# Another question about negative work

Bipolarity
Unfortunately I still have not completely grasped the idea of negative work. I appreciate all the help in understanding this concept!

Suppose that you lift a block of mass M an upwards distance of D. The force you applied on the block is a constant F directed parallel to the displacement of the block. Then by the definition of work, you did work equal to FD on the block. This quantity is positive. I think we can all agree on that.

What about the work that the block does on you?

Argument 1:
Since you applied an upward force F on the block, the block exerts a downward force F on you. But your displacement relative to the block is also downwards, and it has magnitude D.
Thus, the work that the block does on you is FD and this quantity is positive.

Argument 2:
You worked on the block and transferred kinetic energy to it. You lost energy, the block gained energy. Since you lost energy, the block did "negative work" on you. This is an immediate consequence of the work-kinetic energy theorem. The magnitude of this work is FD but it is a negative quantity because the block gains energy and you lose energy.

Which of these arguments is valid? Why is the other argument invalid? Hopefully I am not the only one having trouble to understand this...

Thanks!

BiP

Homework Helper
Argument 1:
Since you applied an upward force F on the block, the block exerts a downward force F on you. But your displacement relative to the block is also downwards, and it has magnitude D.
Thus, the work that the block does on you is FD and this quantity is positive.

Displacement is measured relative to a coordinate system (aka frame of reference).

For a fixed frame of reference, the work that you do on the block is equal and opposite to the work that the block does on you.

For contact forces, this is an immediate consequence of Newton's third law.

Argument 2:
You worked on the block and transferred kinetic energy to it. You lost energy, the block gained energy. Since you lost energy, the block did "negative work" on you. This is an immediate consequence of the work-kinetic energy theorem. The magnitude of this work is FD but it is a negative quantity because the block gains energy and you lose energy.

Bingo. This latter argument is correct.

Bipolarity
Ok so the block does negative work on you and the magnitude of that work is FD.

So the force it applies on you must be opposite direction to your displacement. The force it applies to you is obviously directed downwards, right? Which means your displacement must be upwards... but that is not correct? BiP

salzrah
The reason why argument 1 is invalid is because the displacement is not negative. The displacement for this situation is 0 because you do not move. You cannot say the displacement is negative because that would take you into another FoR where the box doesn't move. I think to reason negative work you have to find out what is responsible for the positive work on an object and subtract the energy it took to do that work from the source because of the conservation of energy.

Bipolarity
The reason why argument 1 is invalid is because the displacement is not negative. The displacement for this situation is 0 because you do not move. You cannot say the displacement is negative because that would take you into another FoR where the box doesn't move. I think to reason negative work you have to find out what is responsible for the positive work on an object and subtract the energy it took to do that work from the source because of the conservation of energy.

I understand work in terms of kinetic energy, but the calculations must still be reconciled with the force-displacement definition of work.

If your displacement having moved the block is 0, then the work that the block does on you should also be 0. And yet, it is equal to -W. BiP