# Power

Power is the rate at which work is done or at which energy is used or expended

Pavg = W / t

P = dW / dt

P = dW / dt = d( F s) / dt = F ds / dt = F v

P = F v

Units?

[ P ] = watts = W = J / s

This unit of power is rightfully named after James Watt who patented the steam engine in 1769. Watt's steam engines were "sold" to British coal mines. In order to describe his steam engine, Watt told the coal mine owners how many horses his steam engines would replace. Horses were used by the coal mines to run pumps and windlasses to pump water from the coal mines. Watt initially gave his steam engines to the coal mines under contract that they pay him one-half of the money they saved by not needing horses. In these discussions, then, he needed to know how much power a typical British workhorse could produce. Watt was rather conservative; very few work horses can actually produce one horsepower of work!

[ P ] = ft-lb/s

1 hp = 550 ft-lb / s

1 hp = 746 W = 0.746 kW

1 W-s = 1 J

1 kW-h = (103 W) (3600 s) = 3.6 x 106 W-s = 3.6 x 106 J

However, power is power. Either type of units could be used. It would be -- and is -- entirely proper and correct to state that a certain car has an engine which produces 98 kW (that is 132 hp).

As you can see from these graphics from a 1983 Pontiac brochure, General Motors has used SI (International System) units internally for many, many years. Of course, that is true for all other large US companies.

Like the engineers in other multi-national companies, GM's engineers recorded data in SI units. Power is measured in kilowatts (kW) and torque -- the rotational effect of a force -- is measured in newton-meters (NM or N-m). This is not something new; remember these graphics are from a 1983 Pontiac brochure!

Here are excerpts from Francophone Canadian automobile brochures that do, indeed, show the engine power in kilowatts (kW) and in horsepower ("ch" for chavox in French).

 Work-Energy Theorem KE at High Speeds Return to ToC, Ch7, Work and Energy