PHYSICAL POWER: FORMULAS, TYPES OF POWER AND EXAMPLES - PHYSICAL - 2025

The physical power refers to the amount of work (or energy consumed) per unit time. Power is a scalar magnitude, its unit of measurement in the International System of Units being the joule per second (J / s), known as the watt in honor of James Watt.

Another fairly common unit of measurement is the traditional horsepower. In physics, different types of power are studied: mechanical power, sound power, calorific power, among others. In general there is an intuitive idea of ​​the meaning of potency. It is usually associated with greater power, greater consumption.

Thus, a light bulb consumes more electrical energy if its power is greater; The same goes for a hair dryer, a radiator or a personal computer.

For this reason, it is necessary to fully understand its meaning, the different types of powers that exist and understand how it is calculated and what are the relationships between its most common units of measurement.

Formulas

By definition, to calculate the power consumed or supplied in a time interval, the following expression is used:

P = W / t

In this expression P is power, W is work, and t is time.

If what you want is to calculate the instantaneous power, you should use the following formula:

In this formula ∆t is the increment of time, F is the force and v is the velocity.

Units

The uniqueness of power in the International System of Units is the joule per second (J / s), known as watt (W). It is also quite common in certain contexts to use other units such as kilowatt (kW), horsepower (CV), among others.

Of course, the kilowatt equals 1000 watts. For its part, the equivalence between horsepower and watt is as follows:

1 CV = 745.35 W

Another unit of power, although its use is much less common, is the erg per second (erg / s), which is equivalent to 10 ^-7 W.

It is important to distinguish kilowatt from kilowatt hour (kWh), since the latter is a unit of energy or work and not of power.

Power types

Among the different types of power that exist, some of the most important are those that are going to be studied below.

Mechanical power

The mechanical power exerted on a rigid solid is obtained by making the product between the total resultant force applied and the speed transmitted to that body.

P = F ∙ v

This expression is equivalent to the expression: P = W / t, and in fact it is obtained from it.

In the event that a rotational movement of the rigid solid also occurs and that, therefore, the forces exerted on it modify its angular velocity, giving rise to an angular acceleration, it follows that:

P = F ∙ v + M ∙ ω

In this expression M is the moment resulting from the applied forces and ω is the angular velocity of the body.

Electric power

The electrical power supplied or consumed by an electrical component is the result of dividing the amount of electrical energy delivered or absorbed by said component and the time spent on it. It is calculated from the following expression:

P = V ∙ I

In this equation V is the potential difference across the component and I is the intensity of electric current that passes through it.

In the particular case that the component is an electrical resistance, the following expressions can be used to calculate the power: P = R ∙ I ² = V ² / R, where R is the value of the electrical resistance of the component in question.

Heating power

The calorific power of a component is defined as the amount of energy dissipated or released as heat by said component in a unit of time. It is calculated from the following expression:

P = E / t

In this expression E is the energy released in the form of heat.

Sound power

Sound power is defined as the energy transported by a sound wave in a unit of time through a certain surface.

Thus, the sound power depends on both the intensity of the sound wave and the surface crossed by said wave, and is calculated by means of the following integral:

P _S = ⌠ _S I _S ∙ d S

In this integral Ps is the sound power of the wave, Is is the sound intensity of the wave, and dS is the surface differential crossed by the wave.

Rated power and real power

Nominal power is the maximum power that a machine or motor requires or can offer under normal conditions of use; that is to say, the maximum power that the machine or motor can support or offer.

The nominal term is used because that power in general is used to characterize the machine, to name it.

On the other hand, the real or useful power -that is, the power that is actually used, generated or used by the machine or motor- is generally different from the nominal, being usually less.

Examples

First example

You want to lift a 100 kg piano to a seventh floor that is at a height of 20 meters. The crane takes 4 seconds to raise the piano. Calculate the power of the crane.

Solution

To calculate the power the following expression is used:

P = W / t

However, first of all it is required to calculate the work done by the crane.

W = F ∙ d ∙ cos α = 100 ∙ 9.8 ∙ 20 ∙ 1 = 19,600 N

Therefore, the power of the crane will be:

P = 19,600 / 4 = 4900 W

Second example

Calculate the power dissipated by a 10 Ω resistor if a current of 10 A.

Solution

In this case, it is necessary to calculate the electrical power, for which the following formula is used:

P = R ∙ I ² = 10 ∙ 10 ² = 1000 W

References

1. Resnik, Halliday & Krane (2002). Physics Volume 1. Cecsa.
2. Power (physical). (nd). In Wikipedia. Retrieved on May 3, 2018, from es.wikipedia.org.
3. Power (physics). (nd). In Wikipedia. Retrieved on May 3, 2018, from en.wikipedia.org.
4. Resnick, Robert & Halliday, David (2004). Physics 4th. CECSA, Mexico.
5. Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th edition). Brooks / Cole.