SINK vs. FLOAT THE CASE OF THE CARTESIAN DIVER INTRODUCTION: This lesson provides practice making observations and formulating hypotheses. It also provides opportunities to explore the concepts of buoyancy, density, Pascal's principle and the properties of liquids and gasses. OBJECTIVES: 1. Students will be able to articulate why an object floats or sinks in water. 2. Students will be able to understand the relationship between and object s density and the object s volume and mass. 3. Students will be able to apply concepts they learn in the context of the Cartesian Diver activity to a similar phenomenon in another context THEORY: A Cartesian diver can be made with a capped bottle of water (sealed container) and a suitable "diver." There are three basic concepts you need to understand: buoyancy, density, and Pascal's Principle. Buoyancy: When an object is placed in water, it displaces some of the water. The difference between the weight of the water displaced, and the weight of the object displacing it is called the buoyant force. If the buoyant force is greater than the mass of the object, the object will float. For example, a cube that measures one cm on a side has the capacity to displace one cm 3 of water. Since one cubic centimeter of water weighs one gram, if your cube weighs more than one gram, it will sink. If it weighs less than one gram, it will float Density: The relationship between an object s mass and its volume is usually expressed in terms of the object s density. Density is equal to the object s mass divided by the object s volume (D=M/V). Objects that are denser than water sink and objects that are less dense than water float. Water has a density of 1 gram/cm 3. Squeezing a sealed container increases pressure everywhere on the inside of the bottle; this concept is called Pascal's Principle. Water is virtually incompressible, but air is very compressible. So if that outside pressure squeezes an air bubble that is trapped anywhere inside the container the air bubble shrinks. This would then leave more room for more the water that is located in the container. Since the water itself is incompressible, nothing happens to its volume thus allowing this water to move into the space once occupied by the air. When you release your grip, the air in the container expands again and expels the extra water that had moved into its space.
EXPERIMENTAL PROCEDURE: You will explore four sets of diver stations in order to come to a more complete understanding of how density, buoyancy, and Pascal's Principle relate to the properties of liquids and gases; in particular, how these physical concepts relate to the operation of a Cartesian Diver. As you play with the divers at each station, think about why the diver behaves the way that it does; paying particular attention to the differences in each of the two divers/setups at each station. Your explanations at each station should include not only a labeled illustration of what is happening but a brief discussion of the same; incorporating the terms density, pressure, buoyancy, gas, liquid, and Pascal's principle. Your illustrations and explanations should include both when you squeeze the sides of the bottle and when you release the sides of the bottle. With respect to the illustrations they should be LARGE! At least a half-page in size in order to show the detail of what you re trying to convey! At EACH station you are to complete the following tasks and/or to contemplate the following questions when completing your illustrations and descriptions: Squeeze on the sides of each of the diver's bottles, respectively, and then release the sides; what do you observe? Does your observation depend on how hard you squeeze? Be as precise and as specific as you can with your observations. Are these two divers/setups exactly the same? Explain any differences (particularly major ones) and how each diver is able to behave the way it does; taking into consideration the scientific principles involved. Look carefully at the water level inside the diver as you apply and relieve pressure to the fluid by squeezing and releasing the outside of the bottle. Consider... What happens to the amount of air in the dropper when you press the sides of the bottle? What happens to the water level in the diver when you squeeze the bottle? What happens to the amount of the air in the dropper when you release the pressure? What happens to the water level when you release the bottle? What is the relationship between pressure and volume of air trapped in the dropper? Does the volume of the diver change? Is there any air/water entering or leaving the diver, or is something else causing the water level to change? Does the mass of the diver change? Again, do not forget to incorporate the terms density, pressure, buoyancy, gas, liquid, and Pascal's principle in your explanations!
Station #1: Are they really the same? Look carefully and note that one of the divers is open at the bottom while the other is sealed with glue. Your goal here is to explain the operation of each diver given these differences. Keep in mind that the main difference is the sealed vs. unsealed ends...not the amount of water in each, their relative mass, the respective bottle they are in, etc. The sketch should show enlarged detail of the diver(s) and what occurs as it/they dive.the bottle is not important here. Station #2: 1 vs. 2 Look carefully and note that there are two divers in the container; one labeled with a #1 and the other with a #2. Both of these divers are open at the bottom. Your goal here is to explain the operation of the divers compared to each other. The sketch should show enlarged detail of the diver(s) and what occurs as it/they dive.the bottle is not important here. Station #3: Unsinkable vs. Unfloatable Look carefully and note that one of the divers is floating at the top of its bottle while the other is sitting on the bottom of its bottle. Both of these divers are open at the bottom. Your goal here is to explain the operation of each diver given these differences. Keep in mind that the main difference is that one starts at the top of its bottle and the other at the bottom of its...not the physical appearance, stuff attached to it, the respective bottle they are in, etc; i.e. the fact that one of the divers has a wire wrapped around it and the other a nut is not, in appearance, relevant! The sketch should show enlarged detail of the diver(s) and what occurs as it/they dive.the bottle is not important here. Station #4: Full 2L vs. Partial 2L Look carefully and note that one of the divers is floating in a bottle that is completely full of water while the other is floating in a bottle that is half-full of water. Both of these divers are open at the bottom. Your goal here is to explain the operation of each diver given the difference(s) is the containers NOT the divers themselves; they are as identical as possible. The sketch should show enlarged detail of the bottles themselves.the divers are identical and will behave similarly. BEFORE you individually continue with Station #5, your group must complete the Post-Lab Questions and have them checked-off by Dr. Arts
Station #5: Create Your Own Having now investigated several diver stations and seen the variety of ways in which the divers operate, it is now time for you to design your own diver. Feel free to take a look at the sample divers around the room. Your goal is to create not only a working diver but one that is as unique (personalized) as possible. Step one would be to actually make a very simple diver and have it work properly. From there you will then "doll-it-up," so to speak...making it unique. Materials Pipette (plastic dropper) & metal nut Your bottle (2L or 3L), clear plastic bottle with an airtight lid Procedure Get a pipette (plastic dropper) and metal nut. Cut the pipette to the desired length; about ½ cm from the bottom of the large bulb. Screw the metal nut over this smaller, trimmed end of the pipette. It may be screwed as far up the stem as you'd like. Test your diver in the green test containers of water to see if it sinks (too dense) or is too buoyant (floats REALLY high up). Completely fill your bottle with water. Place the diver in the bottle of water. The water should over flow slightly...this ensures that you placed enough water in the bottle to begin with and did not leave an undesirable air pocket (remember that station??). So please do this part over a sink. Screw the cap on tightly. No water should leak out when the bottle is squeezed Squeeze the sides of the bottle. Release the sides of the bottle. If the diver does not operate properly, remove it from the bottle with the extraction tool and retest it in the green testing containers. Step two is to create your own personalized diver. Extract your diver from your bottle. You have a large collection of items to choose from in creating this operational "work of art": colored wire colored foam string and yarn colored plastic markers googly eyes pipe cleaners Be sure that any of the items you attach to your diver will still allow your diver to fit through the opening of your bottle!! Be Creative!! There are also hot glue guns and scissors available for construction purposes. Be sure not to actually touch the hot glue gun tip to the body of the plastic "diver." A melted hole in your diver's body is just like a hole melted into your body...undesirable consequences result! Once "personalized," retest the diver in the green testing container to be sure it has the proper buoyancy. Place it into your bottle and test it out. Good Luck!
REPORT ITEMS (To be submitted and stapled in the order indicated below) (-5 points if this is not done properly) COVER PAGE Lab Title Each lab group member s first and last name printed clearly Date DATA (worth up to 25 points) (10 points) Sketches/illustrations from each of the four stations. (15 points) A completed, and operational, Station #5 Diver. DATA ANALYSIS (worth up to 40 points) The completed task/contemplation questions and descriptions to accompany each of your illustrations; in order from Station #1, #2, #3, and then #4. These should be grouped with their corresponding sketch/illustration (if not already completed on the same page) GRAPHS (worth up to 0 points) None Required GRAPH ANALYSIS (worth up to 0 points) None Required CONCLUSION (worth up to 0 points) None Required
POST-LABORATORY QUESTIONS (worth up to 25 points) 1. If you wanted to make a series of divers (all sealed in the same bottle) that spell out the word H-E-L-L-O as they descended. Using diagrams and words, how would you do it? 2. A nail is pushed into a piece of Styrofoam packing material. Do you think that would work as a diver? Explain. 3. What, if anything, would you have had to do differently in order to make the diver operate correctly if our diver/bottle had used... a)...oil instead of water? b)...a heavier hex nut? c)...a smaller dropper? d)...a larger bottle? e)...helium instead of air? f)...the water in the bottle was hotter but the diver was room temperature? 4. A Cartesian diver is stuck on the bottom, with not quite enough air to get it to the top. List four different ways to get the sunken diver out of the top of the bottle, and explain why you think each would work. These may be simple or complex...don't over think a perfectly viable solution to the problem if one exists. You can also consider the different factors that affect a gas volume. a) b) c) d) 5. In the final "create your own station" we will top off the water in your bottle, before we seal it, to make your diver work better. Why do we do this? 6. Can you think of anything outside the laboratory that works on the same principles as the Cartesian Diver? Explain the connection. One example would be submarine...sorry, you can't use this one! Feel free to explore the internet!