# B Two observers and work

1. Jan 25, 2017

### Arman777

Think, theres an elevator going upward with constant velocity.Theres two observers, one of them is in the elevator , the other one is on earth observing the elevator.
The observer in the elevator A carries a book and holds it still.And B is outside

A will think that the total work done to the book is zero.

I am confused here about B.Does B also see the total net work done to the book is zero ?

2. Jan 25, 2017

### Staff: Mentor

No. Work is frame variant, so it can be 0 in A's frame and nonzero in B's frame. This is not a relativistic effect, it is true in normal Newtonian physics.

3. Jan 25, 2017

### Arman777

I know that work is frame variant.In this special case what will be the total work done for B ? If its nonzero how ?

Can someone help pls why its non-zero ??

Last edited: Jan 25, 2017
4. Jan 25, 2017

### jbriggs444

As I understand the question, you are asking about the total (by all forces) work done on the book according to observer B.
Dale has answered about the work (by the supporting force alone) done on the book according to observer B.

In this scenario and if we consider gravity as an external force, the total work done by all forces is zero for both observers. One can see this as an immediate consequence of the work-energy theorem. Both observers see the kinetic energy of the book to be unchanged. Accordingly, both observers must compute the total work done to be zero.

5. Jan 25, 2017

### Arman777

Thanks for confirming.My Professor said thats its non-zero.Thats why I am confused

6. Jan 25, 2017

### jbriggs444

If one regards gravity as a potential field (putting it over on the energy side of the work-energy relation) and not as an external force (which would put it over on the work side) then the professor's answer becomes correct.

According to B, the total mechanical energy of the system has increased and positive work has been done by the single external force.

According to A, the total mechanical energy of the system has remained unchanged and no work has been done by the single external force.

Edit: First draft of this had reversed A and B. I think I have it right now.

7. Jan 25, 2017

### Arman777

I dont still know the exteral force idea

8. Jan 25, 2017

### Arman777

ohh you are talking about mgh...no I dont think he included that

9. Jan 25, 2017

### Staff: Mentor

The work is $f\cdot d$. The force is the same in both frames but d is 0 for A and non zero for B. So the work is 0 for A and non zero for B. Both use the same law, $f \cdot d$ , to determine the answer, even though the answers are different.

10. Jan 25, 2017

### Arman777

For B F total is zero ?

11. Jan 25, 2017

### jbriggs444

If you count gravity as one of the forces acting on the book, yes. If not, no.

12. Jan 25, 2017

### Arman777

A holds a book in hand theres gravity acting on it and theres normal force.They cancel out.And for B the book velocity didnt changed.Cause the elevator goes with constant velocity.

13. Jan 25, 2017

### Staff: Mentor

Calculate the work done by both forces individually on the book from each observer's perspective. Assume that the elevator travels at a constant velocity for 10 meters.

14. Jan 25, 2017

### Arman777

For A its obvious zero.For B theres no other force then G and N.This is not homework question..

15. Jan 25, 2017

### Staff: Mentor

So your description of the problem is slightly ambiguous. The general principle is that $W=f\cdot d$. You may be interested in the work done only by the force holding the book (my response), or you may be interested in the work done by the force holding the book plus the force of gravity, which is also called the net force (@jbriggs444 responses).

You can apply the work formula for any single force to get the work done by that single force, or you can apply it for the net force to get the net work.

Your professor seems to be taking my approach and talking about just the force holding the book.

16. Jan 25, 2017

### Arman777

I see theres also gravity acts to the book

17. Jan 25, 2017

### Arman777

18. Jan 25, 2017

### Staff: Mentor

So the reason that your professor is confusing you is that you may be thinking about the net work and he is talking about the normal force work only.

19. Jan 25, 2017

### Arman777

14:20

20. Jan 25, 2017

### Staff: Mentor

Perhaps, but it is often helpful to do a quick calculation. If you calculate the work done by each force from B's perspective, would that not answer your question about what observer B sees?