MCAT topics → Fluids in Circulation and Gas Exchange → Buoyancy and Archimedes' Principle

Buoyancy and Archimedes' Principle

MCAT trap: Confuses weight of the object with weight of displaced fluid in Archimedes' principle. Buoyant force equals the weight of the fluid displaced by the submerged portion of the object (F_b = ρ_fluid × V_displaced × g).

Buoyancy is the upward force a fluid exerts on any object submerged in it, and the MCAT tests it from Archimedes' principle through lab-style passage interpretation. The single most common error: confusing the object's properties with the fluid's. Archimedes' principle gives you the magnitude — F_b = ρ_fluid × V_displaced × g — and the buoyant force depends only on the fluid's density and the displaced volume, not on the object's weight, material, or shape. If you anchor on the object rather than the fluid, every downstream calculation falls apart.

The tricky part is that students consistently conflate the object with the fluid. The buoyant force has nothing to do with the object's weight — it's purely about the fluid that got pushed out of the way. This confusion gets worse when floating is involved, because a floating object is only partially submerged. The displaced volume is less than the object's total volume, and the equilibrium condition is that the weight of that displaced fluid equals the object's total weight — not its submerged volume times anything.

The MCAT also loves the ice-melting classic and apparent weight problems because both require you to distinguish between what the object weighs versus what the fluid 'gives back.' If you can fluently convert between true weight, buoyant force, and apparent weight — and understand what fraction of an object sticks out of water — you'll handle every buoyancy question confidently.

Common misconceptions

Common mistake
Wrong: Buoyant force equals the weight of the entire object, not the fluid displaced.
Right: Buoyant force equals the weight of the fluid displaced by the submerged portion of the object (F_b = ρ_fluid × V_displaced × g).
The buoyant force is generated by the fluid, not the object — it equals the weight of the fluid that was displaced, period. If a 10 kg object displaces only 0.003 m³ of water, F_b = 1000 × 0.003 × 10 = 30 N, not 100 N. Anchoring to the object's weight here will give you a wrong answer every time. Always ask: how much fluid was pushed aside, and how much does that fluid weigh?
Common mistake
Wrong: A floating object is fully submerged and displaces a volume of fluid equal to its total volume.
Right: A floating object is only partially submerged, displacing a volume of fluid whose weight equals the object's total weight.
A floating object is in equilibrium, which means net force is zero: F_b = W_object. Since F_b = ρ_fluid × V_submerged × g and W = ρ_object × V_total × g, setting them equal gives V_submerged / V_total = ρ_object / ρ_fluid. If ρ_object < ρ_fluid (which is why it floats), that ratio is less than 1 — so only a fraction is underwater. Ice floats with about 90% submerged because ρ_ice / ρ_water ≈ 0.9. Never assume a floating object is fully submerged.
Common mistake
Wrong: Apparent weight of a submerged object equals its true weight.
Right: Apparent weight equals true weight minus buoyant force (W_apparent = W_true − F_b).
When you weigh something underwater, the scale reads less because the fluid is pushing up on the object, partially supporting it. Apparent weight = W_true − F_b. If a rock weighs 50 N in air and the buoyant force is 12 N, the scale reads 38 N underwater. Ignoring F_b makes you overestimate the submerged weight, which breaks density calculations in passage problems.
Common mistake
Wrong: When ice melts in water, the water level rises because the ice adds volume.
Right: When ice melts, the water level stays the same because ice displaces water equal to its own mass, and melted ice occupies that same volume.
When ice floats, it displaces a volume of liquid water whose weight equals the ice's weight. When that ice melts, it turns into liquid water — and that liquid water has the exact same mass (and nearly the same volume at standard conditions) as what was displaced. So the water level doesn't change. This is a classic MCAT trap: adding volume from the melting ice sounds intuitive but ignores that the ice was already 'accounting for' that water by displacing it while frozen.
Free Deck audit

See if your Anki deck covers this topic.

Upload your deck →
Guided session

Stuck on this? An AI tutor that probes your understanding.

Start a session →

What the exam tests

  1. Know Archimedes' principle cold: buoyant force equals ρ_fluid × V_displaced × g, where V_displaced is only the submerged portion of the object.
  2. Understand floating equilibrium: a floating object sinks until the weight of fluid displaced equals the object's total weight, meaning it's only partially submerged — and you should be able to find the submerged fraction from the density ratio (ρ_object / ρ_fluid).
  3. Execute buoyancy calculations: solve for submerged fraction, apparent weight underwater, or what volume of a material is needed to keep something afloat, starting from a force balance.
  4. Interpret immersed-object lab data: use apparent weight and true weight together to calculate buoyant force, then back out the fluid or object density — a common passage setup.

Can you avoid these mistakes?

A wooden block (density 600 kg/m³, volume 0.01 m³) floats in fresh water (density 1000 kg/m³). What fraction of the block is submerged, and what is the buoyant force acting on it?
A metal sphere weighs 80 N in air and 55 N when fully submerged in fresh water. What is the buoyant force, and what is the volume of the sphere?
A sealed hollow sphere has a total mass of 2 kg and a total volume of 0.004 m³. Will it sink or float in seawater (density 1025 kg/m³)? If it floats, what fraction is above the surface?
A glass of water contains floating ice cubes that extend above the water surface. When the ice fully melts, does the water level rise, fall, or stay the same? Explain using Archimedes' principle, not intuition.

Related topics

Pressure in a Fluid (Pascal's Principle, Hydrostatic) Density and Specific Gravity Continuity Equation (Conservation of Flow) Bernoulli's Equation

See how your Anki deck covers this topic.

Upload your deck for a free audit →