We already found that the work done by the man on the lawnmower is equal to the magnitude of the force exerted by the man on the lawnmower multiplied by the displacement of the lawnmower multiplied by cosine theta, where theta is the angle between the force exerted by the man and the displacement of the lawnmower.

If we adjust theta so that it is zero degrees (in other words, if the force exerted by the man is pointed in exactly the same direction as the displacement of the lawnmower), then the work formula becomes

work = + (magnitude of force) x (magnitude of displacement).

If we adjust theta so that it is 180 degrees (in other words, if the force exerted by the man is pointed in the direction exactly opposite that of the lawnmower's displacement), then the work formula becomes

work = - (magnitude of force) x (magnitude of displacement).

If we adjust theta so that it is zero degrees (in other words, if the force exerted by the man is pointed in exactly the same direction as the displacement of the lawnmower), then the work formula becomes

work = + (magnitude of force) x (magnitude of displacement).

If we adjust theta so that it is 180 degrees (in other words, if the force exerted by the man is pointed in the direction exactly opposite that of the lawnmower's displacement), then the work formula becomes

work = - (magnitude of force) x (magnitude of displacement).

*See the image below.*So, even though work is a scalar quantity, it can be either positive or negative, and the sign of work depends upon how the external force vector is arranged relative to the displacement vector. Use the self-quiz below to see if you can determine when work is positive and when it is negative.

## When Work is Positive and When it is Negative Self-Quiz

Scroll to the top of the page and read before attempting the quiz.

- When is the work done by an external force positive? Choose all answers which are correct.
- When is the work done by an external force negative? Choose all answers which are correct.