I Can a Tower of Books Move with Lighter Forces?

AI Thread Summary
The discussion centers on the mechanics of a stack of books and the forces acting on them. It clarifies that the "last book" refers to the bottom book in the stack, which exerts a force on the surface equal to N=nmg. When considering the application of force, the placement of that force affects the motion of the stack, as pushing below the center of mass is generally easier than at the top. The conversation also emphasizes the importance of clear terminology, suggesting the use of "top book" and "bottom book" for clarity. Overall, the interaction of forces in a stack of books is complex and influenced by the distribution of weight and the point of force application.
Clockclocle
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Suppose n book stack on each other. Since each book have the same weigh then the last book exert a force N=nmg on the surface so it has the biggest static friction. But if we treat the whole tower of books as one particle it also has N=nmg. This mean if we exert enough force in the last book, the tower keep moving as we exert lighter force on all the book at the same time?
 
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Clockclocle said:
the last book exert a force N=nmg on the surface
The last book does not make contact with the surface. It exerts a friction force only on the book it's on top of.

##\ ##
 
BvU said:
The last book does not make contact with the surface. It exerts a friction force only on the book it's on top of.
What? I think the last book would both contact with the surface and the top of it?
 
I think the OP is using "last book" to mean the one at the bottom of the stack. (I would call the top one the last book, since it was the last one placed on the stack, but the question makes more sense if it means the bottom book.)

In that case, the answer to the question depends on what idealisation you make. If you idealise the books as non-compressible and much wider than the stack is tall so there's no significant difference in torque between the two cases, then yes you can get the same motion by applying ##n## forces of magnitude ##F## or one of magnitude ##nF##.

In reality, books are typically slightly compressible and a stack of books will frequently be taller than it is wide. In that case where you apply the force matters because it will change how the weight is distributed which may affect how easily it slides. It's a fairly common experience that pushing something at a point below its center of mass is easier than pushing it at the top.
 
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Clockclocle said:
Suppose n book stack on each other
This is not possible: you can place a book on top of another book, but then the lower book is not on top of the top one. Langauge .. :rolleyes:

Clockclocle said:
What? I think the last book would both contact with the surface and the top of it?
It seems we mean different things when we mention 'the last book'. Langauge ... :rolleyes:

Easier to only use 'top book' and 'bottom book'. Even better to make a sketch to clarify.

Clockclocle said:
This mean if we exert enough force in the last book, the tower keep moving as we exert lighter force on all the book at the same time?
Could you now clarify your question ? I have difficuty understanding the last part...

(and let's assume the books all behave as identical ideal incompressible blocks, with a friction coefficient ##\mu## -- both between books and between bottom book and table. OK?)

##\ ##
 
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