PICTURES COMING SOON

Control a tiny “submarine” with a hard squeeze… and learn the principle of how anything floats, from an ice cube to a ship. All you need is a handy plastic bottle, a test tube, some water, and a ruler.

Cartesian diver – squeeze a bottle and make it sink:

Equipment: minimal, cheap.

The Cartesian diver is a small item such as a test tube with an air space that just barely floats because it has an air bubble giving it buoyancy; it sinks when the air pressure on it increases to compress the bubble. To create the higher pressure, the diver is contained in a sealed vessel such as a plastic drink bottle. Squeezing the bottle (with its cap on!) creates the extra pressure. The Cartesian diver illustrates the principle of hydrostatics, that the upward force on an immersed object is equal to the weight of water (I presume you’ll use water) that the object displaces. With the right-sized air bubble, the object and its contained air bubble displaces a greater weight of water than its own weight. Squeezing the bottle compresses the air bubble and allow water to enter. Now the diver is not displacing as much weight of water as its own weight; it sinks. Relieving the pressure lets the diver rise. The cycle can be repeated endlessly. The hydrostatic principle applies to SCUBA divers, submarines, fish with swim bladders, and more. A note: I do mean weight, which is mass multiplied by the acceleration of gravity. People often confuse weight and mass, and, here, it’s actual weight.

Here are two images of the diver, afloat and sunk:

PICTURES

My combined sketch

Photo, filled bottle

Photo, dropping in the test tube

Photo, test tube floating

Photo? Measuring the float height

Photo, filling in the test tube

Video, quickly slipping in the partly filled test tube, then seeing it barely float, then squeezing it to make it sink, then letting up P to have it float again

Needed:

* A squeezable plastic bottle with its cap available.

* A “diver” – here, I use a simple glass test tube. You can use any clear item that will float with the air bubble up (not overturning). Be sure the test tube is glass and not plastic. Plastic won’t ever sink. Use a thin-walled glass test tube; a heavy one might not float, even empty.

* Water to fill the plastic bottle and to fill part of the volume of the diver.

* A short ruler

* A place to do this, away from computers and anything else that can be damaged by water

Fill the bottle with water nearly to the top. Do this over a basin because you’re going to spill some water.

  • Fill the bottle all the way to the top. Holding the test tube upside down, slip it into the bottle. It will bob up so that about half of it will be above the water line. We’ll get to why it reaches that level, later.
  • Now measure the height from the top of the water to the top of the tube. You’re going to want to take the test tube out of the water and fill it with almost the same volume of water as there was empty (air) space bobbing up; that will cancel the extra displacement of water that keeps the tube floating. So, suppose you had a 10 cm (4”) test tube and it floated with 4 cm above the water.
  • Take the test tube out and, holding it upright with the opening at the top, fill it with a little less water, say, 3.6 cm or 90% of the empty space. You can measure out the water slowly or be a little cavalier and then shake the tube sideways as needed to reduce any overfilling.
  • Now insert the test tube, again upside down, into the bottle. You want to keep all the water in the test tube, so do this quickly. Hold the water bottle at an angle just short of spilling out its water. Hold the test tube also at an angle, facing the water bottle. Swiftly push the test tube into the bottle.
  • If you didn’t spill any significant amount of water, the test tube, your diver, should just barely float. Now cap the bottle, tightly. When you squeeze the bottle tightly enough, the diver will sink to the bottom. Release the pressure and the diver will rise. You can do this indefinitely.
  • If the diver floats too high, it won’t sink with the highest pressure squeeze you can make. Take the diver out (easy: squeeze the bottle to bring the diver just above the rim of the bottle). If the diver sinks, retrieve it and fill it with less water. The easiest or least messy way is to hold the bottle upside down over a basin. Let your thumb off the bottle opening and grab the divers as it begins to come out. Refill the water bottle again.

A little more detail: Why use a glass test tube: Glass is denser than water; about 2.5 times more. By itself, it will sink. You have to give it a bit of air with water in its interior to make its filled weight match the weight of water it displaces. Plastic, on the other hand, is less dense than water and you can never get it to sink.

Making it a more quantitative demo: Calculate the level of air you need in the diver. You need to get the “weight” (mass) of the test tube, either using a small electronic scale or using geometry and the density of glass. Contact me if you’d like to see the sample calculations using the test tube dimensions.

 


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