(5 minutes or less)
Fill the tall drinking glass with room-temperature water. Gradually draw water into the eyedropper until the eyedropper floats in the glass with its top barely above the surface.
Fill the soda bottle almost to the top with room-temperature water. Transfer the eyedropper into the soda bottle. Be careful not to change the amount of water in the dropper while doing this. Screw the cap onto the bottle tightly.
(5 minutes or less)
Remove the ink cartridge from the pen with a pair of pliers: It will come out easily. Notice that the empty pen body is open at one end and plugged at the other. Attach a small amount of clay around the outside of the tube near the open end, without plugging the hole. This is just for weight.
You can use another bit of clay to plug the small air hole in the side of the tube, or you can leave the air hole unplugged, allowing the water to rise higher in the tube. If you like, you can also saw the tube off to a shorter length to make a smaller diver. If you shorten the tube or leave the hole open, you will need less clay to adjust the diver's buoyancy.
Test and adjust the diver by placing it open-end-down in the drinking glass or other wide-mouthed container. Add or remove clay until the diver floats with about 1/4 inch (6.25 mm) sticking out of the water.
Fill the soda bottle almost to the top with room-temperature water. Place the diver open-end-down in the almost-full bottle, and screw the cap on tightly.
Squeeze the soda bottle to make the diver sink, rise, or hover at any depth. You also want to test your diver's responses in a thin, flat bottle, such as a bottle that originally contained dishwashing liquid or shampoo.
To add a little spice, you can decorate the top of the eyedropper so that it becomes a diver with a funny face, or find small, hollow, open-bottomed toy figures to use as divers. You can also decorate the bottle. Use your imagination and creativity!
The Greek philosopher Archimedes was the first person to notice that the upward force that water exerts on an object, whether floating or submerged, is equal to the weight of the volume of water that the object displaces. That is, the buoyant force is equal to the weight of the displaced water.
As you squeeze the bottle, you increase the pressure everywhere in the bottle. The higher pressure forces more water into the eyedropper, compressing the air in the eyedropper. This causes the dropper to displace less water, thus decreasing its buoyancy and causing it to sink. When you release the sides of the bottle, the pressure decreases, and the air inside the bulb expands once again. The dropper's buoyancy increases, and the diver rises. If you look carefully, you can see the level of water changing in the dropper as you vary the pressure on the bottle.
If you use a thin, flat bottle, squeezing on the wide sides of the bottle will increase the pressure inside the bottle, but squeezing on the narrow sides will cause the volume of the bottle to expand and the pressure inside to decrease. If you use such a bottle, adjust the weight or water content of a Cartesian diver so that it barely floats. When this diver reaches the bottom of the bottle, it will stay there, even when you stop squeezing on the wide sides. You must squeeze the narrow sides to drive the diver to the surface. It will then stay at the surface even when the squeezing stops.
The key to this behavior is to carefully adjust the diver initially, so that it barely floats. As the diver sinks, the pressure outside the diver increases slightly with the water's depth. This increase is in addition to the increase in pressure you cause by squeezing the bottle. When the diver reaches the bottom and you stop squeezing, the pressure resulting from the increase in depth remains and continues to compress the air bubble a little. If the diver has been carefully balanced, this small compression of the bubble will be enough to keep the diver submerged. The process reverses when you squeeze the narrow sides to raise the diver.
Since ships float, their weight must be equal to the buoyant force of the water. The weight of a ship is therefore called its displacement.