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. Two related questions.
1. When submarines traveling underwater in the oceans pass through the outflow regions of rivers they have a tendency to sink. Why does this happen? (Answer this part of the question in a way that will help you answer the next part.)
2. When submarines traveling underwater pass eastward through the Straits of Gibraltar from the Atlantic Ocean to the Mediterranean Sea they have a tendency to rise. What does this tell you about the water in the Mediterranean? Why is the water in the Mediterranean different than the Atlantic Ocean?
3. Should footballs (American footballs that is — not soccerballs) be filled with helium to ensure longer passes and punts?

### numerical

1. 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)