Study Guide

Energy and Momentum - Power

Power

Finally, with our knowledge of momentum and energy, we've reached the end goal of every physics student, aspiring politician, and James Bond villain: unlimited power. And while Auric Goldfinger might have had to achieve this via some exceedingly complicated plot involving nerve gas, gold paint, and a squat manservant with a penchant for nice hats, our route to power is much more straightforward.

Power (P) is the rate at which an object can do work (W). In contrast to Goldfinger's plans, the power expended by an object in interval Δt is given by a very simple formula.

No need to run from the nerve gas, either. Because work is the product of force and distance, we can express the power expended by object A equivalently in terms of the force (F) object A is exerting on object B and the speed (v>/em>) object B is moving at.

P = Fv

Remember, v would be given by the distance object B traveled divided by the time it took to travel that distance, Δt, so this works out. Just like work, however, this formula only applies if F is applied in the same direction as motion.

The SI unit of power is J/s, which is called a watt (W). Be careful not to confuse power and energy—power is an instantaneous rate of energy transfer. You might have some 60 W light bulbs in your house, meaning they radiate 60 J of energy per second as light and heat when you turn them on. But your electricity provider will charge you by the kilowatt-hour (kWh)*, a unit of energy representing the total of all the light bulbs in your house multiplied by all the seconds they've been on.

*1 kWh = 3.6 × 106 J, so it tends to remove a lot of zeros from their spreadsheets.

Common Mistakes

The formula P = Fv is straightforward, but you have to remember that the object expending the power to make the force doesn't have to be the object moving at speed v. Two examples: in a car, the engine combusts gasoline to generate power that makes a force to move the car forward; the more horsepower*, the faster the car can move. But a hang glider uses force from the wind to move (so F would come from the wind) and v from the glider, together giving us the power the wind uses to move the glider.

*1 hp = 746 W

Brain Snack

Perhaps the most famous use of a watt in history (past, present, and future) comes from Back to the Future, when Marty McFly tries to convince the past version of Doc Brown to generate 1.21 GW by hitting his DeLorean with lightning—which is a huge amount of power.

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