Work

Work
Definition: The work done by an agent exerting a constant force ( ) and causing a displacement ( ) equals the magnitude of the displacement, s, times the component of along the direction of . In Figure 5.1, the work done by is:

W = s Fcos .



Figure 5.1: Work



Note:

If = 0 W = 0. (ie: no work is done when holding a heavy box, or pushing against a wall).
W = 0 if (ie: no work is done by carrying a bucket of water horizontally).
The sign of W depends on the direction of relative to : W > 0 when component of along is in the same direction as , and W < 0 when it is in the opposite direction. This sign is given automatically if we write as the angle between and and write W = Fscos .
If acts along the direction of then W = Fs , since cos = cos 0 = 1.
Work is a scalar.
The SI units of work are Joules (J) (1 Joule = 1 Newton meter). In cgs units: 1 erg = 1 dyne cm.