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 66400 cm3 gas-filled balloon will provide enough lift for a 43.4 g package to be accelerated upward at a rate of 2.95 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

According to the given problem,

mass of displaced air M = air*V = 1.16kg/m³ * 0.0664m³ = 0.0770 kg
buoyant force Fb = air*V*g = 1.16kg/m³ * 0.0664m³ * 9.81m/s² = 0.7556 N

mass of gas m = *V = *0.0664m³
weight of gas Fg = *V*g = *0.0664m³*9.81m/s² = *0.6514m/s²

acceleration a = Fnet / totalmass = (Fb - Fg - m*g) / (*V + m)
Dropping units for ease ( is in kg/m³):
2.95 = (0.7556 - *0.6514 - 0.0434*9.81) / (*0.0664 + 0.0434)
2.95(*0.0664 + 0.0434) = 0.329846 - *0.6514
*0.19588 + 0.12803 = 0.329846 - *0.6514
*0.525726 = 0.201816
= 0.384 kg/m³

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