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 2.65 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

mass of air displaced

M = pair*V = 1.16*(6*104*10-6) = 0.0696 kg

Buouancy force

Fb =Mg= 0.0696*9.81 = 0.683 N
mass of gas

m =pV =0.06p

weight of gas

Fg =mg =0.0600p*9.81 = 0.5886p

acceleration

a = Fnet /Mtotal = (Fb - Fg - mg) / (pV + m)

2.65 = (0.683 - 0.5886p - 0.04*9.81) / (0.06p+ 0.04)

2.65(0.06 p+ 0.04) = 0.2906 - 0.5886p

0.159p + 0.106 = 0.2906 - 0.5886p

0.7476p=0.1846

p=0.247 Kg/m3

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