4.1 Work: the scientific definition  (Page 2/5)

Work can be positive or negative. In [link] work done lifting the mass is positive because both force and displacement are in the same direction. Likewise, when the mass is lowered the work done is negative because the force and displacement are in opposite directions. We will soon see that positive work adds energy to the system and negative work removes energy from a system.

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 ${\displaystyle W}$ that a force $\mathbf{F}$ does on an object is the product of the magnitude ${\displaystyle F}$ of the force parallel to the motion, times the magnitude ${\displaystyle d}$ of the displacement. In symbols, $$W=Fd.$$
• 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 on a crate pushed 4.00 m up along a ramp (see [link] ). The man exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed.

$${\displaystyle 2.00\times {10}^3\text{J}}$$