HOW IT FLIES

The Envelope of the balloon is filled with the heated air heated by the burner, that is a gas that is less dense than the surrounding air. This lighter air gives the balloon buoyancy and causes it to rise. The principle behind this is Archimedes' principle which describes how a body in a fluid (which air is considered), is acted upon by a force equal to the weight of the fluid displaced by the body.

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Volume 'V' is the volume of the balloon, equal to the volume displaced by the balloon.
V_{air displaced}=V_balloon
The force F_B is the upward buoyant force equal to the weight of the cooler air displaced by the balloon.
F_B=Mass_{cool air displaced}
The cooler surrounding air has a greater mass than the heated air, so F_B is greater than the mass of the balloon. When it exceeds the weight of the heated air, the envelope, basket and everything inside it, then it will lift off of the ground.
F_B>Weight _{total balloon}
Since all of this mass is near the base of the balloon it remains stable throughout the flight.

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