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 79200 cm3 gas-filled balloon will provide enough lift for a 43.4 g package to be accelerated upward at a rate of 3.40 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 rho air = 1.16 kg/m3. Neglect the mass of the balloon material and the volume of the package.

Explanation / Answer

Volume of balloon = 79200 cm^3

mass of gas be m kg

Wt of baloon(gas) and package = (0.0434 + m)*9.81 N

Buoyancy = Volume*density of air *9.81 = 0.0792*1.16*9.81 = 0.90126 N

Wt - B = Total mass * a

(0.0434 + m)*9.81 - 0.90126 = (0.0434 + m) * 3.4

m = 0.0972 kg = 97.2 g

Density = mass/volume = 0.0972 / 0.0792 = 1.227 kg/m^3

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