Blocks stacked on an edge - max dist. b4 they fall?

• lizzyb
In summary, the conversation is discussing the question of finding the maximum distance for two identical uniform bricks stacked over the edge of a horizontal surface without falling. The answer can be found by setting up the center of gravity for each book and then combining them to find the center of mass for both books. The distance is not the same as the length of one book because the center of mass must be over the table, not past the edge.
lizzyb
The question is "Two identical uniform bricks of length 18 cm are stacked over the edge of a horizontal surface with the maximum overhand possible without falling."

Code:
|<-- 18 cm -->|
+-------------+
|    block 1  |
+-------------+
+-------------+
|    block 2  |
+-------------+
|<-- x -->|+-----------------
|XXXXXXXXXXXXXXXXX
|XXXXX ledge XXXXX
|XXXXXXXXXXXXXXXXX

find the maximum distance x. answer in cm.

Is this a center of gravity question? if so, then how do i set it up? thank you.

But in that thread, OlderDan wrote: "The condition for one book to not fall off the table is the same condition for the second book to not fall off the first book."

Why then is the answer not 18? The condition of the second book to not fall off of the first is that it's center of gravity is over the first book, hence .5L = 9, and the first book must have it's COG at 9 too. hmmm

lizzyb said:
But in that thread, OlderDan wrote: "The condition for one book to not fall off the table is the same condition for the second book to not fall off the first book."

Why then is the answer not 18? The condition of the second book to not fall off of the first is that it's center of gravity is over the first book, hence .5L = 9, and the first book must have it's COG at 9 too. hmmm
OlderDan can't remember anything he did that long ago.:yuck: The condition is the same, but that does not mean the distance is the same. If you put one book on top of another, the center of mass of the top book has to be somewhere above the bottom book. If you take the combination of the two books arranged as close as possible to this limiting arrangement, the center of mass of the two books combined has to be somewhere over the table, not past the edge. Find the center of mass of the two books and see how far that is from the farthest edge of the top book.

ok i think i understand it now. thanks!

1. How does the height of the blocks affect their stability?

The height of the blocks does not directly affect their stability. However, as the height increases, the center of gravity shifts higher, making the tower more prone to tipping over.

2. What material is best for building a stable tower?

The material used for the blocks does not significantly impact the tower's stability. However, denser and more uniform materials, such as wood or plastic, tend to provide better stability compared to lighter materials like foam or cardboard.

3. Is there a maximum number of blocks that can be stacked before the tower falls?

There is no definitive maximum number of blocks that can be stacked before the tower falls. The stability of the tower depends on various factors, including the shape and weight distribution of the blocks, the surface they are stacked on, and external forces like wind or vibrations.

4. How does the shape of the blocks affect the tower's stability?

The shape of the blocks can play a role in the tower's stability. Blocks with flat sides and uniform shapes tend to stack more easily and provide better stability compared to irregularly shaped blocks.

5. Can the distance between the blocks affect the tower's stability?

The distance between the blocks can affect the tower's stability. If the blocks are stacked too close together, they may not have enough support from neighboring blocks, making the tower more likely to fall. On the other hand, if the blocks are stacked too far apart, the tower may become top-heavy and prone to tipping over.

• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
24
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
3K