The Comprehensive Guide to Calculating Power Output

Credit: Public Domain

By Andrew Bennett

What Does Power Mean in Physics?

The word "power" is used to mean energy and electricity outside of physics. In physics, however, power is specifically the rate at which energy changes. This could be a transfer of energy from one object to another (for example, though work being done). It could also be a change from one type of energy to another (for example, chemical energy turning to kinetic energy). Regardless, power describes how rapidly that change takes place.

Since power deals with energy and work, there are a number of different connections you can make with power.

Power Equations

Power is a rate. All rate measurements are calculated in a similar way: the change in some quantity divided by the amount of time it takes for that change to happen. With power being the rate at which energy changes, we can write the equation for power as:

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We also frequently deal with work in introductory physics classes (see my post about work in physics). In many situations (when energy is not lost or gained as heat), the work done on a system is equal to the change in energy of that system, or

.

Using this fact, we can rewrite the power formula as:

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Power Equation Shortcuts and Tricks

Work can be calculated as:

,

where r is the displacement vector, F is the force vector, and theta is the angle between those two vectors. If we substitute this expression for work in the above power formula, we get:

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In this form, we see that we have the displacement (r) over the change in time. Displacement divided by time is equal to average velocity, so this equation can be written as:

.

This is a really convenient form of the power formula to work with in certain situations. For example, if you are trying to determine the force exerted by a car's engine when we know the speed of the car and the power delivered by the engine. We could also use this to determine the necessary power capabilities of a motor –– for example, to lift a roller coaster car to the stop of the starting hill with a known mass of the car and a predetermined speed.

Other Formulas That Use Power

Since power can be calculated using the change in energy, it is often useful to substitute in some of the energy formulas.

For example, if a car is accelerating from one speed to another, but not changing height, then we would likely focus on the change in kinetic energy of the car. (Although in this example, a significant amount of energy would also end up as thermal energy as well.) To account for situations in which only kinetic energy is changing, we would substitute the kinetic energy formula for the energy and get:

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We could use a similar technique to find an equation to use when only gravitational potential energy is changing:

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Video: How to Do Power Physics Example Problems

In this video, you will learn more about the meaning of power and useful equation tricks. You also will learn how to calculate the power output in an example problem involving a motor lifting an elevator.

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