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 6.00 × 104 cm3 gas-filled balloon will provide enough lift for a 40.0 g package to be accelerated upward at a rate of 3.25 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

Fb = pgV

'p' is the density, 'g' is the acceleration due to gravity, 'V' is the volume

Fb = may + mg

pgV = may + mg

1.16*9.81*(60000*10-6) = m(3.25) + m(9.81)

m = 0.05228 (this is the mass of both the air in the balloon and the package, you need just the air)

0.05228 - 0.040 = 0.01228 kg (mass of air in the balloon)

density = mass/volume

0.01228 kg / 0.0600 m3 = 0.2047 kg/m3

the density of the gas the consumer fills the balloon with is 0.2047 kg/m3

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