What is the power in physics?

We explain what is the power in physics, the types that exist and various examples. In addition, the formulas to calculate it.

1. What is the power in physics?

In physics, power (represented by the symbol P ) is a certain amount of work done in some way in a given unit of time . That is, it is the amount of work per unit of time that an object or system produces.

Power is measured in watts (W) , a unit that pays tribute to Scottish inventor James Watt and is equivalent to one July (J) of work done per second (s), that is:

W = J / s

In the Anglo-Saxon measurement system, this unit is replaced by horsepower ( hp ).

The ability to understand and measure power accurately was a determining factor in the development of the first steam engines, an apparatus on which the Industrial Revolution was sustained . Nowadays, on the other hand, it is usually associated with electricity and other modern energy resources , since it can also designate the amount of energy transmitted.

2. Types of power

There are the following types of power:

• Mechanical power . That which is derived from the application of a force on a rigid solid, or a deformable solid.
• Electrical power . Instead of work, it refers to the amount of energy transmitted per unit of time in a system or circuit.
• Heat output . It refers to the amount of heat that a body releases to the environment per unit of time.
• Sound power . It is understood as the amount of energy that a sound wave carries per unit of time across a given surface.

3. Power formulas

The power is calculated, in general terms, according to the following formula:

P = ΔE / Δt

ΔE represents the change of energy or the variation of work.

Δt represents the time measured in seconds.

However, each type of potency is expressed by its own formulation, for example:

• Mechanical power : P (t) = Fv, although if there is a rotation of the solid and the applied forces alter its angular velocity, we will use P (t) = Fv + M.ω instead. F and M will be the resulting force and the resulting moment, respectively; while V and ω will be the velocity of the point on which the resultant was calculated, and the angular velocity of the body.
• Electric power : P (t) = I (t). V (t), where I is the current flowing, measured in amps, and V is the potential difference (the voltage drop ) measured in volts. In the case of a resistor instead of an electricity conductor, the formula to be used will be P = I ² R = V ² / R, where R is the resistance of the material, measured in ohms.
• Heat output . P = E / t, where E is the caloric energy provided, measured in joules (J). Notice how this is indifferent to the degrees of heat.
• Sound power . P _S = ʃ I _s dS, where I _s is the sound intensity and dS the element reached by the wave.

4. Power examples

• Power to move a dough

We want to raise 100 kg of construction materials to the seventh floor of a building under construction, that is, about 20 meters from the ground. We want to do it using a crane and in 4 seconds of time, so we must find out the necessary power of it.

To use the formula P = w / t, we must calculate the work done by the crane first. For that we use the formula W = F. d. cos a = 100 x 9.8 x 20 x 1 = 19.600 N. Then: P = 19.600 N / 4 s, that is, the crane’s power must be 4900 W.

• Power that dissipates a resistance

We must calculate the amount of power that dissipates an electrical resistance of 10 ohms, when we cross it with a current of 10 amps. We apply in this case the formula P = R x I ² , as follows: P = 10 x 10 ² , which results in a dissipated power of 1000 watts.