A large balloon of mass 220 kg is filled with helium gas until its volume is 321

Question

A large balloon of mass 220 kg is filled with helium gas until its volume is 321 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3.

(a) Draw a force diagram for the balloon. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Calculate the buoyant force acting on the balloon.
. N


Your response differs from the correct answer by more than 10%. Double check your calculations.
...........N




(d) What maximum additional mass can the balloon support in equilibrium?
............ kg

Explanation / Answer

a) The force diagram would have one arrow going up labeled Fb (the buoyant force) and one arrow going down labeled Fg (the force due to gravity).

b) The buoyant force is equal to the weight of the air that is displaced, which is Vg = (1.29 kg/m3)(321m3)(9.8 m/s2) = 4058.082 N

d) First, we find the mass that could be supported by this buoyant force. This mass is (4058.082N)/(9.8m/s2) = 414.09kg. The mass of the helium gas is V = (0.179 kg/m3)(321 m3) = 57.459 kg. Therefore, the total mass of the balloon currently is 220kg + 57.459 kg = 277.459 kg. The maximum additional mass that can be supported is therefore 414.09kg - 277.459 kg = 136.631 kg.

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