Consider a man whose weight is w = 238lb. Find the minimum radius (m) of a heliu

Question

Consider a man whose weight is w = 238lb. Find the minimum radius (m) of
a helium balloon that will lift him off the ground. The density of helium gas is
0.178 kg/m3, and the density of air is 1.29 kg/m3. Neglect the weight of the deflated
balloon itself. Assume that the shape of the balloon is a sphere. Neglect the buoyant
force of the air on the man. (b) If we replace the helium with hydrogen gas, how much
more weight (lb) can the balloon lift? The density of hydrogen gas is 0.089 kg/m3. (Find
how much weight in excess of w the same balloon inflated to the same volume can lift.)
Caution: the answer is not w anymore. The buoyant force is the same. Only the weight
of the gas has changed.

Explanation / Answer

a)4*pi/3*r3(1.29-0.178)g=235*0.4536g
r3=22.889
r=2.84 m
b)It can lift the excess weight 4*pi/3*r3(1.29-0.089) -235*0.4536=4*pi/3*2.843(1.29-0.089) -235*0.4536=8.64 kg wt

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