This virtual lab shows how an aerostatic balloon works. It is a nice example of application of the Archimedes' principle
The buoyant force (F_l) of the aerostatic baloon is obtained by heating air inside its cavity. The buotant force is due to the difference of density between the hot air inside and the cold air outside the balloon cavity. The buoyant force compensate the balloon weigth (w) (having into account the ballast (w_l ) and people weight).
The following assumptions have been made in the model:

• The air is a perfect gas. Therefore air density can be computed with the following equation : density=P/R*M /T. Where R is the constant of ideal gases, M is the molecular weigth of the air, P is the air pressure and T the air temperature.

• The standard atmosphere model from the surface to 11 km altitude is used to describe the variations of the temperature and pressure with altitude. This model states that the temperature decreases 6.5 K per Km (T=T0-6.5K/Km*h(km)) and the pressure follows the following equation: P=P0*(T0/T(h))^-5.256. Where T0 and P0 are the temperature and pressure at sea level.