Buoyant force

Also called Buoyancy, Upthrust

The buoyant force is the net upward force a fluid exerts on an object placed in it. Its magnitude equals the weight of the fluid the object displaces, so it depends on the fluid density and the displaced volume.

Essential knowledge 8.3.B.1 defines it as a net upward force exerted on an object by a fluid, and 8.3.B.2 says where it comes from: the fluid particles collectively push harder on the bottom of the object than on the top, because pressure rises with depth. The AP Physics 1 sheet prints the result as

F_b = \rho V g

Every symbol in that line is the one students get wrong. $\rho$ is the density of the fluid, never the object. $V$ is the volume of fluid displaced, which equals the object's total volume only when it is fully submerged. And $g = 9.8\ \text{m/s}^2$ .

Two standard cases follow. Fully submerged: $V$ is the whole object, and whether it rises or sinks is settled by comparing $\rho_{\text{fluid}}$ with the object's average density. Floating at rest: the buoyant force exactly balances the weight, so $\rho_{\text{fluid}} V_{\text{sub}} g = mg$ , and the submerged volume adjusts until that holds.

Note what is missing from the equation. Depth does not appear, so a fully submerged block feels the same buoyant force at one metre down as at ten. Neither does the object's mass.

Free-body diagrams and numbers for both cases are in Fluids in AP Physics 1.

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