How can the three bricks be stacked so that the top brick...

How can the three bricks be stacked so that the top brick has maximum horizontal displacement from the bottom brick? For example, stacking them like the dotted lines suggest would be unstable and the bricks would topple. (Hint: Start with the top brick and work down. At every interface the $C G$ of the bricks above must not extend beyond the end of the supporting brick.)

Key Concepts

Torque and Moment Arms

Torque is the rotational force about a pivot point, calculated as the product of the force and the perpendicular distance (moment arm) from the pivot. Understanding torque is essential in stacking problems because each brick’s displacement creates a moment that must be counteracted by the bricks below to maintain stability.

Sequential Stacking Strategy

When stacking objects to maximize overhang, a sequential strategy is often used. This involves starting at the top and working downwards to ensure that at each interface, the combined center of mass of the bricks above remains over the supporting brick below. This methodical approach is vital to determine the maximum horizontal displacement possible without causing a topple.

Static Equilibrium

Static equilibrium occurs when a system is at rest and the sum of all forces and moments (torques) acting on it is zero. In the context of stacking bricks, static equilibrium ensures that the gravitational force acting through the center of mass does not create an unbalanced torque that would cause the structure to topple.

Center of Mass

The center of mass of an object or a system of objects is the point at which the mass of the system can be considered to be concentrated. It is crucial for balance because for an object to remain stable, its center of mass must be located over its base of support. In stacking scenarios, knowing the center of mass helps determine how far an object can be displaced before it becomes unstable.

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