Positive and negative work
The sign of the work.
Stopping a football
A goalkeeper dives and stops a fast football. Her hands push against the direction in which the ball is moving.
What do you think is special about the work she does on the ball?
What this lesson covers
The idea
Work done by a force is positive when the displacement is in the same direction as the force and negative when the displacement is opposite to the force.
Stopping a football
A goalkeeper dives and stops a fast football. Her hands push against the direction in which the ball is moving.
What do you think is special about the work she does on the ball?
- It is negative
- It is positive
- It is zero
Force and displacement
Keep the force fixed. Choose the direction of the displacement.
The sign comes from the directions
When the displacement was along the force, the work came out positive. When the displacement was opposite to the force, the displacement counts as negative, so the work came out negative. A wheelchair pushed forward gets positive work. A goalkeeper stopping a ball pushes opposite to the ball's displacement and does negative work on it.
Work done by a force is positive when the displacement is in the same direction as the force, and negative when the displacement is opposite to the force.
Notes
Work is positive if the displacement is along the force and negative if it is opposite to the force.
Check yourself
You push a wheelchair forward and it moves forward. The work you do on it is…
A goalkeeper stops a ball by applying a force opposite to the ball's displacement. The work she does on the ball is…
A goalkeeper applies a force of 200 N opposite to the ball's displacement. The displacement of the ball in the direction of the force is −0.15 m. What is the work done on the ball, in J?
Answer: -30 J
W = 200 N × (−0.15 m) = −30 J.
A girl lowers a dumbbell slowly. The force she applies is upward, and the dumbbell moves down. The work done by her force is…
- positive — correct. Yes!
- negative. Your force and the displacement are in the same direction, so the work is positive.
- zero. The wheelchair is displaced in the direction of your force, so work is done.
- positive. Work is positive when the displacement is in the direction of the force. Here it is opposite.
- negative — correct. Yes!
- zero. The ball is displaced while she pushes, so the work is not zero. It is negative.
- positive. The dumbbell moves down, opposite to her upward force, so the work is negative.
- zero. The dumbbell is displaced along the line of her force, so the work is not zero. It is negative.
- negative — correct. Yes!