Buoyancy and Archimedes' Principle — AP Physics 1
1. Core Concepts of Buoyancy ★★☆☆☆ ⏱ 3 min
Buoyancy is the net upward force exerted by a static fluid on any object immersed partially or fully in it. It arises because hydrostatic pressure increases with depth: upward pressure on the object's bottom surface is greater than downward pressure on the top surface, creating the net upward force called *buoyant force* ($F_b$).
Exam tip: Buoyancy is tested conceptually as often as numerically on the AP exam. Be prepared to explain why buoyant force does not change with depth for fully submerged objects.
2. Buoyant Force Calculations ★★☆☆☆ ⏱ 3 min
From Archimedes' Principle, the core formula for buoyant force is:
F_b = \rho_f V_d g
Where $\rho_f$ = fluid density, $V_d$ = volume of displaced fluid, and $g$ = acceleration due to gravity. For fully submerged objects, $V_d$ equals the total volume of the object $V_o$. For partially submerged objects, $V_d$ is only the volume of the object below the fluid surface.
Exam tip: Always label $\rho_f$ (fluid density) and $\rho_o$ (object density) at the start of every problem to avoid mixing the two up.
3. Equilibrium of Floating Objects ★★★☆☆ ⏱ 4 min
A floating object at rest is in static equilibrium, so net vertical force is zero. The only vertical forces are the downward weight of the object $W_o$ and upward buoyant force $F_b$, so force balance gives:
F_b = W_o
Substituting the formulas for $F_b$ and $W_o$ and canceling $g$ from both sides gives the useful relationship for floating objects:
\frac{V_d}{V_o} = \frac{\rho_o}{\rho_f}
Exam tip: AP questions almost always ask for the fraction of volume *above* the fluid surface, not the submerged fraction. Double-check which quantity the question asks for.
4. Apparent Weight of Submerged Objects ★★★★☆ ⏱ 4 min
When an object is suspended and held at rest fully submerged in a fluid, its apparent weight (the force required to support it) is less than its actual weight, because the upward buoyant force counteracts part of the object's weight. For static equilibrium:
W_{app} + F_b = W_o \implies W_{app} = W_o - F_b
For a fully submerged object, this can be rewritten in terms of densities as:
W_{app} = W_o \left(1 - \frac{\rho_f}{\rho_o}\right)
This relationship is commonly used to find the density of irregular solid objects by measuring weight in air and apparent weight in a fluid of known density, a common lab-based AP exam problem.
Exam tip: If a problem gives you the tension in a string holding a submerged object, that tension equals $W_{app}$ — use it directly in your force balance.
Common Pitfalls
Why: Students often mix up which density is relevant, since object density determines whether an object sinks or floats
Why: Students forget only neutral buoyancy (fully submerged floating) has $V_d = V_o$, not surface floating
Why: Students confuse increasing pressure with depth with increasing net pressure difference, which does not change for a fixed volume
Why: Students memorize the ratio instead of deriving it from force balance
Why: Students forget buoyant force acts upward, opposite to weight