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# 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.

1. ### 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.
1. ### 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 s dS, where s is the sound intensity and dS the element reached by the wave.
1. ### 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.

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