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Difficulty: MediumBuoyancy and Archimedes' Principle

A rigid, sealed cylindrical pontoon is pushed completely underwater in a testing pool, where it displaces 200 liters200 \text{ liters} of water. The empty pontoon weighs 400 N400 \text{ N}. A technician then pulls the pontoon out, places 150 N150 \text{ N} of solid lead weights inside it, seals it, and forces it completely back under the water. Which of the following best describes the change in the upward buoyant force acting on the completely submerged pontoon?

  1. It remains exactly the same because the exterior volume of the pontoon displacing the water has not changed.Answer
  2. B
    It increases by 150 N150 \text{ N} to directly counteract the additional weight of the lead inside.
  3. C
    It decreases because the overall density of the pontoon assembly has become significantly greater.
  4. D
    It increases due to the heavier pontoon creating a stronger downward force, which produces a larger upward reaction from the water.

Answer

The upward buoyant force remains exactly the same because the rigid exterior volume displacing the water does not change.
Archimedes' principle states that the buoyant force on a completely submerged object is equal to the weight of the fluid it displaces. Because the pontoon is rigid, its exterior volume does not change when lead weights are added inside. Since it displaces the exact same volume of water when forced completely underwater in both scenarios, the upward buoyant force acting on it remains perfectly constant, regardless of its increased internal weight.

Step-by-Step Solution

1
Identify the factors that determine buoyant force according to Archimedes' Principle.
Buoyant force depends only on the density of the fluid and the volume of the fluid displaced by the object (Fb=ρ⋅V⋅gF_b = \rho \cdot V \cdot g).
This establishes the fundamental physics rule needed to solve the problem.
2
Analyze what changes between the first and second scenario.
The total weight of the pontoon increases from 400 N400 \text{ N} to 550 N550 \text{ N}.
To see if any variables in the buoyant force equation have been affected.
3
Determine if the volume of displaced fluid changes.
Because the pontoon is rigid, its exterior dimensions do not expand or shrink. Since it is completely submerged in both cases, the displaced volume remains exactly 200 liters200 \text{ liters}.
To calculate the final impact on the buoyant force.
4
Evaluate the final state of the buoyant force.
Since both the fluid (water) and the displaced volume (200 liters200 \text{ liters}) remain constant, the buoyant force remains identical.
To arrive at the final conceptual conclusion.

Key Concept

Archimedes' Principle states that buoyant force is equal to the weight of the fluid displaced, meaning it depends on the object's volume, not its mass.
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Topics

Buoyancy and Archimedes' Principle

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