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Difficulty: EasyBuoyancy and Archimedes' Principle

A deep-sea recovery team locates a lost concrete mooring block resting on the ocean floor. The solid concrete block has a physical volume of 2 m32 \text{ m}^3 and a total downward weight of 45,000 N45,000 \text{ N}. The surrounding seawater has a weight density of 10,000 N/m310,000 \text{ N/m}^3. According to Archimedes' principle, what is the magnitude of the upward buoyant force acting on the completely submerged block?

  1. A
    45,000 N45,000 \text{ N}
  2. 20,000 N20,000 \text{ N}Answer
  3. C
    25,000 N25,000 \text{ N}
  4. D
    65,000 N65,000 \text{ N}

Answer

The correct answer is 20,000 N20,000 \text{ N}, which is found by multiplying the block's volume by the weight density of the seawater.
According to Archimedes' Principle, the buoyant force exerted on an object is exactly equal to the weight of the fluid that the object displaces. Because the block is completely submerged, it displaces a volume of water equal to its own volume (2 m32 \text{ m}^3). Multiplying this volume by the water's weight density (10,000 N/m310,000 \text{ N/m}^3) yields an upward buoyant force of 20,000 N20,000 \text{ N}. The actual weight of the concrete block is irrelevant to calculating the buoyant force.

Step-by-Step Solution

1
Identify the formula for buoyant force based on Archimedes' Principle.
Buoyant Force = Volume of displaced fluid × Weight density of the fluid.
To establish that buoyancy depends exclusively on fluid properties and displaced volume, rather than the object's own weight.
2
Extract the necessary physical values from the problem description.
The displaced volume is equal to the block's volume (2 m32 \text{ m}^3), and the fluid's weight density is 10,000 N/m310,000 \text{ N/m}^3.
To separate the relevant variables needed for the calculation from the distractor information (the block's 45,000 N45,000 \text{ N} weight).
3
Calculate the magnitude of the upward buoyant force.
2 m3×10,000 N/m3=20,000 N2 \text{ m}^3 \times 10,000 \text{ N/m}^3 = 20,000 \text{ N}.
To determine the final upward thrust exerted by the seawater.

Key Concept

Archimedes' Principle states that the buoyant force on a completely submerged object equals the weight of the fluid it displaces, independent of the object's own downward weight.
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Topics

Buoyancy and Archimedes' Principle

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