How Far Can the Bottom Book Overhang the Table Without Falling?

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Homework Help Overview

The problem involves three identical books stacked over the edge of a table, with specific overhangs defined for the top and middle books. The objective is to determine how far the bottom book can overhang the table without causing the stack to fall.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to analyze the forces and torques acting on the books, particularly focusing on the top two books before considering the bottom book. They express confusion regarding their calculations and whether their setup is correct. Other participants suggest applying the sum of torques about the edge of the table and inquire about the meaning of "sum of their moments."

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding the application of torque and moments, but there is no explicit consensus on the correct method or solution yet.

Contextual Notes

The original poster indicates that their calculated answer seems incorrect, prompting questions about their setup and approach. There may be assumptions regarding the distribution of mass and the definition of the center of mass that are under discussion.

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Homework Statement


Three identical books of length L are stacked over the edge of a table as shown in the figure. The top book overhangs the middle one by .5L, so it just barely avoids falling. The middle book overhangs the bottom one by .25L. How far can the bottom book overhang the table without the books falling?

RW-12-56.jpg

Homework Equations


Torque = rFsin(angle)
Newton's second law

The Attempt at a Solution


In approaching this problem, I look at the top two books first. I noticed that the force on book 3 from 2 has to equal the gravitational force of book 3, and the torque is zero using the center of gravity of book 3 as the pivot point.
A similar situation occurred for book 2, where the force of book 3 acts on the end, and while the force of book 1 and gravity act at the center of mass. From this, I got that the force of book 1 on 2 = 2mg.

My work for book 1:
-2mgx-(.5L-x)mg+(.5L-x)3mg = 0
The answer I get when I solve for x is 1/4 L, but that is wrong?

What exactly am I doing wrong, am I setting up the problem correctly?
 
Last edited:
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Maybe try applying the ∑ T = 0 about the edge of the table?

Figure the distance that the CofM of each book is from that point and then the sum of their moments will need to sum to 0 right?
 
What do you mean by the sum of their moments?
 
a_narain said:
What do you mean by the sum of their moments?

http://en.wikipedia.org/wiki/Torque

That would be Torque, insofar as you are taking the moment about a point as in r X F.
 

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