# Work done by action and reaction

It is said in the test book that in general, when one body does negative work on a second body, the second body does an equal amount of positive work on the first body.

However, when consider two magnets repelling each other and there is also a normal force acted on one of magnets by a wall, so that it stays at rest while the other magnet moves away from it. The work done by the first magnet on the second is positive while the work done by the second magnet on the first magnet is zero.

Does that mean that work done by action and reaction is not relative to each other?

No. The first magnet is applying a force on the one against the wall. If you take the wall out of the way, what would happen? The magnet would move further back of course. Whats happening here is that the force is being applied to the magnet, but the magnet is applying that force to the wall, and the wall applying an equal and opposite force as well. Does this answer your question?

Even in your example, there is evidence of simultaneous positive and negative works. The magnet is definitely pushed towards the wall and so it is also applying force on the wall itself.

The thing is that there is some sort work done on both sides (ALWAYS), whether you may be able to observe it or not

Dale
Mentor
2020 Award
It is important to know that EM fields can carry energy and momentum. So it is possible that the energy lost by one magnet is not equal to the energy gained by the other, in which case the remaining energy goes into the fields themselves.

rcgldr
Homework Helper
I'm not sure about the negative versus positive work reaction. In the case of a rocket in space, starting with the rocket's initial velocity as a frame of reference, so that the rockets velocity is zero, then thrust from the engine does positive work on the rocket, and positive work on the fuel, causing both to accelerate, and an increase in kinetic energy.

Reversing the situation, imagine two objects approaching each other in space, then experience an inelastic collision, resulting in negative work done on both objects, which end up with zero kinetic energy.

Dale
Mentor
2020 Award
It is possible for the engine to do positive work on the rocket and negative work on the fuel. For example, in the reference frame where the rocket is moving forward at the exhaust velocity.

rcgldr
Homework Helper
It is possible for the engine to do positive work on the rocket and negative work on the fuel. For example, in the reference frame where the rocket is moving forward at the exhaust velocity.
That's part of what I was getting at. Kinetic energy is relative to some frame of reference, so the positive = negative work requires choosing a particular frame of reference, and only holds true for an instant in time if there are accelerations.

Dale
Mentor
2020 Award
I agree completely.