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Buoyancy and Archimedes' Principle

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A laboratory container is filled to the very brim with water. A 3-kilogram solid wood block is gently placed into the water, where it floats, and the water that spills over is collected and weighed. The wood is then removed, the container is completely refilled, and a 3-kilogram solid steel weight is lowered into the water until it rests on the bottom. The water that spills over from the steel is also collected and weighed. Based on Archimedes' principle, which of the following statements correctly compares the weight of the water displaced by the two objects?

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Answer: The wood block displaces a greater weight of water than the steel weight.

Answer

The wood block displaces a greater weight of water than the steel weight.
According to Archimedes' principle, a floating object (like the wood) displaces a weight of fluid equal to its own weight, meaning the wood displaces 3 kg of water. A sinking object (like the steel) displaces a volume of fluid equal to its own volume. Since steel is very dense, a 3 kg piece of steel takes up very little volume and therefore displaces much less than 3 kg of water. Thus, the floating wood displaces more water than the sinking steel.

Step-by-Step Solution

1
Analyze the displaced water for the floating wood block.
According to Archimedes' principle, a floating object displaces a weight of fluid equal to its own weight. Therefore, the 3-kilogram wood block displaces exactly 3 kilograms of water.
This establishes the buoyant force required to keep the wood in equilibrium on the surface of the water.
2
Analyze the displaced water for the sinking steel weight.
A sinking object displaces a volume of fluid equal to its own total volume. Because steel is much denser than water, a 3-kilogram piece of steel has a very small volume.
This determines how much water is physically pushed out of the container by the fully submerged steel.
3
Compare the weight of the water displaced by both objects.
The wood displaces 3 kilograms of water. The steel displaces a volume of water equal to its own small volume, which weighs much less than 3 kilograms. Therefore, the floating wood displaces a greater weight of water.
Directly answering the question by comparing the calculated fluid displacements.

Key Concept

Buoyancy and Archimedes' Principle
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