A spherical weather balloon is filled with hydrogen until its radius is 2.20 m.

Question

A spherical weather balloon is filled with hydrogen until its radius is 2.20 m. Its total mass including the instruments it carries is 10.0 kg.

(a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3.
kN

(b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground?
kN

(c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

Because the external pressure (increase/decrease) with increasing altitude.

Explanation / Answer

V=4/3(pi)r^3
V=4/3(3.14)(2.2)^3=44.58m^3
F(air)=(density of air)(volume displaced)(gravity)
a) F(air)=(1.29)(44.58)(9.8)=563.58N =0.56358 kN
F(net)=F(air) - Fg(balloon)
b) F(net)=563.58N - (10 x 9.8) = 465.58 N upward = 0.46558 kN
c) The balloon gets bigger because the air pressure decreases with increasing altitude

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