10.

# Power

Power

\(P\)

W $$P={\Delta E\over\Delta t}$$

which we measure in units of watts (or joules per second: $1\u{W} = 1\u{J/s}$.

If the energy transfer in question is the work done by a force moving an object, then we can write this equation as $$P={Fd\cos\theta\over\Delta t}=F{d\over\Delta t}\cos\theta$$ but $d\over\Delta t$ is the speed of the object the work is done on, so we could also write the work done by a force *F* as $$P=Fv\cos\theta$$ where $v$ is the speed of the object, and $\theta$ is the angle between the force and the motion.

### Example

You are probably more familiar with watts in the context of electricity, when the power in question is related to the flow of electrical energy into a house (on an electrical bill) or the output of heat and light energy from a light bulb (although these days, a "60W light bulb" is more likely to mean "an LED or CFL light bulb that has the same brightness as a 60W incandescent bulb").Electric consumption is usually listed in kilowatt-hours, or $\u{kW\cdot hr}$, which is a unit of energy equal to 3.6 *million* joules.