The Physics
Hypertextbook
Opus in profectus

# Buoyancy

## Problems

### practice

1. Your mother gives you a kilogram of aluminum and a kilogram of lead. Both objects are solid, rectangular blocks.
1. Which is more massive on the surface of the Earth?
2. Which is more massive on the surface of the moon?
3. Which will have the greater "weight" when placed on a spring scale on the surface of the Earth?
4. Which will have the greater "weight" when placed on a spring scale on the surface of the moon?
Special notes:
• The phrase "more massive" should be read literally as "has more mass" not "fills more space".
• All "weights" measured on the surface of the moon are not made inside the protective environment of a human habitation.
A variation on this practice problem appeared earlier in the section on density.
2. What fraction of an iceberg is above water?
3. Verify the rule of thumb that one cubic meter of helium can lift about one kilogram of load at sea level.
4. Write something completely different.

### conceptual

1. Two related questions.
1. How does the buoyant force on an airplane compare to the buoyant force on a helium-filled, party balloon; that is, which is greater and why?
2. Does the magnitude of the buoyant force alone explain why airplanes crash and balloons float? If not, why then do balloons float? (Explain your answer in either case.)
2. Should footballs (American footballs that is — not soccerballs) be filled with helium to ensure longer passes and punts?

### numerical

1. [FINISH IT] The Trieste was a research bathyscaphe famous for its record dive of 10,911 m (35,797 ft) to the deepest part of the ocean — the Challenger Deep in the Mariana Trench near Guam — on 23 January 1960. The vessel consisted of a 2.16 m (7.09 ft) diameter pressurized steel sphere for the two crew members suspended below a series of floatation tanks filled with 85,000 liters (22,000 gallons) of gasoline.
2. In order for a balloon to be successful, the buoyant force provided by the lifting gas must be greater than the weight of the material that makes up the balloon. The buoyant force is determined by the volume of the balloon (V) and the relative density of the gas contained within (Δρ). The weight of the balloon is determined by it's surface area (A) and the area density of the balloon material (σ). At some critical radius (rc) the lifting force of the gas within a spherical balloon will exceed the weight of the material used to make up the balloon and the balloon will work as intended.
1. Derive an equation for the critical radius described above in terms of the given quantities and physical constants.
2. Complete a table like the one below when the lifting gas is helium (ρHe = 0.164 kg/m3) and the surrounding gas is air (ρair = 1.161 kg/m3) at room temperature (T ~ 300 K).

material
area density
(kg/m2)