You are part of a mission to Mars and have been assigned the task of designing balloons for the purpose of carrying scientific instruments over the surface of the planet. You have been told that the density of the atmosphere at the surface is 0.0154 kg m3 . You have with you a tough plastic that has a mass of 5.0 grams per square meter. You plan to use the plastic to construct the balloons and inflate them with hydrogen gas. What would be the radius of a balloon that could hover over the surface
Answer:
The radius of the balloon is R= 0.974 m
Explanation:
Atmospheric density on the surface of mars ρ = 0.0154 kg/m³
Mass density of balloon σ 5 gm/m² = 0.005 kg/m²
Total mass of balloon M = density of balloon* surface area
The balloon is considered as sphere
Surface area of sphere is given by 4π R²
Mass of balloon is M =σ *4πR²
M= (0.005 kg/m²)*(4π R²)
Volume of balloon is given by [tex]\frac{4}{3}[/tex] πR³
Density of atmosphere of mass is given by
ρ = Mass of balloon/volume of balloon
=(0.005 kg/m²)*(4π R²)/ [tex]\frac{4}{3}[/tex] πR³
Re arranging R
R = [tex]\frac{3*0.005 kg/m²}{ 0.0154 kg/m³}[/tex]
R = 0.974 m
The radius of the balloon is R= 0.974 m