0.1 5.2 work: the scientific definition  (Page 2/5)

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.

Section summary

• Work is the transfer of energy by a force acting on an object as it is displaced.
• The work $W$ that a force $\mathbf{F}$ does on an object is the product of the magnitude $F$ of the force, times the magnitude $d$ of the displacement, times the cosine of the angle $\theta$ between them. In symbols,
  $W=\text{Fd}\text{cos}\theta \text{.}$
• The SI unit for work and energy is the joule (J), where $1\text{J}=1\text{N}\cdot \text{m}=\text{1 kg}\cdot {\text{m}}^2{\text{/s}}^2$ .
• The work done by a force is zero if the displacement is either zero or perpendicular to the force.
• The work done is positive if the force and displacement have the same direction, and negative if they have opposite direction.

Conceptual questions

Problems&Exercises

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of $\text{20}\text{.}0\text{º}$ with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.

$3\text{.}\text{14}\times {\text{10}}^3\text{J}$

Suppose the ski patrol lowers a rescue sled and victim, having a total mass of 90.0 kg, down a $\text{60}\text{.}0\text{º}$ slope at constant speed, as shown in [link] . The coefficient of friction between the sled and the snow is 0.100. (a) How much work is done by friction as the sled moves 30.0 m along the hill? (b) How much work is done by the rope on the sled in this distance? (c) What is the work done by the gravitational force on the sled? (d) What is the total work done?