Work and power: two concepts that should not be confused

Reminder: the work done by a force

In mechanics, the work done by a force F, denoted W(F), measures the energy transferred when the point of application of the force moves. For a constant force and a linear displacement d, we write:

W = F × d × cos(theta)

where theta is the angle between the force and the displacement. Work is expressed in joules (J).

Power: a question of speed

Two motors may perform exactly the same amount of work, but one may do so in 2 seconds and the other in 2 minutes. It is power that distinguishes these two situations: it measures the rate at which work is carried out, i.e. the energy transferred per unit of time.

Average power is defined as:

P = W / t

where W is in joules, t is in seconds, and P is in watts (W).

A common pitfall

Never confuse work (in joules, a quantity of energy) with power (in watts, a rate of energy). A lift that slowly raises a heavy load can do the same amount of work as a fast lift carrying a light load, but their powers will be very different.

Example

A winch lifts a load and does 4000 J of work in 8 s.

P = 4000 / 8 = 500 W