The three identical containers in FIGURE 15-46 are open to...

The three identical containers in FIGURE 15-46 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 B, supporting a small lead weight; container C holds only water. (a) Rank the three containers in order of increasing weight of water they contain. Indicate ties where appropriate. (b) Rank the three containers in order of increasing weight of the container plus its contents. Indicate ties where appropriate.

The three identical containers in FIGURE 15-46 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 B,
supporting a small lead weight; container C holds only water.
(a) Rank the three containers in order of increasing weight of
water they contain. Indicate ties where appropriate. (b) Rank the
three containers in order of increasing weight of the container
plus its contents. Indicate ties where appropriate.

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Key Concepts

Mass Conservation in Brimful Containers

In a brimful container, when objects float, they displace a volume of fluid whose weight is exactly the same as the weight of the objects. This displacement ensures that the overall weight of the container plus its contents remains constant regardless of the objects placed inside, even though the fluid’s weight decreases. Understanding this concept is essential when comparing the weights of the fluid alone versus the total system weight.

Archimedes’ Principle

This principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid that the object displaces. When an object floats, the weight of the fluid displaced is exactly equal to its own weight, which is key to understanding problems where floating objects are introduced into fluids.

Fluid Displacement

When a floating object is added to a container that is filled to the same level, it occupies some of the space normally taken up by the fluid. The displaced fluid's weight is equal to the object’s weight, meaning that the amount of fluid (and hence its weight) in the container decreases accordingly. This concept helps in determining how the fluid’s weight changes without altering the overall level.

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