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 destinations. A 6.00×104 cm3 gas-filled balloon will provide enough lift for a 43.4 g package to be accelerated upward at a rate of 2.80 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*(60000*10^-6)=m(2.80)+m(9.81)

m=0.05415 kg (this is the mass of both the air in the balloon and the package, you need just the air)

0.05415-0.0434 = 0.01075kg (mass of air in the balloon)

density=mass/volume

= 0.01075/(60000*10^-6)

= 0.179 kg/m^3

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