Question

The largest ballon ever flown had a volume of 53 million cubic feet. The thickness of the fabric is only 0.013mm. The balloon would reach an altitude of 150,000 ft. ( 46 km). The atmospheric pressure at that altitude is about 2*10^-3kg/m^3. The pressure of the helium was the same as the outside air pressure.
What is the buoyant force, in N, on the balloon at that altitude?
a. 30N; b. 300N; c. 3000N; d. 30,000N. I answered 3000N which is incorrect.
Assume that the mass of the balloon ( including the fabric and the helium) is 800kg. What is the approximate mass hanging below the balloon (that keeps it afloat at that altitude)?
a. 20 kg; b. 200 kg; c. 2000kg; 20,000kg.
I answered 200 kg which was incorrect. Thanks for your help.

Answer 1

V=53•10⁶ ft³=1.5•10⁶ m³
h=45720≈46000 m
The density of the air
ρ=2•10⁻³ kg/m³
The buoyant force is
F=mg= ρVg=2•10⁻³•1.5•10⁶•9.8 =29400≈ 30000 N
Answer (d)
M=800 kg
m₀=(F-Mg)/g= F/g – M= ρVg/g –M=
=ρV-M = 2•10⁻³•1.5•10⁶ -800 =
= 3•10³ -800 =2200 ≈2000 kg
Answer (c)