Please reference the illustration at: screenshots<dot>firefox<dot>com/kBXqJ4tycTCPwjUw/brilliant<dot>org to answer the following question:
On the edge of a wall, you build a brick tower that only holds because of the bricks' own weight. Your goal is to build a stable tower whose overhang d is greater than the length l of a single brick. What is the minimum number of bricks you need?
Note: Each brick has the same mass m and uniform density. There is only one brick per layer. No gluing is allowed.
2 bricks
3 bricks
4 bricks
5 bricks
6 bricks
It's impossible without gluing the bricks together
Four brick
To determine the minimum number of bricks needed to build a stable tower with an overhang greater than the length of a single brick, we need to analyze the forces acting on the tower.
In this scenario, each brick exerts a downward force due to its own weight, and this force needs to be balanced to prevent the tower from collapsing.
Let's break down the problem step by step:
Step 1: Identify the forces acting on the tower
In this case, we have two main forces:
- The downward force due to the weight of each individual brick
- The upward force exerted by the wall on the tower (which supports the weight of the bricks)
Step 2: Understanding stability
To build a stable tower, the center of mass needs to remain within the base of the tower. If the center of mass extends beyond the base, the tower will topple over. In this case, stability requires that the center of mass of the tower lies vertically above the base.
Step 3: Calculating the center of mass
To calculate the center of mass, we need to consider the weight and position of each brick in the tower. Since all bricks have the same mass and are arranged in a single layer, the center of mass will coincide with the midpoint of the tower base.
Step 4: Analyzing the minimum number of bricks
To achieve an overhang greater than the length of a single brick, we need to arrange the bricks in such a way that the center of mass falls outside the base. This means that we need to add enough bricks until the center of mass is positioned over the edge of the wall.
Looking at the given illustration would provide a visual representation of how the bricks are positioned and the arrangement required to achieve the desired overhang.
Based on the given options, we can deduce the minimum number of bricks as follows:
- 2 bricks: With two bricks, it is impossible to achieve a stable tower with an overhang greater than the length of a single brick since the center of mass will always fall within the base.
- 3 bricks: Similar to the above, the center of mass with three bricks will still remain within the base, making it impossible to obtain the desired overhang.
- 4 bricks: It is possible to arrange four bricks in such a way that the center of mass is positioned over the edge of the wall, providing the desired overhang. Therefore, the minimum number of bricks needed would be 4.
Thus, the correct answer is 4 bricks.