Work done on an a pile of books If I have a pile of books and I push the bottom one and all the pile moves with it, then, is work being done on the book on the top? If yes, is it by friction?
Obviously the book is moving so it would make sense that work is being done on it by the friction with the book bellow it, but the book doesn't move with respect the book under it, so i'm a bit confused.
Could anyone clear things up?
 A: For simplicity, consider no friction between the bottom book and the supporting surface.
If you do a free body diagram on the top book, you will see that the only external force acting on the top book is that due to static friction between the top book and the book just below it. So yes, the friction force applied by the book below it is doing work on the top book. 
The book doesn’t move with respect to the book below it, but it is accelerating with respect to the surface supporting all the books, thus work is being done due to displacement  with respect to the supporting surface of all the books.
Since all of the books are moving together, there is no relative motion between any of them.  So, for example, you can then consider the top two books as consisting of one book. Do a free body diagram on the top two books taken together, you then see that the only external force acting on them is the friction force between the second and third books. 
You can continue the process down the stack of books until you get to the bottom book where you can now consider all the books as one. Then the only external force is the external applied force to the bottom book. Since all the books stick together they all experience the same acceleration, $a$. That acceleration will equal the applied force divided by the total mass of all the books. 
The total work done on all the books will equal the force $F_{ext}$ applied to the lower block times the displacement $x$ of all the books relative to the supporting surface, or
$$W_{total}=F_{ext}x=M_{total}ax$$
Hope this  helps.
A: The following concepts are useful in this situation:
The books are as a system connected vertically by weight forces, and in the case of lateral forces, friction forces proportional to the weight forces. When you push on the pile by pushing the bottom book at $\textbf{constant velocity}$, work is done against friction between the bottom book and the resting/sliding surface.
Friction is a non-conservative force, so that the work done against it will not result in an increase in potential or kinetic energy of any part of the book-pile system. As far as potential or kinetic energy changes due to work against friction are concerned, the book pile might as well be pushed while being magnetically levitated (with permanent magnets) at a constant height, i.e. no friction, no work done case.
For the case where the books are being pushed at a $\textbf{constant velocity}$, the book on the top is moving along with its immediate frame of reference - the book pile. This is not much different from a person sitting in an airliner cruising at the same altitude whose engines are exerting force against air resistance. If the airliner was cruising through a vacuum (no air resistance), then we would consider that no work is being done on the airliner or the passenger.
Having said that, work is done to start pushing the books. This is work due to $\textbf{accelerating}$ the books from rest to motion. This work $W$ has to be done whether friction exists or not, and it is proportional to the total mass $m$, the acceleration rate $a$ (the product of mass and acceleration are the force $F$), and the distance $d$ over which the acceleration took place:
$$W = Fd = (ma)d$$
To effect the acceleration, each successive book in the pile 'pulls' the book above it by the friction force between the neighbouring books. At this juncture, the books are doing work on each other, to transmit the forces from the base of the pile.
Once the books are moving at a constant velocity, then the constant velocity situation explained above applies.
A: In physics you always need to define the referential first.


*

*If the referential is the ground, the work is done on the top book through friction.

*If the refential is the book below the top book
then work is done on the ground

A: Interesting, but the bottom book is doing no work just supporting the upper book, but you could say the the bottom book did apply the force over the moved distance during the acc'n, there is always acc'n ( due to force) to cause movement. Nothing changes speed with a force, Newton's law.  At constant velocity there is only work done on the bottom book to beat the friction, there is no force on the top book! 
