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Difficulty: MediumBuoyancy and Archimedes' Principle

Four solid machine parts are completely submerged in a deep vat of hydraulic fluid. Their respective masses and physical volumes are listed below. Arrange the machine parts in order from the LEAST buoyant force experienced to the GREATEST buoyant force experienced.

  1. 1Machine Part 3: Mass = 80 kg80 \text{ kg}, Volume = 4 L4 \text{ L}
  2. 2Machine Part 1: Mass = 45 kg45 \text{ kg}, Volume = 6 L6 \text{ L}
  3. 3Machine Part 4: Mass = 30 kg30 \text{ kg}, Volume = 8 L8 \text{ L}
  4. 4Machine Part 2: Mass = 15 kg15 \text{ kg}, Volume = 12 L12 \text{ L}

Answer

The correct sequence from least to greatest buoyant force is based entirely on the objects' volumes: Machine Part 3, Machine Part 1, Machine Part 4, and Machine Part 2.
Archimedes' Principle states that the buoyant force on an object equals the weight of the fluid it displaces. Because all the machine parts are entirely submerged in the exact same hydraulic fluid, the buoyant force is determined exclusively by their physical volumes. Therefore, ordering them from least to greatest buoyant force simply requires ordering them from smallest to largest volume: 4 L4 \text{ L}, 6 L6 \text{ L}, 8 L8 \text{ L}, and 12 L12 \text{ L}.

Step-by-Step Solution

1
Identify the relevant variable for determining buoyant force on fully submerged objects.
Buoyant force depends solely on the volume of displaced fluid, not the mass of the object.
According to Archimedes' Principle, the buoyant force equals the weight of the displaced fluid. Since all parts are submerged in the same fluid, displaced volume is the only variable.
2
Compare the volumes of all four machine parts.
The volumes are: Part 3 (4 L4 \text{ L}), Part 1 (6 L6 \text{ L}), Part 4 (8 L8 \text{ L}), and Part 2 (12 L12 \text{ L}).
Extracting the volume metric from each item allows for direct comparison.
3
Arrange the parts in ascending order based on their volume.
The correct order is Part 3, Part 1, Part 4, Part 2.
A smaller physical volume displaces less fluid, resulting in a proportionally smaller upward buoyant force.

Key Concept

For fully submerged objects, the buoyant force is directly proportional to the object's volume (which dictates the volume of fluid displaced), completely independent of the object's mass.
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Topics

Buoyancy and Archimedes' Principle

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