Archimedes Principle - Bounancy - Balloons

The ground work story is an atom has mass and since molecules are made of atoms a molecule has mass. Liquids and gases contain molecules that are displaced, under certain conditions.

Liquids are first, since we swim in liquids, float things in liquids ...you get the point. When an object, you or a boat, is immersed in a liquid the liquid exerts an upward force which is known as buoyant force and it is proportional to the weight of displaced liquid.

For instance, you float better in salt water than fresh water since salt water's density is greater than fresh water. 

If you have a constant size object that weighs, let say, twenty five pounds, and it  is a toy boat with high sides, it will ride higher in salt water than fresh water. Why? The toy boat will have to displace more fresh water (lower density) with a buoyant (upward force) of twenty five pounds to match the twenty five pound weight, hence it rides lower in the fresh water. The boat will displace less salt water to equal the buoyant upward force of twenty five pounds.  The sum force acting on the boat, then, is proportional to the difference between the weight of the boat('down' force of twenty five pounds) and the weight of displaced liquid ('up' force of twenty five pounds), hence equilibrium buoyancy is achieved when these two weights (and thus forces) are equal. Wow!

Isn't that neat! Same thing happens to you when you first swim in fresh water and then go on a vacation by the sea. You discover it is easier to swim in the ocean.

Density (mass per unit volume in liquids) is important. Salt water is more dense than fresh water.

Lets turn to air. It is a gas rather than a liquid. Same rules hold for objects immersed in air as they are in a liquid. Now we get into balloons immersed in air. 

Why do they float? If a balloon doesn't displace its weight in air molecules the upward buoyant forces exerted by the air molecules isn't as great as the weight of the balloon and it sinks. Think of a Birthday Balloon that, at first, rises to the top of a room but, after a few days air leaks out and the balloon displaces less and less air. It sinks! (Another story is when the balloon is filled with helium!)

The Hot Air Balloons make for a wonderful scenic ride. They are a perfect example of a controlled displacement volume aircraft.

Since air has a relatively constant density, the balloon, as it fills, will swell and displace more and more air. When the balloon fills and finally displaces more upward buoyant force exerted by the air than the downward force of the weight of the balloon, its basket and passengers - it float and begin to rise.

The more you increase the size of the balloon the more it will rise. If you let air out of the balloon and the size of the balloon decreases it will begin to sink. That is where the phrase, controlled displacement volume aircraft originated.