# The Cartesian Driver

## The Cartesian Diver – Archimedes and Boyle

The Cartesian Diver is a classic physics experiment providing a great visual representation of two important scientific principles: buoyancy and the ideal gas law.

Buoyancy, also called Archimedes’ Principle, is the force exerted on an object by a fluid being displaced by the object. In other words, buoyancy is the weight of the fluid displaced by the object. If the buoyancy force is greater than the weight of the object, the object will float. If the buoyancy force is less than the weight of the object, the object will sink. The ideal gas law serves as a good approximation of many gases under a variety of conditions. The air in our apparatus can be approximated fairly well as an ideal gas. Principles derived from the ideal gas law, particularly Boyle’s Law, will help us understand how our Cartesian Diver works. Boyle’s Law states that, for ideal gases, pressure and volume are inversely proportional. This means as pressure increases, volume decreases and vice/versa.

### Experiment:

We will use a Cartesian Diver to show how Boyle’s Law and buoyancy are related. We will manipulate our diver’s ascent and descent throughout our apparatus.

### Equipment/Materials:

• A container that can be sealed air tight and remain flexible (2L soda bottles work well)
• An eye dropper or other diver (see alternatives below)
• Small weight such as a hex nut, paper clip, or staples

### Procedure:

1. Fill the container with water until there is approximately 2-3 cm of air left at the top.
2. Place the diver in the container.
1. For divers such as the eye dropper or straw, you will need to fill them with a small amount of water and/or place a small weight on them in order to get them to “stand up” in the water.
2. Only add enough water so that the diver is mostly or completely submerged near the top of the container.
3. Seal the container air tight.
4. Squeeze the container.
5. Observe the motion of the diver.

### Discussion:

When the container is squeezed the diver “dives.” This is because when you squeeze the container, you increase the pressure of the system. This is most notable in the gap left at the top of the container. When you increase the pressure of the system, the gap becomes smaller. This is Boyle’s Law made visible. The increasing pressure decreases the volume of the air in the gap. What may not be readily perceivable however; is this same process is occurring in the diver. The increased pressure also decreases the volume of air in the diver. As the volume of air decreases, the amount of water displaced by the air decreases as well which in turn decreases the buoyant force keeping the diver afloat. Once the buoyant force is no longer greater than the weight of the diver, the diver will sink to the bottom of the container.

Manipulating buoyancy is how submarines dive and surface in their travels.

### Alternatives:

1. Your diver does not have to be an eye dropper. Many different divers are possible including ketchup packets, soy sauce packets and individually wrapped candies. You can also make a diver using half of a drinking straw that is sealed on one end (usually with a paperclip). Any diver which is sealed with a pocket of air can work. Try using 2 divers in the same system and see if they dive at the same time. Take care adding and removing your divers to protect their seals.

2. See how quickly or how slowly you can raise and lower your divers. Can you make the diver hold in the middle of the container? How long can you hold it there?

### Fun Fact:

Legend states that Archimedes’ discovered this principle while taking a bath. He was so overjoyed to inform the king of his discovery that he ran naked through the streets shouting “Eureka!”