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Picture this…you are at war with a group of aliens, we will call “Gatorians” for lack of a better term. They look like big lizards with green skin and orange eyes. Yuck! They have taken over your world and have isolated you and 15 others on an island somewhere in the South Pacific. But you have hope. If you can rendezvous with the military in Hawaii, you and your friends will be protected. Your only problem is how to get there. The “Gatorians” patrol the ocean surface continuously, and Hawaii is hundreds of miles from your position. Then someone in your group suggests that you build a submarine. That way you can avoid the “Gatorians” and still make it to Hawaii. You all decide that a submarine is the only way to go and then begin to design it. In order for the design to work, the submarine must float off the bottom of the ocean but not break the surface. This means that the density of the sub as a whole has to be very similar to the density of the water that surrounds the island. Real submarines use ballast systems, of course, but you have limited time and supplies so a design based on density is your only option (not to mention none of you are physicists and a workable ballast system is way out of your league). The group decides that they want you (the only scientist in the group) to design the sub and to make sure it will work. Before using what little resources you have, building the actual submarine, you devise the following experiment to test the idea first.

Using 16 metal pellets to represent masses of the 16 people that have to travel inside the submarine and a balloon to represent the sub itself, you calculate the density of the salt water and inflate the balloon to just the right volume so that the “submarine’s” density allows it to hover between the bottom of a pail of water and the surface. Your model system is quite a bit smaller than the sub will have to be, but if you can get the model to work then simply making the real sub 100 times bigger should also work as long as the density of the sub and the water remains the same.