The three containers in Figure 12.39 are open to the air and...

The three containers in Figure $12.39$ are open to the air and filled with water to the same level. A block of wood floats in container A. An identical block of wood floats in container $\mathrm{B}$ and supports a small lead weight. Container C holds only water. Rank the three containers in order of increasing weight of the water they contain. Indicate ties where appropriate.

Key Concepts

Fixed Water Level and Spillover Dynamics

When a container is open to the air and filled to a fixed level, any additional volume introduced by inserted objects forces some water to spill over in order to maintain that constant level. This concept is important because it means that the total weight of water inside the container can vary depending on how much water is displaced by floating objects.

Effect of Added Mass on Displacement

Adding extra weight to a floating entity increases the volume of water that must be displaced to achieve buoyant equilibrium. When a heavier load is supported by the same floating object, it displaces more water, which in a container filled to a set level results in more water being expelled. This directly influences the total water weight contained in the system.

Archimedes’ Principle

This principle states that any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. It is essential for understanding why floating objects displace an amount of water whose weight is identical to their own weight, and it forms the basis for analyzing buoyancy in different scenarios.

Buoyancy and Water Displacement

Buoyancy arises because a floating object displaces water, and the weight of that displaced water must equal the weight of the object (or the total weight when extra loads are added) for the object to float. This displacement is the key factor in determining how much water remains in a container that is kept at a constant level when objects are added.

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