1. Understanding Positive, Negative and Zero Work
The sign of work (positive, negative or zero) depends on the angle between the force and the direction of motion. This helps us understand how forces aid, oppose or do not affect motion.
We use the formula:
\( W = Fd \cos \theta \)
The value of \( \cos \theta \) decides the type of work.
2. Positive Work
Work is positive when the force and the displacement are in the same direction. In this case, \( \theta = 0° \) and:
\( W = Fd \cos 0° = Fd \)
2.1. Examples
- Lifting a book upward — force is upward, displacement is upward.
- Pushing a trolley forward — both force and motion are forward.
- A motor pulling water upward — force helps the motion.
3. Negative Work
Work is negative when the force and displacement are in opposite directions. Here, \( \theta = 180° \) and:
\( W = Fd \cos 180° = -Fd \)
3.1. Examples
- Friction slowing down a moving object — friction acts opposite to motion.
- A person lowering a bucket — gravity acts downward and displacement is downward, but the person applies an upward force, doing negative work.
- Brakes applied on a bicycle — braking force opposes movement.
4. Zero Work
Work is zero when:
- There is no displacement, even if force is applied.
- Force is perpendicular to the displacement.
In perpendicular cases, \( \theta = 90° \) and:
\( W = Fd \cos 90° = 0 \)
4.1. Examples When Force Is Applied but No Work Is Done
- Pushing a wall that doesn’t move.
- Holding a heavy suitcase without moving it.
4.2. Examples of Perpendicular Forces
- Carrying a bag horizontally — upward force holds the bag, but displacement is sideways.
- A satellite moving around Earth — gravitational force is toward Earth, motion is circular, so force is perpendicular.
5. Why the Sign of Work Matters
The sign of work tells us how a force affects motion:
- Positive work speeds up or supports motion.
- Negative work slows down or opposes motion.
- Zero work has no effect on speed.
5.1. Connections to Energy
Positive work increases kinetic energy, negative work decreases kinetic energy, and zero work makes no change.