Defining and characterising the work done by a force
Driving, resisting, and zero work
Three cases depending on the sign of the work
The sign of the work of a force depends on the angle alpha between the force and the displacement, via the term cos(alpha).
| Angle alpha | cos(alpha) | Type of work | Effect |
|---|---|---|---|
| 0 <= alpha < 90 | positive | driving work | accelerates the motion |
| alpha = 90 | zero | zero work | has no effect |
| 90 < alpha <= 180 | negative | resisting work | slows down the motion |
Driving work
When the force pushes in the direction of motion (acute alpha), it supplies energy to the system: this is driving work, W > 0. Example: the force from a car's engine as it moves forward.
Resisting work
When the force opposes the motion (obtuse alpha, up to 180 degrees), it removes energy from the system: this is resisting work, W < 0. Example: air friction on a cyclist, or braking force.
Zero work
When alpha = 90 degrees, the force is perpendicular to the displacement: W = 0. Example: the normal reaction from the ground on a rolling suitcase pulled horizontally.
Classic pitfall
Do not confuse "zero force" with "zero work": a force can be very intense (like the weight of an object) and yet have zero work if it is perpendicular to the displacement.