Work For the Trigonometrically Inclined:

In the four special cases we have investigated so far:

- force in the direction of the motion
- force in the opposite direction of the motion
- force perpendicular to the direction of the motion
- no motion

work appears to behave differently in each one. Actually, of course, this is not the case. All four cases (and much more) can be calculated from a single equation (as long as the force is constant), which is:

Where:

- F = the magnitude of the force
- = the magnitude of the displacement
- q = the angle between the force on the object and the object's displacement

(Why?) This equation fits the four special cases of motion as follows:

If the Force is in the Direction of Motion:

In
this case, q = 0^{o},
so:

If the Force is in the Opposite Direction of Motion:

In
this case, q = 180^{o}, so:

If the Force is Perpendicular to the Direction of Motion:

In
this case, q = 90^{o},
so:

If the Object Being Pushed Doesn't Move:

In this case, Dx = 0, so:

last update December 13, 2003 by JL Stanbrough