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Difficulty: MediumBuoyancy and Archimedes' Principle

A marine salvage team is recovering two solid objects resting on the ocean floor: a 100-pound lead weight and a 100-pound concrete block. Lead has a significantly higher density than concrete. While both objects are completely submerged, which of the following statements is correct regarding the buoyant forces acting on them?

  1. A
    Both objects experience the same buoyant force because they have identical weights.
  2. The concrete block experiences a greater buoyant force because it displaces a larger volume of water.Answer
  3. C
    The lead weight experiences a greater buoyant force because its higher density creates a stronger downward reaction.
  4. D
    The lead weight experiences a greater buoyant force because its concentrated mass exerts more pressure on the water.

Answer

The concrete block experiences a greater buoyant force because it displaces a larger volume of water.
According to Archimedes' Principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces. Because both objects weigh 100 pounds but concrete is less dense than lead, the concrete block must take up more space (larger volume). When completely submerged, the larger volume of the concrete block displaces a larger volume of water, resulting in a significantly greater upward buoyant force compared to the smaller, denser lead weight.

Step-by-Step Solution

1
Analyze the relationship between weight, density, and volume for both objects.
Both weigh 100 pounds, but lead is denser than concrete. Therefore, the 100-pound concrete block must have a larger physical volume than the 100-pound lead weight.
Density is mass per unit volume. For objects of equal mass, the less dense material takes up more space.
2
Apply Archimedes' Principle to completely submerged objects.
The buoyant force is equal to the weight of the displaced fluid. The volume of displaced fluid equals the volume of the submerged object.
Archimedes' Principle states that an object fully or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid that it displaces.
3
Compare the displaced fluid volumes and resulting buoyant forces.
Because the concrete block has a larger volume, it displaces more water than the lead weight. Consequently, the concrete block experiences a greater upward buoyant force.
Greater displaced volume directly results in a proportionally greater buoyant force, regardless of the object's interior weight.

Key Concept

Buoyancy and Archimedes' Principle
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Topics

Buoyancy and Archimedes' Principle

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