Answer key: Buoyancy & Floating Worksheet
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Goal: Compare an object’s weight with the buoyant force F = ρ_fluid g V_submerged to explain why objects float, sink, or float at a particular depth.
Completed results table
| Setting | Buoyant force | Weight | Net force (up +) | Floating fraction |
|---|---|---|---|---|
| Wood in water, 50% under | 9.81 N | 9.81 N | 0 N | 50% |
| Ice in water, 92% under | 18.05 N | 18.05 N | 0 N | 92% |
| Steel in water, fully under | 19.62 N | 153.036 N | -133.416 N | Sinks |
| Wood pushed fully under | 19.62 N | 9.81 N | 9.81 N | 50% |
| Wood only 20% under | 3.924 N | 9.81 N | -5.886 N | 50% |
Answers
When the wood is half submerged, the net force is 0. Explain why it floats at exactly that depth.
Its weight is 9.81 N, and the water it pushes aside (half of its 2 L) also weighs 9.81 N, so the forces balance. Wood is half as dense as water (500 ÷ 1000), so it floats with 50% of its volume under water.
What happens to the wood if you push it fully under, or hold it only 20% under? Use the net force to explain.
Fully under, the buoyant force rises to 19.62 N, so a net upward force of 9.81 N pushes it back up. At 20% the buoyant force is only 3.924 N, and a net force of −5.886 N pulls it down. Either way it returns to floating 50% under.
Why does steel sink even though the buoyant force on it is bigger than on the floating wood?
Steel is 7.8 times denser than water, so its weight (153.036 N) is far more than the 19.62 N buoyant force even when it is completely under water. Floating depends on comparing the weight with the largest possible buoyant force.
Ice floats with 92% of its volume under water. Use the densities to explain the “tip of the iceberg”.
Ice’s density, 920 kg/m³, is 92% of water’s 1000 kg/m³, so it sinks until 92% of its volume is under water and the displaced water weighs as much as the ice (18.05 N). Only 8% stays above the surface.
Predict, then test: in seawater (1025 kg/m³), will ice float higher or lower than in fresh water?
Higher: its floating fraction drops to 89.76%. Denser water gives more buoyant force for each liter pushed aside, so less of the ice needs to be under the surface.
Challenge: a 500 kg/m³ object floats in a fluid of 1250 kg/m³. What fraction of it will be submerged?
40%, because the submerged fraction equals ρ_object ÷ ρ_fluid = 500 ÷ 1250 = 0.4.