Can a Tower of Books Move with Lighter Forces?

  • Context: Undergrad 
  • Thread starter Thread starter Clockclocle
  • Start date Start date
  • Tags Tags
    Books Forces Tower
Click For Summary

Discussion Overview

The discussion revolves around the mechanics of a stack of books and the forces required to move them. Participants explore the implications of applying forces to different books in the stack and the resulting frictional effects. The conversation touches on theoretical considerations, idealizations of the books' properties, and the practical aspects of force application.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that if a stack of n books is treated as a single particle, the force exerted by the last book (interpreted as the bottom book) is N=nmg, leading to questions about moving the entire tower with lighter forces.
  • Another participant clarifies that the last book does not contact the surface but exerts a friction force only on the book it is on top of, prompting confusion about the terminology used.
  • There is a discussion about the interpretation of "last book," with one participant suggesting it refers to the bottom book, while another argues it could mean the top book.
  • A participant introduces the idea that the answer depends on the idealization of the books, noting that if books are considered non-compressible and much wider than they are tall, the same motion could be achieved with different force applications.
  • Concerns are raised about the real-world behavior of books, emphasizing that the point of force application affects weight distribution and sliding ease, particularly when pushing below the center of mass.
  • One participant expresses confusion about the original question and suggests clarifying the terminology used to avoid misunderstandings, proposing the use of "top book" and "bottom book" instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the terminology used or the implications of the forces applied to the books. Multiple interpretations of the question and differing views on the mechanics involved remain unresolved.

Contextual Notes

Participants discuss idealizations such as treating books as identical, incompressible blocks with a specific friction coefficient. The implications of these assumptions on the mechanics of the stack are not fully resolved.

Clockclocle
Messages
31
Reaction score
1
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?
 
Physics news on Phys.org
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.

##\ ##
 
Reply
  • Like
Likes   Reactions: topsquark
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.
 
Last edited:
Reply
  • Like
Likes   Reactions: BvU
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. language .. :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'. language ... :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?)

##\ ##
 

Similar threads

High School Are frictional forces action forces or reaction forces?
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad What friction causes objects to decelerate?
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad Reaction force of and its relation to normal force and friction
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Virtual work and constraint forces
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Modeling Coulomb Friction for a Moving Point Mass in a Circular Bowl
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Vectorial issue of friction
  • · Replies 2 ·
Replies
2
Views
1K
High School Why does friction decrease with repeated force application?
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Stuck in understanding Newton's 3 laws
  • · Replies 18 ·
Replies
18
Views
2K
High School Determine forces acting on double inclined plane
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Why don't we "fly up" in an accelerating elevator?
  • · Replies 11 ·
Replies
11
Views
4K