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Difficulty: EasyBuoyancy and Archimedes' Principle

A solid steel engine block with a true weight of 2,000 N2,000 \text{ N} is completely submerged in a freshwater lake. The block displaces a volume of water that weighs 250 N250 \text{ N}. According to Archimedes' principle, what is the magnitude of the upward buoyant force acting on the engine block?

  1. A
    2,000 N2,000 \text{ N}
  2. B
    1,750 N1,750 \text{ N}
  3. C
    2,250 N2,250 \text{ N}
  4. 250 N250 \text{ N}Answer

Answer

250 N250 \text{ N}
According to Archimedes' principle, the upward buoyant force on an object submerged in a fluid is exactly equal to the weight of the fluid it displaces. Since the engine block displaces water weighing 250 N250 \text{ N}, the buoyant force acting upon it is exactly 250 N250 \text{ N}.

Step-by-Step Solution

1
Identify the values provided in the scenario.
The true weight of the block is 2,000 N2,000 \text{ N} and the weight of the displaced water is 250 N250 \text{ N}.
Extracting given values clarifies which numbers represent which physical properties.
2
Apply Archimedes' principle to determine the buoyant force.
Archimedes' principle states that the upward buoyant force is equal to the weight of the displaced fluid.
This principle directly links the volume of fluid displaced to the upward force exerted by the fluid.
3
Select the value that represents the weight of the displaced fluid.
The weight of the displaced water is 250 N250 \text{ N}, therefore the buoyant force is 250 N250 \text{ N}.
The object's own weight does not determine the buoyant force; only the displaced fluid's weight matters.

Key Concept

Archimedes' Principle and Buoyant Force
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Topics

Buoyancy and Archimedes' Principle

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