Buoyant force is the upward force a fluid (liquid or gas) exerts on any object submerged or floating in it, equal in magnitude to the weight of the fluid the object displaces (F_b = ρ_fluid · V_displaced · g). On AP Physics 2, it appears in free-body diagrams in both Unit 1 fluids and Unit 2 thermodynamics.
Buoyant force is the net upward push a fluid exerts on anything sitting in it, whether that's a steel beam in a river or a balloon in air. It exists because pressure in a fluid increases with depth, so the fluid pushes harder on the bottom of an object than on the top. Add up all those pressure forces and you get one net upward force. Its magnitude follows Archimedes' principle, so F_b = ρ_fluid · V_displaced · g, where ρ_fluid is the density of the fluid (not the object) and V_displaced is the volume of fluid the object pushes out of the way.
The single most tested idea is what buoyant force does NOT depend on. It doesn't care about the object's mass, its material, or how deep it sits once fully submerged. A fully submerged bowling ball and a fully submerged balloon of the same volume feel the same buoyant force. What's different is their weight, which determines whether they sink, float, or hover. Floating just means the buoyant force balances the weight, and for a floating object the displaced volume adjusts itself until that balance happens.
Buoyant force is the star contact force of Topic 1.4 (Fluids and Free-Body Diagrams), where you draw it as an upward arrow alongside weight, tension, or normal force and apply Newton's second law to submerged or floating objects. It comes back in Topics 2.4 and 2.5 (Thermodynamics and Free-Body Diagrams / Contact Forces) because gases are fluids too, which is why hot air balloons rise and why a gas sample's density connects pressure, temperature, and buoyancy. That double appearance is the point. Buoyancy is one of the few concepts the CED deliberately threads across Unit 1 fluids and Unit 2 thermodynamics, so you should expect it anywhere a free-body diagram involves a fluid.
Keep studying AP Physics 2 Unit 1
Archimedes' Principle (Unit 1)
Archimedes' principle is the rule that tells you how big the buoyant force is. Buoyant force is the arrow on your free-body diagram; Archimedes' principle says that arrow's length equals the weight of displaced fluid.
Density (Units 1-2)
Compare ρ_object to ρ_fluid and you instantly know the outcome. Less dense floats, more dense sinks, equal density hovers. The fraction of a floating object that's submerged equals ρ_object / ρ_fluid, a classic MCQ shortcut.
Free-Body Diagram (Units 1-2)
Buoyancy problems are really Newton's-laws problems in disguise. Draw buoyant force up, weight down, add any tension or normal force, and set the net force equal to zero (floating) or ma (accelerating). The 2018 boat-loading FRQ is exactly this.
Thermodynamics and Contact Forces (Unit 2)
Air is a fluid, so warm, less-dense gas inside a balloon gets a buoyant force from the cooler, denser air around it. Heating a gas lowers its density, which is the thermodynamic reason things float in air.
Buoyancy shows up in two main flavors. In multiple choice, expect conceptual ranking questions (compare buoyant forces on objects of different masses but equal volumes) and floating-fraction calculations using ρ_object / ρ_fluid. In free-response, buoyant force usually arrives inside a free-body diagram task. The 2018 short answer question gave a boat of mass M_b being loaded with steel beams and asked how many beams it could hold before sinking, which is pure force balance with F_b = ρ_water · V_b · g at maximum displacement. The 2021 long FRQ tied gas density to pressure in an experimental design, the same density reasoning that drives buoyancy in gases. Your jobs are to (1) draw the buoyant force correctly on a free-body diagram, (2) write F_b = ρ_fluid · V_displaced · g with the right ρ and V, and (3) justify in words why the force doesn't change with the object's mass. Symbolic answers in terms of given variables are the norm, so practice solving without numbers.
These aren't competitors; one defines the other. Buoyant force is the physical force itself, the upward push from pressure differences in the fluid. Archimedes' principle is the statement of its magnitude, that the buoyant force equals the weight of displaced fluid. On an FRQ, you cite Archimedes' principle to justify the value you assign to the buoyant force arrow. Saying 'by Archimedes' principle, F_b = ρ_fluid V g' is the move that earns justification points.
Buoyant force always points upward and equals the weight of the displaced fluid, so F_b = ρ_fluid · V_displaced · g.
Use the fluid's density and the displaced volume in the equation, never the object's density or total volume (unless it's fully submerged).
A fully submerged object's buoyant force does not depend on its mass or depth, only on its volume and the fluid's density.
An object floats when buoyant force balances weight, and the submerged fraction of a floating object equals ρ_object divided by ρ_fluid.
Buoyant force exists because fluid pressure increases with depth, so the upward push on an object's bottom beats the downward push on its top.
Gases exert buoyant forces too, which links Unit 1 fluids to Unit 2 thermodynamics through gas density.
It's the upward force a fluid exerts on a submerged or floating object, equal to the weight of the fluid the object displaces. The formula is F_b = ρ_fluid · V_displaced · g, and it shows up in free-body diagram problems in Units 1 and 2.
No. Buoyant force depends only on the fluid's density and the volume of fluid displaced. A 10 kg ball and a 1 kg ball of the same volume, both fully submerged in water, feel identical buoyant forces; they just have different weights.
Buoyant force is the force itself; Archimedes' principle is the rule that tells you its size (the weight of displaced fluid). On FRQs you name Archimedes' principle to justify writing F_b = ρ_fluid · V · g on your free-body diagram.
For a fully submerged object in a roughly incompressible fluid like water, no. The pressure on top and bottom both increase with depth, but their difference stays the same, so the buoyant force is constant once the object is fully under.
Yes. The 2018 short answer question asked how many steel beams a boat of mass M_b and maximum displaced volume V_b could carry before sinking, which is a buoyant force balance, and buoyancy-related density reasoning also anchored the 2021 long FRQ on gas density and pressure.
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