In this experiment, a Cartesian Diver was manipulated to explain relationships between forces.
The “Cartesian” in the Cartesian Diver is often assumed to be derived from the name of the French Mathematician and philosophy Rene Descartes (1596-1650). He is often falsely credited with inventing this quirky experiment. However, there is no historical evidence that he has ever been connected with the diver. In fact the French do not refer to the diver as Cartesian but ludion which is derived from a Latin word meaning actor or jester.
It is more likely that one of Galileo's students, Raffaelo Maggiotti was the inventor as he speaks of the device as “My invention” in a short pamphlet he published in 1648.
Discussion
What Happens throughout the experiment?
As pressure is applied to the side of the bottle the “diver” sinks. As pressure is removed from the side of the bottle the “diver” rises. If just the right amount of pressure is applied to the side of the bottle, the “diver” can be manipulated to remain midway in the bottle.
When does it happen?
The diver only moves as pressure is applied or removed form the side of the bottle.
Why does this happen?
Floating and sinking depends the relationship between the weight of the object due to gravitational force and the weight of water it displaces. For an object to float its volume must displace an equal weight in water. If an object sinks its volume displaces less weight in water. When you apply pressure on the bottle, the air inside the cap gets smaller and denser, making it displace less water.
This can be summed up in one word “buoyancy,” discovered by Archimedes. Archimedes discovered the theory while taking a bath. Once he came to realize what was going on he immediately jumped out of the bath and ran naked through the streets shouting at the top of his voice Eureka “I have found it”.
Imagine a ball of water in a cup, the force on the ball will act in all directions and increase with depth. If the water ball is replaced by a real object then the forces can be assumed to be the same and there will be a resultant upward force on the object equal to the weight of water displaced.
In our diver experiment there is a downward force due do gravity which is dependent on the mass of the object. This is opposed by an upward force that is equal to the amount of water displaced. Squeezing the bottle applies pressure to the water which acts in all directions including on the air inside the pen cap. The air compresses which decreases the volume of water displaced and hence the force due to gravity becomes greater than the upward force and the pen cap sinks. Releasing the bottle reduce the pressure inside the bottle including on the air inside the pen cap. The air will expand increasing the volume of water displaced and the diver will rise. By placing the right amount of force on the bottle the upward and downward forces can be made equal and the diver can be controlled to a position mid way in the bottle.
The Cartesian diver is floating because the downward force (gravity) is less than the force pushing the diver up. It is barley floating, which means that the force pulling downwards is only slightly smaller than the buoyancy pulling it upwards
The diver sinks because the bottle has been squeezed, and the air inside has gotten denser and smaller, causing the diver to displace less water and sink.
- Bottle
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Cap
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Volume of water displaced by the Diver
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BluTak
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Downward force due to gravity
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Upward buoyancy force
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Sinking Diver
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Floating Diver
