AP Physics 2 Buoyancy — AP Physics 2
1. Core Definition and Origin of Buoyancy ★☆☆☆☆ ⏱ 2 min
Buoyancy describes the net upward force exerted on any object immersed in a static fluid. It arises because hydrostatic pressure increases with depth: pressure pushing upward on the bottom surface of an immersed object is always larger than pressure pushing downward on the top surface, creating a net upward force called the buoyant force.
Buoyancy is a core AP Physics 2 Unit 1 topic, contributing approximately 1-2% of your total exam score, and appears regularly in both multiple-choice and free-response sections. It is almost always paired with equilibrium force analysis, a high-yield foundational skill tested across the AP Physics 2 curriculum.
2. Archimedes' Principle ★★☆☆☆ ⏱ 3 min
Archimedes' principle is the fundamental physical law that lets us calculate the magnitude of the buoyant force on any immersed object. It states that the magnitude of the buoyant force equals the weight of the fluid displaced by the object.
F_b = \rho_f V_d g
Where $\rho_f$ is the density of the fluid (not the object, a common point of confusion), $V_d$ is the volume of fluid displaced (equal to the volume of the submerged part of the object), and $g$ is acceleration due to gravity. For a fully submerged object, $V_d = V_o$ (the total volume of the object); for a partially submerged floating object, $V_d < V_o$.
Exam tip: Always label $\rho_f$ (fluid density) and $\rho_o$ (object density) at the start of every problem to avoid swapping values.
3. Floating and Sinking Equilibrium ★★☆☆☆ ⏱ 3 min
Once you can calculate buoyant force, use Newton's first law of static equilibrium to predict whether an object will float, sink, or stay suspended. Any object in a fluid has two primary vertical forces: the downward weight of the object $W = m_o g = \rho_o V_o g$, and the upward buoyant force $F_b$ (horizontal forces cancel out and can be ignored).
- If $F_b > W$: Net upward force, the object rises to the surface and becomes a floating object
- If $F_b < W$: Net downward force, the object sinks to the bottom of the container
- If $F_b = W$: Net force is zero, the object is neutrally buoyant and stays suspended at any depth
For a stationary floating object on the surface, equilibrium always gives $F_b = W$. Substituting the formulas for $F_b$ and $W$ and canceling $g$ gives the very useful relation:
\frac{V_d}{V_o} = \frac{\rho_o}{\rho_f}
This means the fraction of the floating object that is submerged is exactly equal to the ratio of the object density to the fluid density.
Exam tip: If a question asks for volume above the water line, do not stop after calculating submerged volume. Always double-check what the question asks for.
4. Buoyancy with Additional Tension or Normal Force ★★★☆☆ ⏱ 4 min
Most AP exam buoyancy questions do not involve freely floating or sinking objects; they include an additional force from a string, scale, or the bottom of the container, so you need to draw a full force diagram and solve for the unknown force. This is the most common free-response question context for buoyancy on the AP exam.
- **Dense object hanging from a string above water**: Upward forces are $F_b + T$, downward force is $W$. Equilibrium: $T = W - F_b$, where $T$ equals the object's apparent weight.
- **Dense object resting on container bottom**: Normal force $N$ replaces tension: $N = W - F_b$.
- **Low-density object fully submerged, held down by a string**: Upward force is $F_b$, downward forces are $W + T$. Equilibrium: $T = F_b - W$.
The key first step is always to draw a force diagram to confirm the direction of all forces before writing the equilibrium equation.
Exam tip: Never assume tension is always upward. The direction of tension always opposes the motion the object would have if the string were cut.
Common Pitfalls
Why: Students default to the density of the object, which is usually highlighted in the problem statement.
Why: Students practice mostly with fully submerged problems, so they incorrectly assume $V_d = V_o$ for all cases.
Why: Students are used to dense objects hanging from strings above water, so they assume tension is always upward.
Why: Confusion between buoyant force (the upward force from the fluid) and apparent weight (the net downward force the object exerts on a scale).
Why: Students associate buoyancy only with water, so they forget air is a fluid that also exerts a buoyant force.