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 41.7 g package to be accelerated upward at a rate of 2.50 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

Buoyancy force Fb = pgV

from Newton second law , net force along vertical direction F =ma

Fb -mg = ma

Fb = ma+mg

pgV= ma+mg

1.16*9.81*(60000*10^-6)=m(2.5)+m(9.81)

m= 0.0555 kg this is the mass of both the air in the balloon and the package, you need just the air)

0.0555 - 0.0417 =0.0138 kg (mass of air in the balloon)

density=mass/volume

density = 0.0138/(60000*10^-6)=0.23 kg/m^3

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