Archimedes' Principle states that an object partially or fully submerged in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces, written as F_b = ρ_fluid × V_displaced × g. It explains why objects float (buoyant force balances weight) or sink (weight wins).
Archimedes' Principle says the upward buoyant force on any object in a fluid equals the weight of the fluid that object pushes out of the way. As an equation, F_b = ρ_fluid × V_displaced × g. Notice what's in that formula and what isn't. The fluid's density matters. The displaced volume matters. The object's own mass and density do not appear at all. The fluid doesn't know or care what the object is made of; it only responds to the space the object takes up.
The intuition is that pressure in a fluid increases with depth, so the fluid pushes harder on the bottom of a submerged object than on its top. The net result of all that pressure is one upward force. Archimedes' Principle is the shortcut that lets you skip the pressure integration and jump straight to the answer. Floating or sinking then becomes a density comparison. If the object is less dense than the fluid, it floats and displaces only enough fluid to match its weight. If it's denser, the maximum buoyant force (fully submerged) still can't match its weight, so it sinks.
Archimedes' Principle lives in Topic 2.5 (Thermodynamics and Contact Forces), where the buoyant force shows up as one of the contact forces fluids exert on objects. That placement is the point. On the AP exam, buoyancy isn't a standalone trick; it's a force you drop into a free-body diagram next to gravity, tension, and normal forces, then handle with Newton's second law. A block hanging from a scale underwater, a balloon rising in air, a partially submerged floating object, all of these are Newton's-law problems where F_b = ρVg supplies one of the arrows. It also connects fluid statics to the broader fluid story (continuity, Bernoulli) and forces you to reason about density and pressure, two quantities that thread through the whole course.
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Buoyant Force (Unit 2)
Archimedes' Principle is the rule; the buoyant force is the thing it calculates. Whenever a problem says 'buoyant force,' your move is the same equation, F_b = ρ_fluid × V_displaced × g, then a free-body diagram.
Density and Displacement (Unit 2)
Float-or-sink questions are really density-comparison questions. A floating object sinks just deep enough that the weight of displaced fluid equals its own weight, which is why the fraction submerged equals ρ_object/ρ_fluid for a floater.
Bernoulli's Equation and Fluid Dynamics (Unit 2)
Archimedes handles fluids at rest while Bernoulli handles fluids in motion, but both trace back to the same idea that pressure differences in a fluid produce net forces. Together they cover the static and dynamic halves of fluid problems.
Drag Force (Unit 2)
An object sinking or rising through a fluid feels both buoyancy and drag. At terminal velocity, weight, buoyant force, and drag sum to zero, which is a classic three-force equilibrium setup.
Multiple-choice questions love conceptual ranking and comparison setups. Two objects of equal volume but different mass are fully submerged; which feels a larger buoyant force? (Same, because only displaced volume and fluid density matter.) An object moves from fresh water to salt water; does the submerged fraction change? You're expected to reason from F_b = ρ_fluid V g, not memorize outcomes. Free-response questions typically embed buoyancy in a Newton's second law problem, like finding the apparent weight of a block on a scale underwater or the tension in a string holding a balloon down. Draw the free-body diagram, write ΣF = ma with F_b pointing up, and solve. No released FRQ has used the phrase 'Archimedes' Principle' verbatim, but buoyant-force free-body and equilibrium analysis is exactly the kind of multi-force reasoning Physics 2 FRQs reward.
Both describe forces fluids exert, so they blur together. Archimedes' Principle applies to static fluids and gives the upward buoyant force from the pressure-depth difference on a submerged object. Bernoulli's Equation applies to moving fluids and relates pressure, speed, and height along a streamline. Quick test: if the fluid is sitting still and something is submerged in it, think Archimedes. If fluid is flowing through pipes or over surfaces, think Bernoulli.
The buoyant force on a submerged object equals the weight of the fluid it displaces, so F_b = ρ_fluid × V_displaced × g.
The buoyant force depends on the fluid's density and the displaced volume, never on the object's own mass or density.
An object floats if its average density is less than the fluid's density, and a floating object displaces fluid whose weight exactly equals the object's weight.
For a floating object, the fraction of its volume that is submerged equals the ratio ρ_object/ρ_fluid.
For a fully submerged object, the buoyant force does not change with depth, because the displaced volume stays the same.
On the exam, treat buoyancy as one more contact force in a free-body diagram and solve with Newton's second law.
It's the rule that an object partially or fully submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces, F_b = ρ_fluid × V_displaced × g. It's covered in Topic 2.5 alongside other contact forces.
No, not once the object is fully submerged. The displaced volume stays the same at any depth, so F_b = ρVg stays the same. Pressure increases with depth, but the pressure difference between the top and bottom of the object is what matters, and that's constant.
No. Mass doesn't appear in F_b = ρ_fluid × V_displaced × g at all. A 1 kg foam block and a 10 kg steel block of the same volume feel the exact same buoyant force when fully submerged; the steel sinks because its weight exceeds that force.
Archimedes' Principle is for static fluids and gives the buoyant force on a submerged object. Bernoulli's Equation is for flowing fluids and relates pressure, speed, and height along a streamline. Still water with something in it means Archimedes; fluid in motion means Bernoulli.
Set the buoyant force equal to the object's weight. That gives V_submerged/V_total = ρ_object/ρ_fluid. So ice (about 920 kg/m³) in water (1000 kg/m³) floats with roughly 92% of its volume submerged.