Why Hot Air Balloons Rise
Hot air balloons float in the atmosphere for the same reason beach-balls float in the water. Objects float because they weigh less that the buoyancy force exerted on them by the liquid they are immersed in.
http://www.itisz.com/inflatable.htm
It is easiest to understand the buoyancy force as it is applied to water and beach-balls, then apply it to the atmosphere and balloons. Imagine a tank of water. In the tank there is a submerged beach-ball filled with water. The water filled beach-ball will not move in the tank because the forces around it are in equilibrium, all forces are balanced. Because the water filled beach-ball is in equilibrium the downward force of its weight (force due to gravity) must be in balance with some upward force (force due to the liquid surrounding the beach-ball).
If we replace the water filled beach-ball with a beach-ball filled with air. The weight of the beach-ball has changed, but the upward force due to the liquid remains the same. The force due to the weight of the beach-ball is now smaller than the force due to the liquid surrounding it, the beach-ball will rise in the water tank.
http://www.rainbowryders.com/index.html
This is the exact same phenomenon that causes hot air balloons to rise in the atmosphere. The buoyancy force from the atmosphere is greater than the force due to the weight of the balloon. The perceived lighter weight of the hot air balloon is caused by heating the air mass within the balloon. This makes the air in the balloon less dense than the surrounding atmosphere. Just like the air in a beach ball is less dense than the water around it.
http://www.ushotairballoon.com/redtrans1.gif
Created by John Rowley 2005.