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AP Physics 1 Unit 8: Buoyancy & Archimedes

Topic 8.2 (New for 2025, 5–8% exam weight): Why do massive steel ships float while small pebbles sink? The answer is Buoyancy—the upward force a fluid exerts on objects.

1. Archimedes’ Principle

The buoyant force ( $F_B$ ) equals the weight of the displaced fluid.

$F_B = \rho_{fluid} V_{sub} g$

Buoyant force = fluid density × submerged volume × g

Diagram of a Eureka can showing that the volume of water spilled equals the volume of the submerged object.

“Eureka” Experiment: $F_B = m_{fluid} g$ because the displaced water has mass $m_{fluid} = \rho_{fluid} V_{sub}$ .

⚠️ Common Mistake: Use the density of the fluid ( $\rho_{fluid}$ ) and only the submerged volume ( $V_{sub}$ ), not the object’s total volume (unless fully submerged).

2. Float vs Sink (Free-Body Diagrams)

Compare Gravity ( $mg$ , down) and Buoyancy ( $F_B$ , up) to decide floating, sinking, or neutral.

Free body diagrams comparing a floating wood block vs a sinking steel block.

Force Balance: Floating: $F_B = mg$ . Sinking: $F_B < mg$ .

Floating: Equilibrium at surface. $F_B = mg$ and $\rho_{object} < \rho_{fluid}$ .
Sinking: Object denser than fluid. $F_B < mg$ so it accelerates downward until it rests on bottom.
Neutrally Buoyant: $\rho_{object} = \rho_{fluid}$ . It hovers at any depth (like many fish and submarines).

3. Apparent Weight

Underwater, objects feel lighter because the buoyant force “helps” lift them.

$W_{apparent} = W_{actual} - F_B$

Scale reading underwater = true weight minus buoyant force

4. Quick AP Practice

📚 AP Practice Problems

1. A wood block floats with 60% of its volume submerged. What is $\rho_{wood}$ if $\rho_{water}=1000\,kg/m^3$ ?

Answer

$F_B = mg \Rightarrow \rho_f V_{sub} g = \rho_o V_{tot} g$
$\frac{\rho_o}{\rho_f} = \frac{V_{sub}}{V_{tot}} = 0.6$ → $\rho_o = 0.6 \times 1000 = 600\,kg/m^3$ .

2. A rock weighs 10 N in air and 8 N in water. What is the buoyant force?

Answer

$F_B = W_{actual} - W_{apparent} = 10 - 8 = 2\,\text{N}$ .

3. An iron ship floats but a solid iron block sinks. Why?

Answer

The ship is mostly hollow (air inside). Its average density is less than water, so it displaces enough water to match its weight before submerging fully. The solid block’s average density is greater than water, so it sinks.

🔗 Related AP Physics Resources

🎉 Unit 8 Part 2 Complete!

You now understand buoyant force, floating vs sinking, and apparent weight. Next up: moving fluids and Bernoulli’s Equation.

Next: Fluid Dynamics & Bernoulli →