Diesel engine and gasoline: efficiency comparison. What is efficiency? Concept, definition, application

Not a single action is carried out without losses - they are always there. The result obtained is always less than the effort that has to be expended to achieve it. About how great the losses in the performance of work, and evidenced by the coefficient of performance (COP).

What is hidden behind this abbreviation? In fact, it is the coefficient of efficiency of the mechanism or indicator rational use energy. The value of efficiency does not have any units of measurement, it is expressed as a percentage. This coefficient is defined as the ratio of the useful work of the device to the work spent on its operation. To calculate the efficiency, the calculation formula will look like this:

Efficiency \u003d 100 * (useful work performed / work expended)

In various devices, to calculate this ratio, they use different meanings. For electric motors, the efficiency will look like the ratio of useful work done to electrical energy received from the network. For will be defined as the ratio of the useful work done to the amount of heat consumed.

For definitions of efficiency it is necessary that all are different and the work is expressed in the same units. Then it will be possible to compare any objects, such as electricity generators and biological objects, in terms of efficiency.

As already noted, due to inevitable losses during the operation of mechanisms, the efficiency is always less than 1. Thus, the efficiency of thermal plants reaches 90%, for internal combustion engines the efficiency is less than 30%, the efficiency of an electrical transformer is 98%. The concept of efficiency can be applied both to the mechanism as a whole and to its individual nodes. In a general assessment of the effectiveness of the mechanism as a whole (its efficiency), the product of the efficiency of individual constituent parts this device.

Problem effective use fuel did not appear today. With a continuous increase in the cost of energy resources, the issue of increasing the efficiency of mechanisms is turning from a purely theoretical into a practical issue. If the efficiency of a conventional car does not exceed 30%, then we simply throw away 70% of our money spent on fueling a car.

Consideration of the efficiency of the internal combustion engine (internal combustion engine) shows that losses occur at all stages of its operation. So, only 75% of the incoming fuel burns in the engine cylinders, and 25% is released into the atmosphere. Of all the burned fuel, only 30-35% of the released heat is spent on useful work, the rest of the heat is either lost with exhaust gases or remains in the car's cooling system. Of the received power, about 80% is used for useful work, the rest of the power is spent on overcoming friction forces and is used by the auxiliary mechanisms of the car.

Even on such a simple example, the analysis of the effectiveness of the mechanism allows you to determine the directions in which work should be carried out to reduce losses. Yes, one of priority areas- ensuring complete combustion of fuel. This is achieved by additional spraying of fuel and increasing pressure, which is why engines with direct injection and turbocharging are becoming so popular. The heat removed from the engine is used to preheat the fuel in order to improve its volatility, and mechanical losses are reduced through the use of modern grades

Here we have considered such a concept as it is described what it is and what it affects. The efficiency of its work is considered on the example of an internal combustion engine and the directions and ways of increasing the capabilities of this device, and, consequently, the efficiency, are determined.

The coefficient of performance (COP) is a value that expresses in percentage terms the efficiency of a particular mechanism (engine, system) regarding the conversion of the received energy into useful work.

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Why diesel efficiency is higher

The efficiency index for different engines can vary greatly and depends on a number of factors. have a relatively low efficiency due to the large number of mechanical and thermal losses that occur during the operation of a power unit of this type.

The second factor is the friction that occurs during the interaction of mating parts. Most of the useful energy consumption is the driving of the engine pistons, as well as the rotation of the parts inside the motor, which are structurally fixed on the bearings. About 60% of the combustion energy of gasoline is spent only to ensure the operation of these units.

Additional losses are caused by the operation of other mechanisms, systems and attachments. It also takes into account the percentage of losses due to resistance at the time of the next charge of fuel and air, and then the release of exhaust gases from the internal combustion engine cylinder.

If we compare a diesel installation and a gasoline engine, diesel engine has a significantly higher efficiency compared to a gasoline unit. Power units on gasoline have an efficiency of about 25-30% of total received energy.

In other words, out of 10 liters of gasoline spent on the engine, only 3 liters are spent on useful work. The rest of the energy from the combustion of fuel went to waste.

With the same displacement indicator, the power of an atmospheric gasoline engine is higher, but is achieved at higher speeds. The engine needs to be “turned”, losses increase, fuel consumption increases. It is also necessary to mention the torque, which literally means the force that is transmitted from the motor to the wheels and drives the car. Gasoline ICEs reach their maximum torque at higher RPMs.

A similar naturally aspirated diesel achieves peak torque at low rpm, while using less diesel to do useful work, which means higher efficiency and fuel economy.

Diesel fuel generates more heat compared to gasoline, the combustion temperature of diesel fuel is higher, and the knock resistance index is higher. It turns out that a diesel internal combustion engine has more useful work done on a certain amount of fuel.

Energy value of diesel fuel and gasoline

Diesel fuel is made up of heavier hydrocarbons than gasoline. The lower efficiency of a gasoline plant compared to a diesel engine also lies in the energy component of gasoline and the features of its combustion. Complete combustion of an equal amount of diesel fuel and gasoline will give more heat in the first case. Heat in a diesel engine is more fully converted into useful mechanical energy. It turns out that when burning the same amount of fuel per unit of time, it is the diesel engine that will do more work.

It is also worth considering the features of injection and the creation of appropriate conditions for the full combustion of the mixture. In a diesel engine, fuel is supplied separately from air, it is not injected into the intake manifold, but directly into the cylinder at the very end of the compression stroke. The result is more heat and the most complete combustion of a portion of the working fuel-air mixture.

Results

Designers are constantly striving to improve the efficiency of both diesel and gasoline engines. Increase in the number of intake and exhaust valves per cylinder, active use, electronic control fuel injection, throttle and other solutions can significantly increase efficiency. To a greater extent this applies to the diesel engine.

Thanks to these features, a modern diesel engine is able to completely burn a portion of diesel fuel saturated with hydrocarbons in the cylinder and produce a large amount of torque at low revs. Low RPMs mean less friction loss and the resulting drag. For this reason, a diesel engine is today one of the most productive and economical types of internal combustion engines, the efficiency of which often exceeds 50%.

Read also

Why it's better to warm up the engine before driving: lubrication, fuel, wear of cold parts. How to warm up a diesel engine in winter.

  • List of the most reliable gasoline and diesel engines: 4-cylinder power units, in-line 6-cylinder internal combustion engines and V-shaped power plants. Rating.


  • Using this or that mechanism, we do work, which always exceeds that which is necessary to achieve the goal. In accordance with this, a distinction is made between complete or expended work A c and useful work A p. If, for example, our goal is to lift a load of mass m to a height h, then useful work is that which is due only to overcoming the force of gravity acting on the load. With a uniform lifting of the load, when the force applied by us is equal to the force of gravity of the load, this work can be found as follows:

    A p \u003d F t h \u003d mgh. (24.1)

    If we use a block or some other mechanism to lift the load, then, in addition to the gravity of the load, we also have to overcome the gravity of the parts of the mechanism, as well as the friction force acting in the mechanism. For example, using a movable block, we will have to do additional work to lift the block itself with a cable and to overcome the friction force in the axis of the block. In addition, when we win in strength, we always lose on the road (more on this below), which also affects performance. All this leads to the fact that the work we spent is more useful:

    A c > A p

    Useful work is always only a part of full work performed by a person using a mechanism.

    A physical quantity that shows what proportion of useful work from all the work expended is called efficiency mechanism.

    The abbreviation for efficiency is efficiency.

    To find the efficiency of the mechanism, it is necessary to divide the useful work by the work that was expended when using this mechanism.

    Efficiency is often expressed as a percentage and denoted by the Greek letter η (read "this"):

    η =* 100% (24.2)

    Since the numerator A p in this formula is always less than the denominator A c , the efficiency is always less than 1 (or 100%).

    When constructing mechanisms, they strive to increase their efficiency. To do this, reduce the friction in the axes of the mechanisms and their mass. In cases where friction is negligible and the mechanisms used have a mass that is negligible compared to the mass of the load being lifted, the efficiency is only slightly less than 1. In this case, the work expended can be considered approximately equal to the useful work:

    A c ≈ A p (24.3)

    It should be remembered that no gain in work can be obtained with the help of a simple mechanism.

    Since each of the works in equality (24.3) can be expressed as the product of the corresponding force and the path travelled, this equality can be rewritten as follows:

    F 1 s 1 ≈ F 2 s 2 (24.4)

    From this it follows that,

    winning with the help of the mechanism in strength, we lose the same amount on the way, and vice versa.

    This law is called "golden rule" of mechanics. Its author is the ancient Greek scientist Heron of Alexandria, who lived in the 1st century BC. n. e.

    The "golden rule" of mechanics is an approximate law, since it does not take into account the work to overcome friction and gravity of the parts of the devices used. Nevertheless, it can be very useful when analyzing the operation of any simple mechanism.

    So, for example, thanks to this rule, we can immediately say that the worker shown in Figure 47, with a double gain in strength to lift a load by 10 cm, will have to lower the opposite end of the lever by 20 cm. The same will be the case shown in Figure 47. Figure 58. When the hand of the person holding the rope drops 20 cm, the weight attached to the movable block will rise only 10 cm.

    1. Why does the work expended when using mechanisms turn out to be more useful work all the time? 2. What is called the efficiency of the mechanism? 3. Can the efficiency of a mechanism be equal to 1 (or 100%)? Why? 4. How to increase efficiency? 5. What is " Golden Rule» mechanics? Who is its author? 6. Give examples of the manifestation of the "golden rule" of mechanics when using various simple mechanisms.

    Basic theoretical information

    mechanical work

    The energy characteristics of motion are introduced on the basis of the concept mechanical work or force work. Work done by a constant force F, is called physical quantity, equal to the product of the modules of force and displacement, multiplied by the cosine of the angle between the force vectors F and displacement 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, they build a graph of the dependence of the force on the displacement and find the area of ​​\u200b\u200bthe 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 extr = kx).

    Power

    The work done by a force per unit of time is called power. Power P(sometimes referred to as N) is a physical quantity equal to the ratio of work A to the time span 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(unless, 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:

    With this formula, we can calculate instant power(power in this moment time) if instead of speed we substitute the value instantaneous speed. How to know what power to count? If the task asks for power at a point in time or at some point in space, then it is considered instantaneous. If you are asking about power over a certain period of time or a section of the path, then look for the average power.

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

    What work is useful and what is spent is determined from the condition of a particular task by logical reasoning. For example, if a crane does the work of lifting a load to a certain height, then the work of lifting the load will be useful (since the crane was created for it), and the work done by the crane's electric motor will be spent.

    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 purpose of doing the work (useful work or power), and what was the mechanism or way of doing all the work (expended power or work).

    In the general case, the efficiency shows how efficiently the 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 the body's mass and the square of its speed is called kinetic energy of the body (energy of motion):

    That is, if a car with a mass of 2000 kg moves at a speed of 10 m/s, then it has a kinetic energy equal to E k \u003d 100 kJ and is capable of doing work of 100 kJ. This energy can turn into heat (when the car brakes, the tires 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 doesn't matter where the car is going, 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. the energy of motion, and is capable of doing work to deform bodies or impart acceleration to bodies with which a collision occurs.

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

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

    The kinetic energy theorem is also valid in the general case when the body moves under the action 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 of acceleration and deceleration of a body.

    Potential energy

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

    Potential energy is determined by the mutual position of the bodies (for example, the position of the body relative to the Earth's surface). 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 of such forces on a closed trajectory is zero. This property is possessed by the force of gravity and the force of elasticity. 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 the body: the potential energy is equal to the work done by the force of gravity when lowering the body to the zero level ( h is the 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 down to zero. The work of gravity is equal to the change in the potential energy of the body, taken with the opposite sign:

    Often in tasks for energy, you have to find work to lift (turn over, get out of the pit) 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. It is not the potential energy itself that has physical meaning, but its change when the body moves from one position to another. This change does not depend on the choice of the zero level.

    Potential energy of a stretched spring calculated by the formula:

    where: k- spring stiffness. A stretched (or compressed) spring is capable of setting in motion a body attached to it, that is, imparting kinetic energy to this body. Therefore, such a spring has a reserve of energy. Stretch 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 of 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 distance traveled (this type of force whose work depends on the trajectory and the distance traveled is called: dissipative forces). The concept of potential energy for the friction force cannot be introduced.

    Efficiency

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

    Efficiency can be calculated both in terms of work and in terms of power. Useful and expended work (power) is always determined by simple logical reasoning.

    In electric motors, efficiency is the ratio of the performed (useful) mechanical work 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 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 motors, thermal power plants, semiconductor devices, biological objects, etc.

    Due to the inevitable energy losses due to friction, heating of surrounding bodies, etc. The efficiency is always less than unity. Accordingly, the efficiency is expressed in fractions of the energy expended, that is, in the form proper fraction or as a percentage, and is a dimensionless quantity. Efficiency characterizes how efficiently a machine or mechanism works. 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%.

    The task in which you need to find the efficiency or it is known, you need to start with a logical reasoning - what work is useful and what is spent.

    Law of conservation of mechanical energy

    full mechanical energy 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) is called:

    If mechanical energy does not pass into other forms, for example, into internal (thermal) energy, then the sum of kinetic and potential energy remains unchanged. If mechanical energy is converted 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 energies of the bodies that make up a closed system (i.e., one in which no external forces act, and their work is equal to zero, respectively) and interacting with each other by gravitational forces and elastic forces, remains unchanged:

    This statement expresses law of conservation of energy (LSE) in mechanical processes. It is a consequence of Newton's laws. The law of conservation of mechanical energy is fulfilled only when the 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 the system of bodies. The law says 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 connection between the coordinates and velocities of the body in two different points trajectories 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, almost always moving bodies, along with gravitational forces, elastic forces and other forces, are acted upon by friction forces or resistance forces of the medium. The work of 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, the energy as a whole (i.e. not only mechanical energy) is conserved in any case.

    In any physical interactions, energy does not arise and does not disappear. It only changes from one form to another. This experimentally established fact expresses the 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 " perpetual motion machine» (perpetuum mobile) - a machine that could do work indefinitely without expending energy.

    Miscellaneous work tasks

    If the task is to find mechanical work, then first choose a way to find it:

    1. Jobs 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 action of this force in the selected reference frame. Note that the angle must be chosen between the force and displacement vectors.
    2. work external force can be found as the difference between the 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 by the formula: A = mgh, where h- the height to which it rises center of gravity of the body.
    4. Work can be found as the product of power and time, i.e. according to the formula: A = Pt.
    5. Work can be found as the area of ​​a figure under a graph of force versus displacement or power versus time.

    The law of conservation of energy and the dynamics of rotational motion

    The tasks of this topic are quite complex mathematically, but with knowledge of the approach they are solved according to a completely standard algorithm. In all problems you will have to consider the rotation of the body in the vertical plane. The solution will be reduced to the following sequence of actions:

    1. It is necessary to determine the point of interest to you (the point at which it is necessary to determine the speed of the body, the force of the thread tension, weight, and so on).
    2. Write down Newton's second law at this point, given 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 speed squared from one equation and substitute it into another.
    5. Carry out other necessary mathematical operations to get the final result.

    When solving problems, remember that:

    • The condition for passing the upper point during rotation on the threads at a minimum speed is the reaction force of the support N at the top point is 0. The same condition is met when passing through 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 the body from the surface of the sphere is that the reaction force of the support 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 active forces. An example of such problems is the impact interaction of bodies.

    Impact (or collision) It is customary to call the short-term interaction of bodies, as a result of which their velocities experience significant changes. During the 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 with the help of Newton's laws. The application of the laws of conservation of energy and momentum in many cases makes it possible to exclude the process of collision from consideration and obtain a relationship between the velocities of bodies before and after the collision, bypassing all intermediate values ​​of these quantities.

    One often has 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 Such a shock interaction is called, in which the bodies are connected (stick together) with each other and move on as one body.

    In a perfectly inelastic impact, mechanical energy is not conserved. It partially or completely passes 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 released heat (it is highly desirable to draw a drawing first).

    Absolutely elastic impact

    Absolutely elastic impact is 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 fulfilled. A simple example An absolutely elastic collision can be the central impact of two billiard balls, one of which was at rest before the collision.

    center punch balls is called a collision, in which the speeds 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 the collision, if their velocities before the collision are known. The central impact is very rarely realized in practice, especially when it comes to collisions of atoms or molecules. In non-central elastic collision, the velocities of particles (balls) before and after the collision are not directed along the same straight line.

    A special case of a non-central elastic impact is 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 elastic collision are always directed perpendicular to each other.

    Conservation laws. Difficult tasks

    Multiple bodies

    In some tasks on the law of conservation of energy, the cables with which some objects move 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 the potential energy, for example, at the level of the axis of rotation or at the level of the lowest point where one of the loads is located and make a drawing;
    2. the law of conservation of mechanical energy is written, in which the sum of the kinetic and potential energies of both bodies in the initial situation is written on the left side, and the sum of the kinetic and potential energies of both bodies in the final situation is written on the right side;
    3. take into account that angular velocities 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.

    Projectile burst

    In the event of a projectile burst, 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 on selected axes.

    Collisions with a heavy plate

    Let towards a heavy plate that moves at a speed v, a light ball of mass moves m with speed u n. Since the momentum of the ball is much less than the momentum of the plate, the plate's speed will not change after impact, and it will continue to move at the same speed and in the same direction. As a result of elastic impact, the ball will fly off the plate. Here it is important to understand that the speed of the ball relative to the plate will not change. In this case, for the final speed of the ball we get:

    Thus, the speed of the ball after impact is increased by twice the speed of the wall. A similar argument for the case when the ball and the plate were moving in the same direction before the impact leads to the result that the speed of the ball is reduced by twice the speed of the wall:

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

    1. Study all the topics and complete all the tests and tasks given in the study materials on this site. To do this, you need nothing at all, namely: to 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 tasks for different topics and varying complexity. The latter can only be learned by solving thousands of problems.
    2. Learn all formulas and laws in physics, and formulas and methods in mathematics. In fact, it is also very simple to do this, 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. basic level difficulties that can also be learned, and thus, completely automatically and without difficulty to solve at the right time most CT. After that, 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 solve both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and the knowledge of formulas and methods, it is also necessary to be able to properly plan time, distribute forces, and most importantly fill out the answer form correctly, without confusing either the numbers of answers and tasks, or your own name. Also, during the RT, it is important to get used to the style of posing questions in tasks, which may seem very unusual to an unprepared person on the DT.

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

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    Content:

    Each system or device has a certain coefficient of performance (COP). This indicator characterizes the efficiency of their work on the return or transformation of any type of energy. According to its value, the efficiency is a measureless quantity, represented in the form numerical value ranging from 0 to 1, or as a percentage. This characteristic fully 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 factor for these devices determines their effectiveness in performing the main function.

    How to find engine efficiency? The formula for the efficiency of an electric motor looks like this: ƞ \u003d P2 / P1. In this formula, P1 is the supplied electrical power and P2 is the usable mechanical power generated by the engine. The value of electrical power (P) is determined by the formula P \u003d UI, and mechanical - P \u003d A / t, as the ratio of work to a unit of time.

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

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

    To cool the 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 norms, this indicates a possible imminent.

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

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

    Efficiency drop and total losses in the electric motor

    There are many negative factors that influence the amount of total losses in electric motors. Exist 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 terms. First of all, these are the losses associated with and partial remagnetization of the stator core. Steel elements have little effect and are practically not taken into account. This is due to the speed of rotation of the stator, which significantly exceeds the speed of the magnetic flux. In this case, the rotor must rotate in strict accordance with the declared technical characteristics.

    Meaning mechanical power rotor shaft is lower than the electromagnetic power. The difference is the amount of losses that occur in the winding. Mechanical losses include friction in bearings and brushes, as well as the effect of an air barrier 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 occur in individual engine components. All these factors together reduce the efficiency by about 0.5% of the rated power of the unit.

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

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