# Observer A & B's Views on Work Done to Book in Elevator

• Arman777
In summary, both observers see the elevator go up with a constant velocity, but according to one observer, the work done to the book is zero, while according to the other observer, the work done to the book is nonzero.
Arman777
Gold Member
Think, there's 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 ?

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.

Dale said:
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.

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:
Arman777 said:
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 ??
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.

jbriggs444 said:
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.

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

Arman777 said:
Thanks for confirming.My Professor said that's its non-zero.Thats why I am confused
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.

I don't still know the exteral force idea

jbriggs444 said:
According to B, the total mechanical energy of the system has increased and positive work has been done by the single external force.

.

ohh you are talking about mgh...no I don't think he included that

Arman777 said:
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 ??
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.

For B F total is zero ?

Arman777 said:
For B F total is zero ?
If you count gravity as one of the forces acting on the book, yes. If not, no.

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

Arman777 said:
A holds a book in hand there's gravity acting on it and there's normal force.They cancel out.And for B the book velocity didnt changed.Cause the elevator goes with constant velocity.

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.

Drakkith said:
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.

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

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.

jbriggs444
Dale said:
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.

I see there's also gravity acts to the book

Arman777 said:
I see there's also gravity acts to the book
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.

14:20

Arman777 said:
For A its obvious zero.For B there's no other force then G and N.This is not homework question..

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?

## What is the concept of "Observer A & B's Views on Work Done to Book in Elevator"?

The concept of "Observer A & B's Views on Work Done to Book in Elevator" is a thought experiment that explores the relationship between the laws of physics and the perception of observers with different frames of reference. It uses the example of a person dropping a book in an elevator to illustrate how each observer will have a different interpretation of the event based on their own frame of reference.

## Who are Observer A and Observer B in this thought experiment?

Observer A is a person inside the elevator, while Observer B is a person standing outside the elevator, both witnessing the book being dropped.

## What is the significance of this thought experiment in the field of physics?

This thought experiment helps to explain the concept of relativity and how the perception of an event can vary depending on the observer's frame of reference. It also highlights the role of inertial frames in understanding the laws of motion.

## What are the key differences between Observer A and Observer B's views on the work done to the book in the elevator?

The key difference between Observer A and Observer B's views is the interpretation of the work done on the book. Observer A, being in the same frame of reference as the book, will perceive no work being done on the book as it falls. However, Observer B, being in a different frame of reference, will perceive the book as gaining potential energy as it falls and therefore work being done on the book.

## How does this thought experiment relate to the real world?

This thought experiment relates to the real world by showing how perception and interpretation of events can vary based on an individual's frame of reference. It also highlights the importance of considering multiple perspectives in understanding complex systems, such as the laws of physics.

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