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 72800 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

Forces on the balloon are
gravity force will act downward = m*g = m*9.81
where m is the mass of the gas and the package
Buoynacy force will act upward = pairgV
where V is the volume of the ballon
Hence the net force on the ballon
ma = buoynacy force - weight of the balloon
ma = pairgV - mg
m(a+g) = pairgV
m = pairgV /a+g = 1.16*9.81*(72800)*10-6  /(2.8+9.81)
m = 0.0657 kg
So mass of gas (mg) = *1000[0.0657 - (43.4/1000)]= 22.297 gram
Density of the gas = mass of the gas /volume = 22.297 /72800 = 3.063*10-4 g/cm3

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