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Difficulty: EasyBuoyancy and Archimedes' Principle

Four identical airtight containers, each with a total volume of 1 m31 \text{ m}^3, are placed in different situations. Arrange these situations in order from the GREATEST buoyant force acting on the container to the LEAST buoyant force.

  1. 1The container is completely submerged in dense saltwater.
  2. 2The container is completely submerged in standard freshwater.
  3. 3The container floats in standard freshwater with exactly half (0.5 m30.5 \text{ m}^3) of its volume submerged.
  4. 4The container sits on dry land, completely out of the water.

Answer

The correct order from greatest to least buoyant force is: fully submerged in saltwater, fully submerged in freshwater, half-submerged in freshwater, and sitting on dry land.
Buoyant force is determined by the weight of the displaced fluid. A fully submerged object in saltwater displaces the heaviest amount of fluid. A fully submerged object in freshwater displaces slightly less weight because freshwater is less dense. A half-submerged object displaces only half the volume of water, yielding an even smaller force. An object on dry land displaces no water, experiencing zero buoyant force.

Step-by-Step Solution

1
Recall Archimedes' Principle.
The buoyant force is equal to the weight of the displaced fluid (Fb=fluid density×volume displaced×gravityF_b = \text{fluid density} \times \text{volume displaced} \times \text{gravity}).
This formula identifies the two main variables that affect buoyant force: the density of the fluid and the volume of fluid displaced.
2
Compare the volume of fluid displaced in each scenario.
Both completely submerged scenarios displace the full 1 m31 \text{ m}^3 volume. The half-submerged floating scenario displaces 0.5 m30.5 \text{ m}^3. The dry land scenario displaces 0 m30 \text{ m}^3.
Volume displaced is the primary factor in determining the magnitude of buoyant force.
3
Compare the fluid densities for the fully submerged scenarios.
Saltwater has a higher density than standard freshwater. Therefore, 1 m31 \text{ m}^3 of saltwater weighs more than 1 m31 \text{ m}^3 of freshwater.
When displaced volumes are equal, the fluid with the higher density exerts a greater buoyant force.
4
Order the scenarios based on the weight of the displaced fluid.
Submerged in Saltwater > Submerged in Freshwater > Half-submerged in Freshwater > Dry land.
This sequence correctly ranks the situations from greatest to least buoyant force.

Key Concept

According to Archimedes' Principle, buoyant force is directly proportional to both the volume of fluid displaced and the density of that fluid.
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Topics

Buoyancy and Archimedes' Principle

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