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 45.1 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

volume of the ballon, v=79200 cm^3

mass, m=45.1g

acceleration, a=2.65 m/sec^2

density of the air, rho_air=1.16 kg/m^3

now use,

M*a=F_buoancy -M*g

M*a=rho*g*v-M*g

M*2.65=1.16*9.8*79200*10^-6-M*9.8

===> M=0.0723 kg

mass of the both air and balloon, M=0.0723 kg

===>

mass of the air, m_gas=M-m

m_gas=0.0723-0.0451

m_gas=0.0272 kg

and

density of gas, rho_gas=m_gas/V

=0.0272/(79200*10^-6)

=0.343 kg/m^3 --------------->

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