Physics formulas power and work. From the general equation we get the record

What is strength and power? What this indicator is measured in, what devices are used, and how these are used in practice, we will consider later in the article.

Force

In the world, all bodies of physical nature begin to move due to force. When exposed to it, with passing or opposite direction body movements, work is done. Thus, some force acts on the body.

So, a bicycle moves off thanks to the strength of a person’s legs, and the traction force of an electric locomotive acts on a train. A similar effect occurs with any movement. The work of a force is the value in which the module of force is multiplied, the module of displacement of the point of its application and the cosine of the angle between the vectors of these indicators. The formula in this case looks like this:

A = F s cos (F, s)

If the angle between these vectors is not zero, then work is always done. However, it can have both positive and negative values. No force will act on the body at an angle of 90°.

Consider, for example, a cart pulled by the muscular power of a horse. In other words, the work is done by the traction force in the direction of the cart. But directed downwards or perpendicularly, it does no work (by the way, horsepower is what engine power is measured in).

The work of a force is a scalar quantity and is measured in joules. She may be:

• resultant (when several forces act);
• non-constant (then the calculation is performed with the integral).

Power

How is this value measured? First, let's take a look at what it is. It is clear that the movement of the body begins due to the force that performs. However, in practice, in addition to this, it is necessary to know exactly how it is performed.

Work can be completed in different dates. For example, the same action can be performed small motor or big Electrical engine. The only question is how long it will take. The quantity responsible for such a task is power. What it is measured in, it becomes clear from the definition - this is the ratio of work for a specific time to its value:

Through logical actions, we arrive at the following formula:

that is, the product of force vectors by the speed of movement - and there is power. What is it measured in? According to the international SI system, the unit of measurement of this quantity is 1 watt.

Watt and other units of power

Watt means power, where one joule of work is done in one second. The last unit was named after the Englishman J. Watt, who invented and built the first steam engine. But at the same time, he used a different value - horsepower, which is used to this day. approximately equal to 735.5 watts.

Thus, in addition to watts, power is measured in metric horsepower. And with a very small value, Erg is also used, equal to ten to the minus seventh power of Watts. It is also possible to measure in one unit of mass / force / meters per second, which is equal to 9.81 watts.

Engine power

The named value is one of the most important in any motor, which happens to be the most different power. For example, an electric razor has hundredths of a kilowatt, and a rocket spaceship is in the millions.

For different load different power is needed to maintain a certain speed. For example, a car will become heavier if more cargo is placed in it. Then about the road will increase. Therefore, to maintain the same speed as in the unloaded state, more power is required. Accordingly, the engine will eat more fuel. All drivers are aware of this fact.

But at high speed the inertia of the machine is also important, which is directly proportional to its mass. Experienced drivers who are aware of this fact find when driving the best combination fuel and speed, so that less gasoline is consumed.

Current power

How is power measured? In the same SI unit. It can be measured directly or indirectly.

The first method is implemented using a wattmeter, which consumes significant energy and heavily loads the current source. With it, it is measured from ten watts or more. The indirect method is used when it is necessary to measure small values. The devices for this are an ammeter and a voltmeter connected to the consumer. The formula in this case will look like this:

With a known load resistance, we measure the current flowing through it and find the power as follows:

P \u003d I 2 ∙ R n.

According to the formula P \u003d I 2 / R n, the current power can also be calculated.

What it is measured in a three-phase current network is also not a secret. For this, a familiar device is used - a wattmeter. Moreover, to solve the problem, what can be measured with the help of one, two or even three devices. For example, a four-wire installation would require three devices. And for a three-wire with an unbalanced load - two.

Executed for a certain period of time, to this period of time.

Effective power, engine power given to the working machine directly or through a power transmission. Distinguish between useful, full and nominal E. m. of the engine. Useful is called the E. m. of the engine, minus the power consumption for actuating the auxiliary units or mechanisms necessary for its operation, but having a separate drive (not directly from the engine). Full E. m. - engine power without deducting the indicated costs. Rated E. m., or simply rated power, - E. m., guaranteed by the manufacturer for certain operating conditions. Depending on the type and purpose of the engine, electric meters are installed, regulated by standards or specifications(For example, highest power ship's reversible engine at a certain crankshaft speed in the case of a reverse ship - the so-called reverse power, the highest power of an aircraft engine with a minimum specific consumption fuel - the so-called cruising power, etc.). E. m. depends on the forcing (intensification) of the working process, the size and mechanical efficiency of the engine.

Units

Another common unit of measure for power is horsepower.

Power in mechanics

If a force acts on a moving body, then this force does work. The power in this case is equal to the scalar product of the force vector and the velocity vector with which the body moves:

M- moment, - angular velocity, - pi, n- rotational speed (rpm).

Electric power

Electric power - physical quantity characterizing the rate of transmission or conversion of electrical energy.

S - Apparent power, VA

P - Active power, W

Q - Reactive power, VAr

Power Meters

Notes

see also

Links

• The influence of the form of electric current on its action. Magazine "Radio", number 6, 1999

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See what "Power (physics)" is in other dictionaries:

A science that studies the simplest and at the same time the most general patterns of natural phenomena, the principles and structure of matter and the laws of its motion. The concepts of F. and its laws underlie all natural science. F. belongs to the exact sciences and studies quantities ... Physical Encyclopedia

Examples of various physical phenomena Physics (from other Greek φύσις ... Wikipedia

I. The subject and structure of physics Physics is a science that studies the simplest and, at the same time, the most general patterns of natural phenomena, the properties and structure of matter, and the laws of its motion. Therefore, the concepts of F. and its laws underlie everything ... ... Great Soviet Encyclopedia

High Energy Density Physics (HED Physics) high density energy. Under high ... Wikipedia

Electrical power is a physical quantity that characterizes the rate of transmission or conversion of electrical energy. Contents 1 Instantaneous electrical power ... Wikipedia

Electrical power is a physical quantity that characterizes the rate of transmission or conversion of electrical energy. Contents 1 Instantaneous electrical power 2 DC power ... Wikipedia

This term has other meanings, see Intensity. Intensity Unit MT−3 SI units W/m² ... Wikipedia

Wattmeter (watt + gr. μετρεω I measure) measuring device, designed to determine the power electric current or electromagnetic signal. Contents 1 Classification 2 Low frequency and DC wattmeters ... Wikipedia

Wattmeter (watt + gr. μετρεω I measure) a measuring device designed to determine the power of an electric current or an electromagnetic signal. Contents 1 Classification 2 Low frequency and DC wattmeters ... Wikipedia

Books

• Physics. 7th grade. Didactic materials for the textbook by A. V. Peryshkin. Vertical. GEF, Maron Abram Evseevich, Maron Evgeny Abramovich. This manual includes training tasks, tests for self-control, independent work, test papers and examples of solving typical problems. In total, in the proposed set of didactic ...

Modern man constantly encounters electricity in everyday life and at work, uses devices that consume electric current and devices that generate it. When working with them, it is always necessary to take into account their capabilities, embedded in the technical specifications.

One of the main indicators of any electrical appliance is such a physical quantity as electric power. It is customary to call it the intensity or speed of generation, transmission or conversion of electricity into other types of energy, for example, thermal, light, mechanical.

Transportation or transmission of large electrical powers for industrial purposes is carried out by.

The conversion is carried out at transformer substations.

Electricity consumption occurs in household and industrial devices for various purposes. One of their common types are.

Electric power of generators, power lines and consumers in DC and alternating current has the same physical meaning, which at the same time is expressed by various ratios depending on the shape of the composite signals. In order to determine the general patterns introduced concepts of instantaneous values. They once again emphasize the dependence of the rate of transformation of electricity on time.

Determination of instantaneous electrical power

In theoretical electrical engineering, to derive the basic relationships between current, voltage and power, their representations are used in the form of instantaneous values ​​that are fixed at a certain time moment.

If for very short span time ∆t, a unit elementary charge q moves from point “1” to point “2” under the action of voltage U, then it does work equal to the potential difference between these points. Dividing it by the time interval ∆t, we obtain the expression for the instantaneous power for a unit charge Pe(1-2).

Since under the action of the applied voltage, not only a single charge moves, but all neighboring ones that are under the influence of this force, the number of which is conveniently represented by the number Q, then for them the instantaneous power value PQ (1-2) can be written.

After performing simple transformations, we obtain an expression for power P and the dependence of its instantaneous value p(t) on the components of the product of instantaneous current i(t) and voltage u(t).

Determination of DC electrical power

The magnitude of the voltage drop in the circuit section and the current flowing through it does not change and remains stable, equal to the instantaneous values. Therefore, you can determine the power in this circuit by multiplying these values ​​​​or dividing the perfect work A by the period of time of its execution, as shown in the explanatory picture.

Determination of AC electrical power

Laws of sinusoidal change of currents and voltages transmitted through electrical networks, impose their influence on the expression of power in such circuits. Here the full power operates, which is described by the power triangle and consists of active and reactive components.

The sinusoidal electric current, when passing through power lines with mixed types of loads in all sections, does not change the shape of its harmonic. And the voltage drop on reactive loads shifts in phase in a certain direction. Expressions of instantaneous values ​​help to understand the effect of applied loads on the change in power in the circuit and its direction.

At the same time, immediately pay attention to the fact that the direction of current flow from the generator to the consumer and the transmitted power through the created circuit are completely different things, which in some cases may not only not coincide, but are also directed in opposite directions.

Consider these relationships in their ideal, pure manifestation for different types loads:

active;

capacitive;

inductive.

Power dissipation on a resistive load

We assume that the generator generates an ideal voltage sine wave u, which is applied to the purely active resistance of the circuit. Ammeter A and voltmeter V measure current I and voltage U at each time t.

The graph shows that the sinusoids of the current and the voltage drop across the active resistance coincide in frequency and phase, making the same oscillations. The power, expressed by their product, fluctuates with a double frequency and always remains positive.

p=u∙i=Um∙sinωt∙Um/R∙sinωt=Um 2 /R∙sin 2 ωt=Um 2 /2R∙(1-cos2ωt).

If we pass to the expression , we get: p=P∙(1-cos2ωt).

Next, we integrate the power over the period of one oscillation T and we can notice that the energy increment ∆W over this period increases. As time goes on, active resistance continues to consume new portions of electricity, as shown in the graph.

On reactive loads, the power consumption characteristics are different, they have a different form.

Power dissipation on a capacitive load

In the power supply circuit of the generator, we replace the resistive element with a capacitor with a capacitance C.

The relationship between current and voltage drop across the capacitance is expressed by the relationship: I=C∙dU/dt=ω∙C ∙Um∙cosωt.

We multiply the values ​​of instantaneous expressions of current with voltage and get the value of the power that is consumed by the capacitive load.

p=u∙i=Um∙sinωt∙ωC ∙Um∙cosωt=ω∙C ∙Um 2 ∙sinωt∙cosωt=Um 2 /(2X c)∙sin2ωt=U 2 /(2X c)∙sin2ωt.

Here you can see that the power oscillates around zero with twice the frequency of the applied voltage. Its total value for the harmonic period, as well as the energy increment, is equal to zero.

This means that energy moves along closed circuit chains in both directions, but does no work. This fact is explained by the fact that with an increase in the source voltage along absolute value the power is positive, and the energy flow through the circuit is directed to the tank, where energy is stored.

After the voltage passes to the falling section of the harmonic, energy begins to return from the capacitance to the circuit to the source. In both of these processes, no useful work is done.

Power dissipation on an inductive load

Now, in the power circuit, we replace the capacitor with inductance L.

Here, the current through the inductance is expressed by the relation:

I=1/L∫udt=-Um/ωL∙cos ωt.

Then we get

p=u∙i=Um∙sinωt∙ωC ∙(-Um/ωL∙cosωt)=-Um 2 /ωL∙sinωt∙cosωt=-Um 2 /(2X L)∙sin2ωt=-U 2 /(2X L) sin2ωt.

The resulting expressions allow us to see the nature of the change in the direction of power and the increment of energy on the inductance, which perform the same oscillations that are useless for doing work, as on the capacitance.

The power released on reactive loads is called the reactive component. She in ideal conditions, when the connecting wires have no active resistance, it seems harmless and does not create any harm. But in real power supply conditions, periodic passages and fluctuations of reactive power cause heating of all active elements, including connecting wires, for which a certain energy is expended and the magnitude of the applied total power of the source decreases.

The main difference between the reactive component of power is that it does not useful work, but leads to losses of electrical energy and excess equipment loads, especially dangerous in critical situations.

For these reasons, special ones are used to eliminate the influence of reactive power.

Power allocation to a mixed load

As an example, we use a load on a generator with an actively capacitive characteristic.

In the above graph, to simplify the picture, the sinusoids of currents and voltages are not shown, but it should be noted that with an active-capacitive nature of the load, the current vector leads the voltage.

p=u∙i=Um∙sinωt∙ωC ∙Im∙sin(ωt+φ).

After transformations, we get: p=P∙(1- cos 2ωt)+Q ∙sin2ωt.

These two terms in the last expression are the active and reactive components of the instantaneous apparent power. Only the first of them does useful work.

Power measuring instruments

To analyze the consumption of electricity and pay for it, metering devices are used, which have long been called. Their work is based on measuring the effective values ​​of current and voltage and automatically multiplying them with the output of information.

The meters display the power consumption, taking into account the operating time of electrical appliances on an incremental basis from the moment the meter is turned on under load.

To measure the active component of power in alternating current circuits, varmeters are used, and the reactive component is used. They have different designations units of measure:

watt (W, W);

var (Var, var, var).

To determine the total power consumption, it is necessary to calculate its value using the power triangle formula based on the readings of the wattmeter and varmeter. It is expressed in its units - volt-amperes.

The accepted designations of the units of each help electricians to judge not only its magnitude, but also the nature of the power component.

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The concept of electric current power

Electric current power

Before talking about electrical power, it is necessary to define the concept of power in a general sense. Usually, when people talk about power, they mean some kind of power that this or that object possesses (a powerful electric motor), or an action (a powerful explosion).

But, as we know from school physics, strength and power are different concepts, although they have a dependence.

Initially, power (N) is a characteristic related to a certain event (action), and if it is tied to a certain object, then the concept of power is also conventionally correlated with it. Any physical action implies the impact of force. The force (F) with which a certain path (S) was traveled will equal the work done (A). And the work done in a certain time (t) will be equated to power.

Power is a physical quantity that is equal to the ratio of the work done, which is performed in a certain period of time, to the same period of time. Since work is a measure of energy change, we can also say this: power is the rate of energy conversion of the system.

Having dealt with the concept of mechanical power, we can proceed to the consideration of electrical power (power of electric current). As you should know, U is the work done by moving 1 C, and the current I is the number of coulombs passing in 1 second. So the product of current and voltage is full work, performed in 1 second, that is, electric power, or electric current power.

Analyzing the above formula, we can draw a very simple conclusion: since the electrical power P is equally dependent on the current I and on the voltage U, then, therefore, the same electrical power can be obtained either at high current and low voltage, or vice versa , at high voltage and low current (this is used when transmitting electricity over remote distances from power plants to places of consumption by transformer conversion at step-up and step-down electrical substations).

Active electrical power (this is power that is irrevocably converted into other types of energy - thermal, light, mechanical, etc.) has its own unit of measurement - W (Watt). It is equal to the product of 1 V per 1 A. In everyday life and in production, it is more convenient to measure power in kW (kilowatts, 1 kW = 1000 W). Power plants are already using larger units - mW (megawatts, 1 mW = 1000 kW = 1,000,000 W).

Reactive electrical power is a value that characterizes the type of electrical load that is created in devices (electrical equipment) by energy fluctuations (inductive and capacitive nature) of the electromagnetic field. For conventional alternating current, it is equal to the product of the operating current I and the voltage drop U times the sine of the phase angle between them: Q = U × I × sin (angle). Reactive power has its own unit of measurement called VAr (volt-ampere reactive). Denoted by the letter Q.

Active and reactive electric power can be expressed as an example: an electrical device is given that has heating elements and an electric motor. The heaters are usually made of high resistance material. With the passage of electric current along the spiral of the heating element Electric Energy completely converted into heat. Such an example is typical of active electric power.

The electric motor of this device has a copper winding inside. It is an inductance. And as we know, inductance has the effect of self-induction, and this contributes to the partial return of electricity back to the network. This energy has some offset in current and voltage values, which causes Negative influence to the mains (additionally overloading it).

Capacitance (capacitors) has similar abilities. It is able to accumulate charge and give it back. The difference between capacitance and inductance is the opposite displacement of current and voltage values ​​relative to each other. Such energy of capacitance and inductance (shifted in phase relative to the value of the supply network) will, in fact, be reactive electrical power.

Who is faster than a man or a crane will lift the entire load to a height? Which lift has more power?

Power refers to the rate at which work is done.

Power (N) is a physical quantity equal to the ratio of work A to the time interval t during which this work is done.

Power shows how much work is done per unit of time.

In the International System of Units (SI), the unit of power is called Watt (W) in honor of the English inventor James Watt (Watt), who built the first steam engine.

[N] = W = J/s

1 W = 1 J/s

1 watt is equal to the power of a force that does 1 joule of work in 1 second, or,
when a mass of 100 g is lifted to a height of 1 m in 1 second.

James Watt (1736 - 1819) himself used a different unit of power - horsepower(1 hp), which he introduced in order to be able to compare the performance of a steam engine and a horse.

1 HP = 735 W

However, in real life the average horse has about 1/2 hp, though horses vary, of course.

"Live engines" can briefly increase their power several times.
When running and jumping, a horse can bring its power up to ten times or more.

Making a jump to a height of 1 m, a horse weighing 500 kg develops a power equal to 5,000 W = 6.8 hp.

It is believed that the average power of a person with a calm walk is approximately 0.1 hp. i.e. 70 - 90W.

Like a horse, when running and jumping, a person can develop power many times greater.

It turns out that the most powerful source of mechanical energy is firearms!

With the help of a cannon, it is possible to throw a core with a mass of 900 kg at a speed of 500 m / s, developing about 110,000,000 J of work in 0.01 seconds. This work is equivalent to the work of lifting 75 tons of cargo to the top of the Cheops pyramid (height 150m).

The power of the cannon shot will be 11,000,000,000 W = 15,000,000 hp.

The tension force of a person's muscles is approximately equal to the force of gravity acting on him. When 2 people of the same weight climb the stairs to the same height, but with different speed, then which of them develops more power?

DON'T FORGET WHAT

This formula is valid for uniform motion with a constant speed and in the case of variable motion for an average speed.

Hence it follows that

From the above formulas it can be seen that at a constant engine power, the speed of movement is inversely proportional to the traction force and vice versa

This is the basis of the principle of operation of the gearbox (gearbox) of various vehicles.

AND HOW ARE YOU WITH "SOOBRAZILKOY"?

Now let's check!

1. Do the engines of a tram car develop the same power when it moves at the same speed without passengers and with passengers?

Answer: Pri nalitshii passashiriv sila tjashesti (ves) vagona bolshe, uvelitshivaetsja sila trenia, ravnaja v dannom slutshae sile tjagi, vosrastaet motshnost, uvelitshivaetsja rashod electroenergii.

2. Why does a ship with cargo move slower than without cargo? After all, the engine power in both cases is the same.

Answer: S uvelitsheniem nagruski korabl bolshe pogrushaetsja v wodu. eto uvelitshivaet silu soprotivlenija wodi dvisheniu korablja, tshto privodit k potere skorosti.

3. The tractor has three speeds: 3.08; 4.18 and 5.95 km/h. At what speed will it develop, with the same power, a greater traction force on the hook?

Answer:

If you figured it out yourself, then you are a GOOD FELLOW!
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