AP Physics 1 · Unit 8 · Topic 2 of 4 · 6 min lesson

Buoyancy

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.

Quiz this topic · 5 questions Watch the review video ↗

The big idea

A fluid pushes up on anything in it. Archimedes’ principle: the buoyant force equals the weight of the fluid displaced, F_B = ρ_fluidV_subg. Use the fluid’s density and the submerged volume.

1. Float or sink?

A floating object sinks just far enough to displace its own weight of water. A dense object can’t displace enough, so it sinks.

F_B = ρ_fluidV_subgbuoyant force

ρ_object < ρ_fluidfloats

Floating: F_B = mgfraction under = ρ_object/ρ_fluid

Apparent weightmg − F_B

2. Where it comes from

Pressure grows with depth, so the fluid pushes harder on the bottom of an object than on its top. That difference is the buoyant force.

Once an object is fully underwater, going deeper doesn’t change F_B: the submerged volume stays the same.

Weighing a rock in water reads less than in air. The scale (or string) supports only mg − F_B, the apparent weight. Draw a free-body diagram: F_B up, tension up, mg down.

3. Example, then try it

Example

A 10 kg rock with volume 0.0040 m³ hangs from a string, fully underwater. Find the buoyant force and the tension in the string. (g = 10 m/s²)

F_B = ρVg = (1000)(0.0040)(10) = 40 N.

Equilibrium: T + F_B = mg → T = 100 − 40 = 60 N, its apparent weight.

Try it · work it on paper first

A wooden block (volume 0.010 m³, density 600 kg/m³) floats in water. What fraction is underwater? How hard must you push down to hold it completely under?

Weight: m = ρV = (600)(0.010) = 6.0 kg, so mg = 60 N.

Floating: F_B = 60 N → V_sub = 60 ÷ (1000 × 10) = 0.0060 m³, which is 60% of the block (= 600/1000).

Fully under: F_B = (1000)(0.010)(10) = 100 N.

Your push: F + mg = F_B → F = 100 − 60 = 40 N down.

Answer: 60% underwater; a 40 N push holds it under.

4. Common mistakes

Using the object’s density.F_B uses the fluid’s density.

Using the whole volume for a floating object.Only the submerged part displaces fluid.

“Heavier objects get more buoyant force.”Two objects with the same submerged volume get the same F_B, whatever their mass.

Check yourself

A steel ball and an aluminum ball have the same volume. Both are held completely underwater. How do the buoyant forces on them compare?

F_B = ρ_fluidV_subg. Same fluid, same submerged volume, so the same buoyant force. The steel ball is heavier, but that changes its weight, not F_B.

Ready to practice?

5 questions on Buoyancy, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 8