Respuesta :
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
Archimedes' principle allows to find the result for the radius of the balloon that floats in the atmosphere of Mars is:
R = 0.974 m
Given parameters
- The density of the atmosphere of Mars ρ= 0.0151 kg / m³
- The mass of the plastic per square meter m = 5.0 g = 5 10⁻³ kg
To find
- The radius of the globe.
Archimedes' principle states that the thrust on a body is equal to the weight of the dislodged fluid.
B = ρ g V
Newton's second law gives a relationship between the force, the mass and the acceleration of the body, in the case that the acceleration is zero, it is called the equilibrium condition.
Σ F = 0
In the attached we see a diagram of the forces in the system, at the point where the balloon floats the acceleration is zero.
B -W = 0
B = W
The surface density is defined by the relation.
[tex]\sigma = \frac{m}{A}[/tex]
in area is a sphere is:
A = 4π R²
m = 4π R² σ
Indicate that the mass and the area therefore.
σ = 5 10⁻³ / 1
σ = 5 10⁻³ kg/m²
The volume of the sphere is:
V = [tex]\frac{4}{3}[/tex] π R³
Let's substitute.
ρ g [tex]\frac{4}{3}[/tex] π R³ = 4π R² σ g
[tex]\rho \ \frac{R}{3} = \sigma[/tex]
[tex]R = \frac{3 \sigma}{\rho}[/tex]
Let's calculate.
R = [tex]\frac{3 \ 5 \ 10^{-3} }{0.0154}[/tex]
R = 0.974 m
In conclusion using Archimedes' principle we can find the result for the radius of the balloon that floats in the atmosphere of Mars is:
R = 0.974 m
Learn more here: brainly.com/question/13106989
