3.3.3 Power

Power is the rate of work done (or the rate of energy transfer, since work done = energy transferred). We can determine power using the equation:

P = W / t

Power has the unit J s^-1 or W (watts). One watt is equal to one joule per second.

In lots of situations a constant force must exerted to maintain a constant speed. For example, the rate of work done (power) by the forward force provided by  cars engine is equal to the rate of work done against the frictional forces acting on the cat (so the net force on the car is 0). We can depict this as:

A constant force F moves the car a distance x in a time t

work done by the force W = F x

P = W/t = Fx/t

The speed of the car (v) is the rate of change of distance: v = x/t

P = Fv


Efficiency
Not all machines/processes convert all their energy into useful work. Lots of energy often is outputted as thermal energy (heat). We can calculate the efficiency of something using the following equation:

efficiency = 100% x useful output energy / total input energy