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slasakai
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Fluid Mechanics Question! Help needed :(
It has been proposed that we could explore Mars with inflatable balloons. the density of the Martian atmosphere is 0.0154kg/m^3 (ignore that this varies with temperature). Suppose we make the balloons out of a thin tough plastic where density is such that each square meter has mass 5.00g, we inflate them with light gas of negligible mass.
(a) what's the radius and mass of the balloons such that they float immediately above the martian surface?
(b) If balloons of the same size were used on Earth, find the initial acceleration. the density of the Earth's atmosphere is 1.20kg/m^3.
(c) If on Mars these balloons have 5X the radius they currently do, how heavy an instrument package could they carry?
density=mass/volume
volume sphere=(4/3)πr^3
area of sphere =4πr^2
f=ma
(a) density of martian atmos. same as balloon's if it floats just above surface.
mass of balloon=(5g * 4πr^2)=0.02πr^2 kg
dens.=mass/volume
0.0154=(0.02πr^2)/((4/3)πr^3)
r=0.974 m and mass=0.0596 kg (both 3sf)
(b) here's where I became unstuck! Volume of balloon= 3.87 m^3 (3sf) therefore mass of air displaced =4.64 kg(3sf). using F=ma.
Mass of air displaced(buoyancy) - Mass of balloon = (mass of balloon)*acceleration.
plugging in my numbers, got a ridiculous answer for a, a=754 m/s^2 , clearly I have made some error.
I would greatly appreciate any help at all.
many thanks,
S.
Homework Statement
It has been proposed that we could explore Mars with inflatable balloons. the density of the Martian atmosphere is 0.0154kg/m^3 (ignore that this varies with temperature). Suppose we make the balloons out of a thin tough plastic where density is such that each square meter has mass 5.00g, we inflate them with light gas of negligible mass.
(a) what's the radius and mass of the balloons such that they float immediately above the martian surface?
(b) If balloons of the same size were used on Earth, find the initial acceleration. the density of the Earth's atmosphere is 1.20kg/m^3.
(c) If on Mars these balloons have 5X the radius they currently do, how heavy an instrument package could they carry?
Homework Equations
density=mass/volume
volume sphere=(4/3)πr^3
area of sphere =4πr^2
f=ma
The Attempt at a Solution
(a) density of martian atmos. same as balloon's if it floats just above surface.
mass of balloon=(5g * 4πr^2)=0.02πr^2 kg
dens.=mass/volume
0.0154=(0.02πr^2)/((4/3)πr^3)
r=0.974 m and mass=0.0596 kg (both 3sf)
(b) here's where I became unstuck! Volume of balloon= 3.87 m^3 (3sf) therefore mass of air displaced =4.64 kg(3sf). using F=ma.
Mass of air displaced(buoyancy) - Mass of balloon = (mass of balloon)*acceleration.
plugging in my numbers, got a ridiculous answer for a, a=754 m/s^2 , clearly I have made some error.
I would greatly appreciate any help at all.
many thanks,
S.
