Buoyant force and submerged volume
Buoyant force equals the weight of fluid displaced — use the submerged volume only.
The common mistake
Using the object's whole volume for a floating object, instead of just the part under the fluid's surface.
Instead: F_b = ρ_fluid · V_submerged · g. A fully submerged object uses its full volume; a floating object only displaces enough fluid to match its own weight.
Worked example with Guide me
A 0.5 m³ block floats with 0.2 m³ under water (ρ = 1000 kg/m³, g = 10 m/s²). Find the buoyant force.
- Sugar · Which volume goes in the formula?Student · The submerged part, 0.2 m³.
- Sugar · Multiply ρ · V · g. What do you get?Student · 1000 × 0.2 × 10 = 2000 N.
- Sugar · What does that say about the block's weight?Student · It weighs 2000 N, since it floats.
Answer: 2000 N.
Try 3 practice questions
1. A 0.01 m³ rock is fully under water. Buoyant force? (ρ = 1000, g = 10)
2. A floating boat weighs 5000 N. Buoyant force on it?
3. A floating block has half its 0.4 m³ volume submerged in water. Buoyant force? (g = 10)
Quick answers
- What is the most common mistake with buoyant force and submerged volume?
- Using the object's whole volume for a floating object, instead of just the part under the fluid's surface.
- How do I get buoyant force and submerged volume right?
- F_b = ρ_fluid · V_submerged · g. A fully submerged object uses its full volume; a floating object only displaces enough fluid to match its own weight.
- Can you show a worked example?
- A 0.5 m³ block floats with 0.2 m³ under water (ρ = 1000 kg/m³, g = 10 m/s²). Find the buoyant force. 2000 N.
Related concepts
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