fтр . A phenomenon in which the mechanism is at rest and condition A dv.s is satisfied<А Fтр, называется self-braking phenomenon mechanism. A mechanism for which η = 1 is called perpetual motion machine .

Thus, the efficiency is within the limits

0 £ η < 1 .

Let's consider the determination of efficiency for various methods of connecting mechanisms.

3.2.2.1. Determination of efficiency in series connection

Let there be n mechanisms connected in series (Figure 3.16).

And the engine 1 A 1 2 A 2 3 A 3 A n-1 n A n

Figure 3.16 - Diagram of series-connected mechanisms

The first mechanism is driven by driving forces that do work A dv.s. Since the useful work of each previous mechanism, spent on production resistance, is the work of the driving forces for each subsequent mechanism, the efficiency of the first mechanism will be equal to:

η 1 =A 1 /A dv.s ..

For the second mechanism, the efficiency is equal to:

η 2 =A 2 /A 1 .

And finally, for the nth mechanism the efficiency will be:

η n =A n /A n-1

The overall efficiency is:

η 1 n =A n /And the engine

The value of the overall efficiency can be obtained by multiplying the efficiency of each individual mechanism, namely:

η 1 n = η 1 η 2 η 3 …η n= .

Hence, general mechanical efficiency in series of connected mechanisms equals work mechanical efficiency of individual mechanisms that make up one overall system:

η 1 n = η 1 η 2 η 3 …η n .(3.63)

3.2.2.2 Determination of efficiency for mixed connection

In practice, connecting mechanisms turns out to be more complex. More often, a serial connection is combined with a parallel one. Such a connection is called mixed. Let's look at an example of a complex connection (Figure 3.17).

The energy flow from mechanism 2 is distributed in two directions. In turn, from mechanism 3 ¢¢ the energy flow is also distributed in two directions. The total work of production resistance forces is equal to:

And p.s. = A¢n + A¢¢n + A¢¢¢n.

The overall efficiency of the entire system will be equal to:

η =A p.s. /A dv.s =(A¢n + A¢¢n + A¢¢¢n)/A dv.s . (3.64)

To determine the overall efficiency, it is necessary to identify energy flows in which the mechanisms are connected in series and calculate the efficiency of each flow. Figure 3.17 shows the solid line I-I, the dashed line II-II and the dash-dotted line III-III three energy flows from a common source.

And the engine A 1 A ¢ 2 A ¢ 3 … A ¢ n-1 A ¢ n

II A ¢¢ 2 II

A ¢¢ 3 4 ¢¢ A ¢¢ 4 A ¢¢ n-1 n ¢¢ A ¢¢ n

Basic theoretical information

Mechanical work

The energy characteristics of motion are introduced based on the concept mechanical work or force work. Work done by a constant force F, is a physical quantity equal to the product of the force and displacement moduli multiplied by the cosine of the angle between the force vectors F and movements S:

Work is a scalar quantity. It can be either positive (0° ≤ α < 90°), так и отрицательна (90° < α ≤ 180°). At α = 90° the work done by the force is zero. In the SI system, work is measured in joules (J). A joule is equal to the work done by a force of 1 newton to move 1 meter in the direction of the force.

If the force changes over time, then to find the work, build a graph of the force versus displacement and find the area of ​​the figure under the graph - this is the work:

An example of a force whose modulus depends on the coordinate (displacement) is the elastic force of a spring, which obeys Hooke’s law ( F control = kx).

Power

The work done by a force per unit time is called power. Power P(sometimes denoted by the letter N) – physical quantity equal to the work ratio A to a period of time t during which this work was completed:

This formula calculates average power, i.e. power generally characterizing the process. So, work can also be expressed in terms of power: A = Pt(if, of course, the power and time of doing the work are known). The unit of power is called the watt (W) or 1 joule per second. If the motion is uniform, then:

Using this formula we can calculate instant power(power at a given time), if instead of speed we substitute the value of instantaneous speed into the formula. How do you know what power to count? If the problem asks for power at a moment in time or at some point in space, then instantaneous is considered. If they ask about power over a certain period of time or part of the route, then look for average power.

Efficiency - efficiency factor, is equal to the ratio of useful work to expended, or useful power to expended:

Which work is useful and which is wasted is determined from the conditions of a specific task through logical reasoning. For example, if a crane does the work of lifting a load to a certain height, then the useful work will be the work of lifting the load (since it is for this purpose that the crane was created), and the expended work will be the work done by the crane’s electric motor.

So, useful and expended power do not have a strict definition, and are found by logical reasoning. In each task, we ourselves must determine what in this task was the goal of doing work (useful work or power), and what was the mechanism or way of doing all the work (expended power or work).

In general, efficiency shows how efficiently a mechanism converts one type of energy into another. If the power changes over time, then the work is found as the area of ​​the figure under the graph of power versus time:

Kinetic energy

A physical quantity equal to half the product of a body’s mass and the square of its speed is called kinetic energy of the body (energy of movement):

That is, if a car weighing 2000 kg moves at a speed of 10 m/s, then it has kinetic energy equal to E k = 100 kJ and is capable of doing 100 kJ of work. This energy can be converted into heat (when a car brakes, the rubber of the wheels, the road and the brake discs heat up) or can be spent on deforming the car and the body that the car collided with (in an accident). When calculating kinetic energy, it does not matter where the car is moving, since energy, like work, is a scalar quantity.

A body has energy if it can do work. For example, a moving body has kinetic energy, i.e. energy of motion, and is capable of doing work to deform bodies or impart acceleration to bodies with which a collision occurs.

The physical meaning of kinetic energy: in order for a body at rest with a mass m began to move at speed v it is necessary to do work equal to the obtained value of kinetic energy. If the body has a mass m moves at speed v, then to stop it it is necessary to do work equal to its initial kinetic energy. When braking, kinetic energy is mainly (except for cases of impact, when the energy goes to deformation) “taken away” by the friction force.

Kinetic energy theorem: the work done by the resultant force is equal to the change in the kinetic energy of the body:

The theorem on kinetic energy is also valid in the general case, when a body moves under the influence of a changing force, the direction of which does not coincide with the direction of movement. It is convenient to apply this theorem in problems involving acceleration and deceleration of a body.

Potential energy

Along with kinetic energy or energy of motion, the concept plays an important role in physics potential energy or energy of interaction of bodies.

Potential energy is determined by the relative position of bodies (for example, the position of the body relative to the surface of the Earth). The concept of potential energy can be introduced only for forces whose work does not depend on the trajectory of the body and is determined only by the initial and final positions (the so-called conservative forces). The work done by such forces on a closed trajectory is zero. This property is possessed by gravity and elastic force. For these forces we can introduce the concept of potential energy.

Potential energy of a body in the Earth's gravity field calculated by the formula:

The physical meaning of the potential energy of a body: potential energy is equal to the work done by gravity when lowering the body to zero level ( h– distance from the center of gravity of the body to the zero level). If a body has potential energy, then it is capable of doing work when this body falls from a height h to zero level. The work done by gravity is equal to the change in the potential energy of the body, taken with the opposite sign:

Often in energy problems one has to find the work of lifting (turning over, getting out of a hole) the body. In all these cases, it is necessary to consider the movement not of the body itself, but only of its center of gravity.

The potential energy Ep depends on the choice of the zero level, that is, on the choice of the origin of the OY axis. In each problem, the zero level is chosen for reasons of convenience. What has a physical meaning is not the potential energy itself, but its change when a body moves from one position to another. This change is independent of the choice of zero level.

Potential energy of a stretched spring calculated by the formula:

Where: k– spring stiffness. An extended (or compressed) spring can set a body attached to it in motion, that is, impart kinetic energy to this body. Consequently, such a spring has a reserve of energy. Tension or compression X must be calculated from the undeformed state of the body.

The potential energy of an elastically deformed body is equal to the work done by the elastic force during the transition from a given state to a state with zero deformation. If in the initial state the spring was already deformed, and its elongation was equal to x 1, then upon transition to a new state with elongation x 2, the elastic force will do work equal to the change in potential energy, taken with the opposite sign (since the elastic force is always directed against the deformation of the body):

Potential energy during elastic deformation is the energy of interaction of individual parts of the body with each other by elastic forces.

The work of the friction force depends on the path traveled (this type of force, whose work depends on the trajectory and the path traveled is called: dissipative forces). The concept of potential energy for the friction force cannot be introduced.

Efficiency

Efficiency factor (efficiency)– characteristic of the efficiency of a system (device, machine) in relation to the conversion or transmission of energy. It is determined by the ratio of usefully used energy to the total amount of energy received by the system (the formula has already been given above).

Efficiency can be calculated both through work and through power. Useful and expended work (power) are always determined by simple logical reasoning.

In electric motors, efficiency is the ratio of the (useful) mechanical work performed to the electrical energy received from the source. In heat engines, the ratio of useful mechanical work to the amount of heat expended. In electrical transformers, the ratio of electromagnetic energy received in the secondary winding to the energy consumed by the primary winding.

Due to its generality, the concept of efficiency makes it possible to compare and evaluate from a unified point of view such different systems as nuclear reactors, electric generators and engines, thermal power plants, semiconductor devices, biological objects, etc.

Due to inevitable energy losses due to friction, heating of surrounding bodies, etc. Efficiency is always less than unity. Accordingly, efficiency is expressed as a fraction of the energy expended, that is, in the form of a proper fraction or as a percentage, and is a dimensionless quantity. Efficiency characterizes how efficiently a machine or mechanism operates. The efficiency of thermal power plants reaches 35-40%, internal combustion engines with supercharging and pre-cooling - 40-50%, dynamos and high-power generators - 95%, transformers - 98%.

A problem in which you need to find the efficiency or it is known, you need to start with logical reasoning - which work is useful and which is wasted.

Law of conservation of mechanical energy

Total mechanical energy is called the sum of kinetic energy (i.e. the energy of motion) and potential (i.e. the energy of interaction of bodies by the forces of gravity and elasticity):

If mechanical energy does not transform into other forms, for example, into internal (thermal) energy, then the sum of kinetic and potential energy remains unchanged. If mechanical energy turns into thermal energy, then the change in mechanical energy is equal to the work of the friction force or energy losses, or the amount of heat released, and so on, in other words, the change in total mechanical energy is equal to the work of external forces:

The sum of the kinetic and potential energy of the bodies that make up a closed system (i.e. one in which there are no external forces acting, and their work is correspondingly zero) and the gravitational and elastic forces interacting with each other remains unchanged:

This statement expresses law of conservation of energy (LEC) in mechanical processes. It is a consequence of Newton's laws. The law of conservation of mechanical energy is satisfied only when bodies in a closed system interact with each other by forces of elasticity and gravity. In all problems on the law of conservation of energy there will always be at least two states of a system of bodies. The law states that the total energy of the first state will be equal to the total energy of the second state.

Algorithm for solving problems on the law of conservation of energy:

1. Find the points of the initial and final position of the body.
2. Write down what or what energies the body has at these points.
3. Equate the initial and final energy of the body.
4. Add other necessary equations from previous physics topics.
5. Solve the resulting equation or system of equations using mathematical methods.

It is important to note that the law of conservation of mechanical energy made it possible to obtain a relationship between the coordinates and velocities of a body at two different points of the trajectory without analyzing the law of motion of the body at all intermediate points. The application of the law of conservation of mechanical energy can greatly simplify the solution of many problems.

In real conditions, moving bodies are almost always acted upon, along with gravitational forces, elastic forces and other forces, by frictional forces or environmental resistance forces. The work done by the friction force depends on the length of the path.

If friction forces act between the bodies that make up a closed system, then mechanical energy is not conserved. Part of the mechanical energy is converted into internal energy of bodies (heating). Thus, energy as a whole (i.e., not only mechanical) is conserved in any case.

During any physical interactions, energy neither appears nor disappears. It just changes from one form to another. This experimentally established fact expresses a fundamental law of nature - law of conservation and transformation of energy.

One of the consequences of the law of conservation and transformation of energy is the statement about the impossibility of creating a “perpetual motion machine” (perpetuum mobile) - a machine that could do work indefinitely without consuming energy.

Various tasks for work

If the problem requires finding mechanical work, then first select a method for finding it:

1. A job can be found using the formula: A = FS∙cos α . Find the force that does the work and the amount of displacement of the body under the influence of this force in the chosen frame of reference. Note that the angle must be chosen between the force and displacement vectors.
2. The work of an external force can be found as the difference in mechanical energy in the final and initial situations. Mechanical energy is equal to the sum of the kinetic and potential energies of the body.
3. The work done to lift a body at a constant speed can be found using the formula: A = mgh, Where h- height to which it rises body center of gravity.
4. Work can be found as the product of power and time, i.e. according to the formula: A = Pt.
5. The work can be found as the area of ​​the figure under the graph of force versus displacement or power versus time.

Law of conservation of energy and dynamics of rotational motion

The problems of this topic are quite complex mathematically, but if you know the approach, they can be solved using a completely standard algorithm. In all problems you will have to consider the rotation of the body in the vertical plane. The solution will come down to the following sequence of actions:

1. You need to determine the point you are interested in (the point at which you need to determine the speed of the body, the tension force of the thread, weight, and so on).
2. Write down Newton’s second law at this point, taking into account that the body rotates, that is, it has centripetal acceleration.
3. Write down the law of conservation of mechanical energy so that it contains the speed of the body at that very interesting point, as well as the characteristics of the state of the body in some state about which something is known.
4. Depending on the condition, express the squared speed from one equation and substitute it into the other.
5. Carry out the remaining necessary mathematical operations to obtain the final result.

When solving problems, you need to remember that:

• The condition for passing the top point when rotating on a thread at a minimum speed is the support reaction force N at the top point is 0. The same condition is met when passing the top point of the dead loop.
• When rotating on a rod, the condition for passing the entire circle is: the minimum speed at the top point is 0.
• The condition for the separation of a body from the surface of the sphere is that the support reaction force at the separation point is zero.

Inelastic collisions

The law of conservation of mechanical energy and the law of conservation of momentum make it possible to find solutions to mechanical problems in cases where the acting forces are unknown. An example of this type of problem is the impact interaction of bodies.

By impact (or collision) It is customary to call a short-term interaction of bodies, as a result of which their speeds experience significant changes. During a collision of bodies, short-term impact forces act between them, the magnitude of which, as a rule, is unknown. Therefore, it is impossible to consider the impact interaction directly using Newton's laws. The application of the laws of conservation of energy and momentum in many cases makes it possible to exclude the collision process itself from consideration and obtain a connection between the velocities of bodies before and after the collision, bypassing all intermediate values ​​of these quantities.

We often have to deal with the impact interaction of bodies in everyday life, in technology and in physics (especially in the physics of the atom and elementary particles). In mechanics, two models of impact interaction are often used - absolutely elastic and absolutely inelastic impacts.

Absolutely inelastic impact They call this impact interaction in which bodies connect (stick together) with each other and move on as one body.

In a completely inelastic collision, mechanical energy is not conserved. It partially or completely turns into the internal energy of bodies (heating). To describe any impacts, you need to write down both the law of conservation of momentum and the law of conservation of mechanical energy, taking into account the heat released (it is highly advisable to make a drawing first).

Absolutely elastic impact

Absolutely elastic impact called a collision in which the mechanical energy of a system of bodies is conserved. In many cases, collisions of atoms, molecules and elementary particles obey the laws of absolutely elastic impact. With an absolutely elastic impact, along with the law of conservation of momentum, the law of conservation of mechanical energy is satisfied. A simple example of a perfectly elastic collision would be the central impact of two billiard balls, one of which was at rest before the collision.

Central strike balls is called a collision in which the velocities of the balls before and after the impact are directed along the line of centers. Thus, using the laws of conservation of mechanical energy and momentum, it is possible to determine the velocities of the balls after a collision if their velocities before the collision are known. Central impact is very rarely implemented in practice, especially when it comes to collisions of atoms or molecules. In a non-central elastic collision, the velocities of particles (balls) before and after the collision are not directed in one straight line.

A special case of an off-central elastic impact can be the collision of two billiard balls of the same mass, one of which was motionless before the collision, and the speed of the second was not directed along the line of the centers of the balls. In this case, the velocity vectors of the balls after an elastic collision are always directed perpendicular to each other.

Conservation laws. Complex tasks

Multiple bodies

In some problems on the law of conservation of energy, the cables with which certain objects are moved can have mass (that is, not be weightless, as you might already be used to). In this case, the work of moving such cables (namely, their centers of gravity) must also be taken into account.

If two bodies connected by a weightless rod rotate in a vertical plane, then:

1. choose a zero level to calculate potential energy, for example at the level of the axis of rotation or at the level of the lowest point of one of the weights and be sure to make a drawing;
2. write down the law of conservation of mechanical energy, in which on the left side we write the sum of the kinetic and potential energy of both bodies in the initial situation, and on the right side we write the sum of the kinetic and potential energy of both bodies in the final situation;
3. take into account that the angular velocities of the bodies are the same, then the linear velocities of the bodies are proportional to the radii of rotation;
4. if necessary, write down Newton's second law for each of the bodies separately.

Shell burst

When a projectile explodes, explosive energy is released. To find this energy, it is necessary to subtract the mechanical energy of the projectile before the explosion from the sum of the mechanical energies of the fragments after the explosion. We will also use the law of conservation of momentum, written in the form of the cosine theorem (vector method) or in the form of projections onto selected axes.

Collisions with a heavy plate

Let us meet a heavy plate that moves at speed v, a light ball of mass moves m at speed u n. Since the momentum of the ball is much less than the momentum of the plate, after the impact the speed of the plate will not change, and it will continue to move at the same speed and in the same direction. As a result of the elastic impact, the ball will fly away from the plate. It is important to understand here that the speed of the ball relative to the plate will not change. In this case, for the final speed of the ball we obtain:

Thus, the speed of the ball after impact increases by twice the speed of the wall. Similar reasoning for the case when before the impact the ball and the plate were moving in the same direction leads to the result that the speed of the ball decreases by twice the speed of the wall:

In physics and mathematics, among other things, three essential conditions must be met:

1. Study all topics and complete all tests and assignments given in the educational materials on this site. To do this, you need nothing at all, namely: devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on different topics and of varying complexity. The latter can only be learned by solving thousands of problems.
2. Learn all the formulas and laws in physics, and formulas and methods in mathematics. In fact, this is also very simple to do; there are only about 200 necessary formulas in physics, and even a little less in mathematics. In each of these subjects there are about a dozen standard methods for solving problems of a basic level of complexity, which can also be learned, and thus, completely automatically and without difficulty solving most of the CT at the right time. After this, you will only have to think about the most difficult tasks.
3. Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to decide on both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and knowledge of formulas and methods, you must also be able to properly plan time, distribute forces, and most importantly, fill out the answer form correctly, without confusing the numbers of answers and problems, or your own last name. Also, during RT, it is important to get used to the style of asking questions in problems, which may seem very unusual to an unprepared person at the DT.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result at the CT, the maximum of what you are capable of.

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Let's say we are relaxing at the dacha, and we need to fetch water from the well. We lower the bucket into it, scoop up the water and begin to lift it. Have you forgotten what our goal is? That's right: get some water. But look: we are lifting not only the water, but also the bucket itself, as well as the heavy chain on which it hangs. This is symbolized by a two-color arrow: the weight of the load we lift is the sum of the weight of the water and the weight of the bucket and chain.

Considering the situation qualitatively, we will say: along with the useful work of raising water, we also perform other work - lifting a bucket and chain. Of course, without the chain and bucket we would not be able to draw water, but from the point of view of the ultimate goal, their weight “harms” us. If this weight were less, then complete perfect work would also be smaller (with the same usefulness).

Now let's move on to quantitative studying these works and introduce a physical quantity called efficiency.

Task. The loader pours the apples selected for processing from the baskets into the truck. The mass of an empty basket is 2 kg, and the apples in it are 18 kg. What is the share of the loader's useful work from his total work?

Solution. The full job is moving apples in baskets. This work consists of lifting apples and lifting baskets. Important: lifting apples is useful work, but lifting baskets is “useless”, because the purpose of the loader’s work is to move only the apples.

Let's introduce the notation: Fя is the force with which the hands lift only apples up, and Fк is the force with which the hands lift only the basket up. Each of these forces is equal to the corresponding force of gravity: F=mg.

Using the formula A = ±(F||· l) , we “write out” the work of these two forces:

Auseful = +Fя · lя = mя g · h and Аuseless = +Fк · lк = mк g · h

The total work consists of two works, that is, it is equal to their sum:

Afull = Auseful + Auseless = mя g h + mк g h = (mя + mк) · g h

In the problem we are asked to calculate the share of the loader's useful work from his total work. Let's do this by dividing the useful work by the total:

In physics, such shares are usually expressed as percentages and denoted by the Greek letter “η” (read: “this”). As a result we get:

η = 0.9 or η = 0.9 100% = 90%, which is the same.

This number shows that out of 100% of the loader's total work, the share of his useful work is 90%. The problem is solved.

Physical quantity equal to the ratio iyu useful work to total work done, in physics has its own name - efficiency - efficiency:

After calculating the efficiency using this formula, it is usually multiplied by 100%. And vice versa: to substitute efficiency into this formula, its value must be converted from percent to decimal fraction, dividing by 100%.