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

  • Thread starter Thread starter a_narain
  • Start date Start date
  • Tags Tags
    Static
AI Thread Summary
The discussion centers on determining how far the bottom book can overhang a table without causing the stack of three identical books to fall. The top book overhangs the middle book by 0.5L, and the middle book overhangs the bottom book by 0.25L. The user attempts to apply torque and Newton's second law to solve the problem but finds their calculation for the overhang distance (1/4 L) to be incorrect. Suggestions include re-evaluating the setup of the problem and considering the sum of moments about the edge of the table. The conversation emphasizes the importance of correctly applying torque principles to find the solution.
a_narain
Messages
5
Reaction score
0

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:
Physics news on Phys.org
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.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Torque: Overhanging Books on Table
Replies
4
Views
11K
Tipping Over a Table: How Much Overhang?
Replies
24
Views
4K
Question about Normal Force and Torque
Replies
5
Views
3K
Calculating the load required to tip a table?
Replies
15
Views
4K
Center of gravity of book overhang
Replies
9
Views
30K
Why does the speed change at the bottom of the loop-the-loop?
Replies
5
Views
2K
How far can the remote control extend without tipping over?
Replies
5
Views
3K
Analyzing the Fall of a Chain: Problem 103 of 200 Puzzling Physics Problems
Replies
7
Views
2K
To find the tipping point of a lamina
Replies
2
Views
1K
How Far Can a Person Walk on a Plank Before It Tips?
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top