Friday, December 6, 2013

Helium Balloon

Helium balloons are a very common sight at carnivals, birthday parties, etc. but how fast do they accelerate when a child accidentally lets go?
Knowns: He=4.0026g/mol, balloon=4.000g, T=20 degrees Celsius, Pressure=101325Pa, Volume of balloon=4.00L

Calculations:

Bouyancy force=(density of fluid)(V of fluid displaced)(gravity)
Fb=1.1839Kg/m^3*(4.00L(1m/10dm)^3)(9.8m/s^2)
    =0.0464N

Mass of gas in the balloon
PV=nRT
101325Pa*(4.00L(1m/10dm)^3)=n*8.314J/molK*(20 degrees C+273K)
n=0.166mol
0.166mol*4.0026g/mol*1kg/1000g=0.000664Kg He gas

Force due to gravity
F=mg
   =(0.000664Kg+0.004000Kg)*-9.8m/s^2
   =-0.0398N

Acceleration of balloon ignoring drag force
F=ma
0.0464N-0.0398N=(0.000664Kg+0.004000Kg)a
a=1.62m/s^2

The drag force increases as the velocity of the balloon increases and at some point keeps the balloon from accelerating further and the balloon will travel upwards at a constant velocity.

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