7.1 Work: the scientific definition  (Page 2/7)

To examine what the definition of work means, let us consider the other situations shown in [link] . The person holding the briefcase in [link] (b) does no work, for example. Here $d=0$ , so $W=0$ . Why is it you get tired just holding a load? The answer is that your muscles are doing work against one another, but they are doing no work on the system of interest (the “briefcase-Earth system”—see Gravitational Potential Energy for more details). There must be displacement for work to be done, and there must be a component of the force in the direction of the motion. For example, the person carrying the briefcase on level ground in [link] (c) does no work on it, because the force is perpendicular to the motion. That is, $\text{cos}\text{90}\text{º =}0$ , and so $W=0$ .

In contrast, when a force exerted on the system has a component in the direction of motion, such as in [link] (d), work is done—energy is transferred to the briefcase. Finally, in [link] (e), energy is transferred from the briefcase to a generator. There are two good ways to interpret this energy transfer. One interpretation is that the briefcase’s weight does work on the generator, giving it energy. The other interpretation is that the generator does negative work on the briefcase, thus removing energy from it. The drawing shows the latter, with the force from the generator upward on the briefcase, and the displacement downward. This makes $\theta =\text{180}\text{º}$ , and $\text{cos 180}\text{º}=\mathrm{–1}$ ; therefore, $W$ is negative.

Calculating work

Work and energy have the same units. From the definition of work, we see that those units are force times distance. Thus, in SI units, work and energy are measured in newton-meters . A newton-meter is given the special name joule    (J), and $1\text{J}=1\text{N}\cdot \text{m}=1\text{kg}\cdot {\text{m}}^2{\text{/s}}^2$ . One joule is not a large amount of energy; it would lift a small 100-gram apple a distance of about 1 meter.