Joe Quigley - Cartesian Divers

Title: Cartesian Divers

Principles Investigated: Buoyancy, Boyle’s Law, and Pascal’s Law

Standards: CA Content Standards for Science

· Grade 8: Physical Sciences

• 8.8 All objects experience a buoyant force when immersed in a fluid.
  • c. Students know the buoyant force on an object in a fluid is an upward force equal to the weight of the fluid the object has displaced.
  • d. Students know how to predict whether an object will float or sink.

· Grades 9-12: Chemistry

• 4.c Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Materials:

• Per Group:
  • clear two-liter bottle with lid
  • two glass eye droppers
  • food coloring
  • two small containers
  • one 16-oz paper cup
  • water
  • paper towels
• Per Student
  • student worksheets

Procedure: This lesson will take one-to-two 55 minute class periods. The experiment and Worksheet 1 take one period. Worksheet two can be homework, a quiz, or used as class work during the second period prior to a class discussion. A summative evaluation for this assignment is attached, and is designed to test all levels of Bloom’s Taxonomy.

Day 1:

1. Distribute all materials except droppers (students will be distracted by them).

2. PowerPoint with lecture introducing everyday examples of Boyle’s Law and Pascal’s Law. (2-3 minutes)

a. (Explain what each thing does but do not explain what the laws are at this time.) A metal submarine cruises deep in the ocean, then rises and surfaces. Bubbles from a diver grow larger as they near the surface. A hospital nurse pulls the plunger on a syringe and blood leaves a patients arm. A family drives down a mountain and all of their ears pop. A father presses down on a pump handle and air enters his child’s bicycle tire. A bus driver presses on a pedal and the bus slows down. A speaker expands his chest and air moves into his lungs. (In Powerpoint)

3. Instruct students to discuss the following question with a neighbor. “What do these have in common?” (2-3 minutes)

4. Next, discuss as a class. ( 2-3 minutes)

5. Distribute Worksheet 1. Each individual must complete a worksheet during group experiments.

6. Show video on how to setup the experiment and allow for questions. (5 minutes)

7. Remind students of the difference between observation and inference. (1 minute)

8. Distribute droppers and announce “begin”.

9. Students work in small groups conducting experiment and recording observations on Worksheet 1. (10-20 minutes)

10. Class discusses observations. (5 minutes)

11. Clean-up

Day 2:

1. Distribute Worksheet 2. Instruct students to complete Worksheet 2 individually, and to answer questions as completely as possible using their data from Worksheet 1.

2. Show Boyle’s Law and Pascal’s Law on overhead for students to record on Worksheet 2.

3. Allow time to complete Worksheet 2. It can be class work, homework, or a quiz. (15-25 minutes)

4. Students compare Worksheet 2 answers in groups. (5 minutes)

5. Class discussion based on both worksheets. (5-10 minutes)

Student Prior Knowledge:

Buoyancy (Archimedes’ Principle): The resultant upward forces exerted by the water on a submerged or floating body, equal to the weight of the water displaced by this body.

Explanation:

This version of the Cartesian Diver demonstrates Archimedes’ Principle, Boyle’s Law and Pascal’s Law. Students should already be familiar with buoyancy (Archimedes’ principle).

Pascal’s Law states that pressure supplied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. In layman’s terms, if pressure is applied to a closed container of fluid, the pressure will be distributed evenly, everywhere in the container. The Cartesian divers in this experiment are inside of a closed container of fluid. As the container walls are squeezed, the pressure is distributed evenly throughout the fluid—it is even transmitted to the fluid inside the divers (observe clear water entering tip), compressing the gas therein (Boyle’s Law).

Boyle’s Law states that at a constant temperature, the volume of a fixed amount of gas is inversely proportional to pressure. In layman’s terms, if the temperature does not change, a sealed amount of gas takes up an amount of space that shrinks consistently as pressure goes up; as pressure goes down the amount of space occupied by the gas grows consistently. The Cartesian divers in this experiment contain a gas—the air bubble trapped inside the dropper. The pressure applied to the container of water is transmitted evenly inside the droppers (Pascal’s Law). The increased pressure in the droppers pushes on the bubble, and the space occupied by the gas shrinks. As the bubble gets smaller more water goes inside the dropper, which changes the weight of the fluid displaced by the dropper, changing the buoyancy, and causing the diver to “dive.”

• Archimedes’ principle: “An object is buoyed up by a force equivalent to the weight of the fluid displaced” (Herr, 87).
• Buoyancy: “The resultant upward forces, exerted by the water on a submerged or floating body, equal to the weight of the water displaced by this body” (www.sciencedictionary.org).
• Boyle’s Law: “At constant temperature, the volume of a fixed amount of gas is inversely proportional to pressure” (www.sciencedictionary.org).
• Pascal’s Law: “A hydrostatic principle that pressure supplied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel” (www.sciencedictionary.org).
• Fluid: "A substance, as a liquid or gas, that is capable of flowing and that changes its shape at a steady rate when acted upon by a force tending to change its shape" (www.dictionary.com).

Questions & Answers

1. Why are the divers floating? The divers are floating because their weight is less than the weight of the fluid they displace. Their lesser relative density causes them to float.
2. What causes the divers to sink? The divers sink because the pressure applied to the container compresses the gas in the droppers, drawing in more water, thereby causing their weight to exceed the weight of the water displaced. Their greater relative density causes them to sink. Gravitational force exceeds buoyant force, pulling the divers down.
3. What causes the divers to resurface? When the pressure on the container is released, the pressure on the gas inside is reduced and the bubble expands, forcing water out of the dropper. This causes the weight of the divers to once again be less than the weight of the fluid displaced, causing them to resurface. Buoyant force exceeds gravitational force, pushing the divers back up.
4. Why did the divers rise and fall at different speeds? The divers rise and fall at different speeds because the amount of gas inside each diver is slightly different. Therefore, the amount of pressure required to cause the first diver to sink is insufficient to cause the second diver to sink. Further increasing pressure causes the second diver to sink. Likewise, when they are both at the bottom and pressure is gradually reduced, the last diver to sink will be the first to resurface.

Applications to Everyday Life:

• Submerged submarines force highly pressurized air into the ballast tanks (Boyle’s Law) to force water out of openings (Pascal’s Law), changing the overall buoyancy, causing the sub to rise (Archimedes’ Principle).
• The volume of a balloon or bubble increases as it ascends due to reduction in pressure (Boyle’s Law).
• A hospital nurse pulls the plunger on a syringe, thereby increasing the volume and creating low pressure, creating suction that draws blood from a patients arm (Boyle’s Law).
• A family drives down a mountain road, exposing their bodies to increasing atmospheric pressure, resulting in the “popping” of their ears as they acclimate (Boyle’s Law).
• A father presses down on a pump handle, reducing the volume and increasing the pressure, forcing air to enter his child’s bicycle tire (Boyle’s Law).
• A bus driver presses on a pedal that transfers the force to brake-fluid in an enclosed system, again transmitting the force to calipers that squeeze the brake discs, causing the bus slows down (Pascal’s Law).
• A speaker expands his chest, increasing the volume and decreasing the pressure, causing air from the higher-pressure system outside to move into his lungs (Boyle’s Law).

Photographs:

Videos:

http://www.youtube.com/watch?v=OR6G0K3JEeg

References:

Benson, T. (2010, July). Gas Pressure. From NASA K-12 Education. http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html (Accessed 2011, February 2).

Daily Motion. How to Make a Submarine. http://www.dailymotion.com/video/xgh4pw_how-to-make-a-submarine_lifestyle (Accessed 2011, February 2).

Dictionary.com. http://dictionary.reference.com/ (Accessed 2011, February 2).

Heiszwolf, J. Submarine Dive Technology. http://www.heiszwolf.com/subs/tech/tech01.html (Accessed 2011, February 3).

Herr, N. (2008). The Sourcebook for Teaching Science: Strategies, Activities, and Instructional Resources. San Francisco: Jossey-Bass.

Huetinck, L., & Adams, S. (2001). Physics. New York: Wiley Publishing, Inc..

Kid’s Science Experiments. http://kids-science-experiments.com/cartesiandiver.html (Accessed 2011, February 1).

Making a Cartesian Diver Toy. http://www.chemistar.com/Student/CartesianDivers.pdf (Accessed 2011, February 2).

Physlink. Physics and Astronomy Online. http://www.physlink.com/education/askexperts/ae518.cfm (Accessed 2011, February 3).

Question Hub. Questions and Answers from Around the Web. http://www.questionhub.com/YahooAnswers/20070903122014AA9qQPF (Accessed 2011, February 2).

Science Dictionary. http://www.sciencedictionary.org/ (Accessed 2011, February 2).

Wikipedia. Cartesian Diver. http://en.wikipedia.org/wiki/Cartesian_diver (Accessed 2011, February 2).

Wikipedia. Boyle’s Law. http://en.wikipedia.org/wiki/Boyle%27s_Law (Accessed 2011, February 2).

Wikipedia. Pascal’s Law. http://en.wikipedia.org/wiki/Pascal%27s_law (Accessed 2011, February 2).