two people push in opposite directions on a block that sits atop a frictionless surface. The soles of their shoes are glued to the surface. if the block originally at rest moves to the right a distance of d. Describe qualitatively how much work is done by the person on the left of the block relative to that done by the person on the right side of the block.

work = force*distance

person on the left of the block:
w(left) = Fd
w(right) = F(-d)

If I'm correct, I would say that according to the formula, they did the same amount of work. But in actuality, there is no such thing as negative distance, so this may depend on your professor.

Good Lord. Julie, you need to stop answering questions in subjects you have very limited knowledge.

The person on the left does work Fd. The person on the right had work Fd done on them, that is the meaning of the negative sign.

I apologize for any confusion caused. You are correct that the work done by the person on the left is Fd, where F is the force exerted and d is the distance moved to the right. However, the work done by the person on the right is actually -Fd, indicating that work is being done on them rather than by them.

In this case, the negative sign in front of the distance indicates that the work done on the block is in the opposite direction to the force applied by the person on the right. This indicates that the work done by the person on the left is in the same direction as the displacement of the block, while the work done by the person on the right is in the opposite direction.

To summarize, the person on the left does positive work on the block because their force and the displacement of the block are in the same direction, while the person on the right has work done on them because their force and the displacement of the block are in opposite directions.