W5.1 Signs of Work

Students often get confused obout the sign of the work done by a force.... if there is any work done at all.

Identify 3 different scenarios where positive work is done, negative work and no work at all.

Consider the following 2 cases of throwing and catching a ball. What is the sign of the work done on the ball in each case, both in total and the individual components of the ball’s motion?

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Solution

In both these cases, no work is done, provided we don’t think too hard about air resistance and that I catch the ball at the same height from which I throw it.

In the first case, negative work is done on the ball by gravity as it travels upwards, and an equal an opposite amount of positive work is done on the downward journey.

In terms of the definition of work you can make sense of this by noting that the direction of motion on the way up / down is antiparallel / parallel to the direction of the force acting on the ball (the gravitational force).

In the second case, the wall exerts a force on the ball to stop it, thus doing negative work on the ball and as it rebounds the wall does an equal amount of postive work