Floating foam block: submerged fraction

A foam block of density 0.4 g/cm³ floats in water of density 1.0 g/cm³. What fraction of its total volume is submerged?

Step-by-step

1. V_sub/V = ρ_object/ρ_fluid = 0.4/1 = 40%
   When floating, buoyancy equals weight: ρ_fluid·g·V_sub = ρ_object·g·V
2. ρ_object = 0.4 , ρ_fluid = 1
   Comparing the object's density with the liquid's tells you whether it floats

Why it works

The upthrust on a floating body equals its weight, so ρ_water × V_submerged = ρ_block × V_total. Its submerged fraction is thus the block's density divided by the water's density.

Common mistakes

• Setting up the ratio as 1.0 ÷ 0.4 and getting 2.5.
• Believing a light block must be completely under the water.

Related

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