Chapter 11, Problem 41A

How can the three bricks in the figure be stacked so that the top brick has maximum horizontal overhang above the bottom brick? For example, stacking them as the dotted lines suggest would be unstable and the bricks would topple. (Hint: Start with the top brick and think your way down. At every interface the CG of the bricks above must not extend beyond the end of the supporting brick.)

To determine

The way three bricks can be stacked such that the top brick is overhung above the bottom one without toppling.

Answer to Problem 41A

The top brick overhangs three fourth of its length above the middle one and the middle one will be at the same three fourth above the bottom brick to remain stationary. Such a position will make sure no brick would topple.

Explanation of Solution

Introduction: For any object to be stable and stationary, the center of gravity must be in stable equilibrium, or else it will start rolling or topple.

Let $L$ be the length of each brick. For a stationary single brick, the center of gravity is at its midpoint length. When a brick is placed at $3/4$ of its length above the bottommost brick and remaining one-fourth in the air, then, it would be stationary and will attain stable equilibrium.

Now, for the topmost brick, it needs to stay at half of its length above bottommost brick and remaining half in the air.

Conclusion: Thus, they are set such that top brick overhangs three fourth of its length above the middle one and the middle one will be at the same three fourth above the bottom brick to remain stationary. Such a position will make sure no brick would topple.