Check out this Bill Nye Buoyancy Video

Buoyant Force (Annika)

The requirement that has to be met for a balloon to be able to rise in outside air is
that the density of the air inside of the balloon be less than the density outside of
the balloon. However, in order for the balloon to not collapse the air inside it must
exert enough pressure on the walls of the balloon to remain inflated.

The formula for buoyant force is

F(b) = (displaced fluid density)x(gravity acceleration)x(displaced volume)

When applied specifically to balloons the outside air is considered to be the liquid the
balloon is submerged in and the gas (inside air) volume is the displaced volume that must
be measured.

F (b) = (air density)x(9.81 m/sec2)x(volume of the gas filled balloon)

Another way to understand buoyant force in the context of hot air balloons
is that the total force on the balloon=buoyant force weight of the balloon.
Since weight is mass multiplied by acceleration due to gravity, the formula is:

F(b)=B-w or F(b)=B-m(9.81 m/sec2)

Air particles must work against the force of gravity to float in the first place,
so it is the air pressure that is greater beneath objects that pushes the air particles
upwards. The force of gravity is stronger than buoyant force so it requires air that
is lighter than the air around it to be light enough to float. Therefore, for something
to rise it must be less dense than the equal volume of air it is displacing. Air pressure,
however, must be equal so that the balloon is not crushed. To do this the air particles
must be bouncing around and putting pressure on the walls of the balloon. If there were
generally just fewer particles then the pressure would not be equal because the particles
would not bounce off the walls as often as the outside air that has more particles.
This is where the heat difference comes into play. With increased temperature the
particles have higher kinetic energy and travel faster, making up for the smaller
number of