Consider a woman whose mass is m=68m=68 kg. (a) Find the minimum radius of a hel
ID: 1561427 • Letter: C
Question
Consider a woman whose mass is m=68m=68 kg.
(a)
Find the minimum radius of a helium balloon that will lift her off the ground. The density of helium gas is 0.178 kg/m33, and the density of air is 1.29 kg/m33. Neglect the weight of the deflated balloon itself (but not the weight of the helium). Assume that the shape of the balloon is a sphere. Neglect the buoyant force of the air on the woman.
m ( ± 0.02 m)
b)
If we replace the helium with hydrogen gas, how much more mass can the balloon lift (in kg)? The density of hydrogen gas is 0.089 kg/m33. (Find how much mass in excess of mm the same balloon inflated to the same volume can lift.) Note: The buoyant force is the same. Only the weight of the gas has changed.
kg ( ± 0.1 kg)
Explanation / Answer
a.)buoyant force acted on ballon should be equal to the mass of man and gas
68*9.81 + 0.178*9.81*V = 1.29*9.81*V
V = 61.15 m^3
(4/3)Pi*r^3 = 61.15
r = 2.44 m
b.)
68*9.81 + 0.089*9.81*61.15 = 1.29*9.81*V
V = 56.61 m^3
(4/3)Pi*r^3 = 56.61
r = 2.38 m