Posted by **steve** on Friday, March 15, 2013 at 4:07pm.

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.

- Physics -
**Damon**, Friday, March 15, 2013 at 4:46pm
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

Notes :

g cancels

that gives you r, multiply by 2 for d

- Physics -
**steve**, Friday, March 15, 2013 at 5:07pm
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

- Physics -
**steve**, Friday, March 15, 2013 at 5:21pm
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

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