Power

Note that the work done on an object is independent of the time taken to travel the distance covered. For example, suppose one lifts a 200 N weight off the floor a distance of 2 m. The work done in this case would be the product of the force exerted (the 200 N) times the distance covered (the 2 m), independent of how fast the weight was lifted. This is somewhat against our everyday idea of what work is; one might be tempted to say that one does more ``work'' if one lifts the weight faster. However, it is true that the same amount of work is done independently of the time taken; rather, it is the power in this case that is different. The power exerted by a force is defined as

Using the definition of work, we see

$\parbox{4.5in}{\vspace*{5pt} change in work = change in ( force x distance ) \vspace*{5pt}}$

and assuming the force is constant, we find, using

$\parbox{4.5in}{\vspace*{5pt} change in distance over time = velocity \vspace*{5pt}}$

that the power can be expressed as

Thus, exerting a force at a larger velocity results in a greater power output, as we intuitively expect.

The units of power can be seen from its definition; they are the units of work (Joules) divided by the units of time (seconds). This combination of units (J/s) is called a Watt (W).

To get an idea of the sizes of the units involved, let us estimate the power output of a person running up a flight of stairs. Assuming the person has a weight of 600 N, and the flight of stairs is 4 m tall, the work done by the person is 600 x 4 = 2400 J. If the person does this in 3 s, the power output is 2400 / 3 = 800 W. One might be familiar with the British unit of power, the horsepower (hp), which was originally defined as the power rate at which an ``typical'' horse could do work, and is still the unit in which the power of car engines is given. The conversion between the two units is that 1 hp = 746 W. The 800 W of power thus exerted by this person is equivalent to 800 W x ( 1 hp / 746 W ) = 1.1 hp.