posted by steve on .
What minimum sized balloon would you have to fill in order to be able to be lifted into the air? Take your mass to be 100 kilograms and the temperature of the outside air to be 20 degrees C. Neglect the mass of the balloon rubber and basket and assume that the balloon is spherical in shape.Determine the minimum diameter of this balloon. Hint: review your notes on buoyant forces.
You do not say what is in the balloon. Is it Helium, Hydrogen, or hot air?
In any case use Archimedes who is very good at lifting things.
Force up = volume of air displaced times density of air times gravity, (4/3)pi r^3 * density of air at 20 degrees C * g
Weight of interior gas down = same equation but use density of interior gas
so in the end
100 * g = (4/3) pi r^3 [ density air - density gas] * g
that gives you r, multiply by 2 for d
the gas is mainly methane gas and has a density of about 0.72 kilograms per cubic meter so you know that a balloon filled with natural gas will float because the density is lower than air
Those are the options.I don't get any of those in my calculation but ill continue to try it. Thanks
about 8.5 meters in diameter
about 10.75 meters in diameter
about 7.3 meters in diameter
about 9.2 meters in diameter
about 7.6 meters in diameter