Can a Tower of Books Move with Lighter Forces?

[Clockclocle]

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?

 

[BvU]

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.

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[Clockclocle]

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?

 

[Ibix]

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.

 

[BvU]

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. language ..

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'. language ...

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

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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