Out of Sink
Change a bottle’s shape to make a Cartesian diver rise when the bottle is squeezed in just the right way.
- Cup (not shown)
- Water (not shown)
- Several condiment packets such as soy sauce, ketchup, or BBQ sauce
- Clear, clean, non-cylindrical plastic bottle with screw-on cap (bottles shaped like elliptical cylinders works best, such as empty dishwashing liquid, mouthwash, ketchup, shampoo, or syrup bottles)
- Fill a cup with water and drop in your packets one by one to see how they’ll work. The best packet to use in this activity is the one that just barely sinks.
- After you’ve found the packet you want to use, fill the non-cylindrical bottle to the very top with water. Insert the unopened condiment packet you’ve chosen, make sure the bottle is topped off with water (no air bubble inside), and seal. That’s it!
Gently but firmly squeeze the narrow sides of the bottle (the major axis of the ellipse) to make the diver rise. (Be careful not to make indents in the sides of the bottle!)
Most Cartesian divers go down when you squeeze them, but this one goes up. Why is that happening?
When you squeeze the narrow sides of the bottle’s major axis you make the bottle’s minor axis a little larger. This causes the volume inside the bottle to increase, lowering the pressure inside.
Your condiment packet contains two things: the condiment sauce and a bubble of air. The air bubble is there to help ensure that the packet doesn’t rupture in transit or from temperature variations. When you squeeze the bottle and increase its volume, the reduced pressure inside the bottle causes the bubble in the condiment packet to expand. Because the mass of the packet stays the same, but the volume increases, the density decreases. This change in density changes the packet’s buoyancy, causing it to rise.
Why does the volume of a non-cylindrical bottle change when you squeeze on it? Here’s a simple way to see:
- Take the top off the bottle so you can see the water level change.
- Squeeze the bottle on its longer sides (its minor axis). Notice that the water rises; it might even spill over the top of the bottle. Rising water means the total volume inside the bottle has gone down (see photo below).
- Now squeeze the bottle on its narrow sides (its major axis). Notice that the water level goes down (see photo below). The lower water level means that the total volume inside the bottle has increased.
