A consumer upset with the latest trend of postal rate increases has decided to t

Question

A consumer upset with the latest trend of postal rate increases has decided to try to send letters by balloon even though they may not reach their intended destination. A 66400 cm3 gas-filled balloon will provide enough lift for a 46.8 g package to be accelerated upward at a rate of 2.95 m/s2. For these circumstances, calculate the density of the gas the consumer fills the balloon with. The acceleration due to gravity is  g = 9.81 m/s2 and the density of air is ?air = 1.16 kg/m3. Neglect the mass of the balloon material and the volume of the package.

Explanation / Answer

F_b = pgV

F_b=ma_y+mg

pgV=ma_y+mg

1.16*9.81*(66400*10^-6)=m(2.95)+m(9.81)

m=0.059216 (this is the mass of both the air in the balloon and the package, you need just the air)
0.059216-0.0468=0.0124kg (mass of air in the balloon)

density=mass/volume

0.0124kg/0.0664m^3=0.187kg/m^3

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