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

[a_narain]

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?

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?

 

[LowlyPion]

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?

 

[a_narain]

What do you mean by the sum of their moments?

 

[LowlyPion]

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.