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Difficulty: HardBuoyancy and Archimedes' Principle

A marine engineering lab is evaluating four solid wooden cubes of identical dimensions for a flotation device. The cubes are set adrift in a freshwater basin (density = 1.00 g/cm31.00 \text{ g/cm}^3) and allowed to reach floating equilibrium. Based on the material densities provided, arrange the wood types in order of the percentage of their volume that remains ABOVE the water line, starting from the SMALLEST percentage exposed and ending with the LARGEST percentage exposed.

  1. 1Oak wood (Density = 0.75 g/cm30.75 \text{ g/cm}^3)
  2. 2Teak wood (Density = 0.65 g/cm30.65 \text{ g/cm}^3)
  3. 3Pine wood (Density = 0.40 g/cm30.40 \text{ g/cm}^3)
  4. 4Balsa wood (Density = 0.20 g/cm30.20 \text{ g/cm}^3)

Answer

The correct order from smallest to largest percentage above water is: Oak wood, Teak wood, Pine wood, and Balsa wood.
The fraction of a floating object submerged is equal to its density divided by the fluid's density. Because fresh water has a density of 1.00 g/cm31.00 \text{ g/cm}^3, a wood block's submerged percentage directly matches its density value as a percentage. The Oak block (0.75 g/cm30.75 \text{ g/cm}^3) is 75%75\% submerged, leaving the smallest amount (25%25\%) exposed above water. Conversely, the Balsa block (0.20 g/cm30.20 \text{ g/cm}^3) is only 20%20\% submerged, leaving the largest amount (80%80\%) exposed.

Step-by-Step Solution

1
Determine the relationship between material density and submerged volume for a floating object.
For a floating object, the fraction of its volume that is submerged is equal to the ratio of the object's density to the fluid's density (Vsub/Vtotal=ρobj/ρfluidV_{sub}/V_{total} = \rho_{obj}/\rho_{fluid}).
This relationship is derived directly from Archimedes' principle, where the upward buoyant force equals the downward weight of the floating object.
2
Calculate the percentage of volume submerged for each type of wood.
Since the water density is 1.00 g/cm31.00 \text{ g/cm}^3, the submerged fraction is simply the wood's density divided by 1. Oak is 75%75\% submerged, Teak is 65%65\% submerged, Pine is 40%40\% submerged, and Balsa is 20%20\% submerged.
This establishes exactly how much of each block is sitting below the water level.
3
Calculate the percentage of volume above water (exposed) for each type of wood.
The exposed percentage is calculated as 100%−submerged percentage100\% - \text{submerged percentage}. Oak = 25%25\%, Teak = 35%35\%, Pine = 60%60\%, Balsa = 80%80\%.
The question specifically asks for the percentage that remains ABOVE the water surface, requiring an inversion of the submerged values.
4
Arrange the wood types from smallest to largest exposed percentage.
Smallest to largest exposed percentage: Oak (25%25\%), Teak (35%35\%), Pine (60%60\%), Balsa (80%80\%).
This directly answers the prompt's final ordering requirement.

Key Concept

For an object floating in equilibrium, the fraction of its volume that is submerged equals the ratio of its density to the fluid's density. A higher density object will sit lower in the fluid, exposing less of its volume above the surface.
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Topics

Buoyancy and Archimedes' Principle

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