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**Grades:** 5-8

**Author:** Joyce Brumberger

**Source:** "Sink and Spill", Prentice Hall Physical Science Explorer. Prentice Hall, Inc., New Jersey.2001. pp.360-361.

Through design and implementation of their own experiments about Archimedes' Principle, students will learn the effects of the force of buoyancy, and the role density plays in the sinking and float of objects.

**What should students know as a result of this lesson?**

- definition of buoyancy force, displacement, and density
- effects of buoyancy
- understand Archimedes' Principle

**What should the students be able to do as a result of this lesson?**

- explain the effects of density on buoyancy
- design and implement their own experiment
- develop a design for a boat that will hold a cargo
- analyze data and draw conclusions from that data

__Engagement:__

- 1 can Diet Coke
- 1 can Regular Coke
- Large glass container (small fish tank is excellent)
- Water supply

__Exploration:__

- Balance scale
- Water supply
- Paper towels
- Pennies

__For Each Group:__

- 1 250 mL beaker
- 1 small, flat plastic container
- 1 clear film canister with lid
- 1 25 mL graduated cylinder

__Elaboration:__

- Pictures/illustrations of various boat designs
- Modeling clay for each group - quantity is dependent on size of plastic container.

**Engagement**

- Show students a can of diet Coke and a can of regular Coke. Ask them the volume of product in each can. Both are 12 ounces
- Place the diet Coke in a large container half filled with water. (A small fish tank works very well for all to see easily.) The can will float.
- Place the regular Coke in the container of water. The can will sink.
- Ask students to draw their observations and then offer explanations as to why the cans behaved the way they did.

*Assessment:* Assessment is on going as students record observations and ideas as well as respond orally during the Engagement phase.

**Exploration**

Divide the students into groups of an appropriate size so that everyone can comfortably contribute.

PART I - Calibrating the volume of a film canister

- Have students fill the film canister with water. The water should then be poured into a graduated cylinder and measured. Note the volume.
- Have students fill the canister with half the volume of water from the graduated cylinder and mark the water level using a permanent marker and label quantity.
- Instruct students to pour varying amounts of water from the graduated cylinder into the film canister so that they continue to make as many volume marks as possible and still clearly be able to read them
- Tell students to dry the interior of the film canister and put on the lid.

PART 2 - Determining the mass of 1 mL of water

- Tell students to find the mass of a dry 250 mL beaker using the balance scale and record.
- Using a graduated cylinder, instruct students to add water to the 10 mL mark and pour the water into the beaker.
- Tell students to find the mass of the 10 mL of water by subtracting the mass of the beaker from the mass of the beaker with water.
- Tell them to calculate the mass of 1 mL of water by dividing their answer above by 10. Record findings.

PART 3 - Observing displacement

- Instruct students to fill the 250 mL beaker 3/4 of the way with water.
- Instruct one participant to put his or her index finger completely into the water and note what happens to the level of the water. Everyone should record and attempt to explain their observations.

PART 4 - Measuring volume displacement and weight

- Have students find the mass of a small, flat plastic container. Multiply the mass by 0.01 to determine the weight of the container in Newtons (N).
- Have students measure the mass of a film canister with the lid on and multiply by 0.01 to determine its weight in Newtons. Instruct them to record their findings on their data table.
- Instruct students to place the 250 mL beaker into the plastic container and fill the beaker to the very top with water without overflowing. If overflow should occur, wipe the plastic container until it is dry.
- Instruct them to place the canister into the beaker of water and illustrate their observations being sure to properly label.
- Using the pennies provided, instruct students to take out the film canister, dry it, and add one penny. Measure the mass of the capped container with the penny, multiply by 0.01 and record.
- Once again, instruct students to place the canister back into the beaker of water insuring that beaker is filled to the very top.
- Tell students to estimate the volume of the canister that is submerged in the water by looking at the markings and record.
- Tell students to remove the canister from the water and take the beaker out of the plastic container.
- Instruct students to find the weight of the overflow water by finding the mass of the plastic container and water and subtracting the mass of the plastic container. Multiply the difference by 0.01 and record findings.
- Ask students to record the buoyant force. The buoyant force is equal to the weight of the water the canister displaces.
- To compare results, tell students to pour the water from the container into the graduated cylinder and record the measurement of the water level.
- Ask students to predict the weight at which they think the canister will sink. Instruct students to repeat the process with varying amounts of pennies to determine the tipping point at which the container sinks.
- Instruct students to calculate the density of the film canister at the point of sinking reminding them the density is determined by dividing the mass by the volume. The units of density are g/mL.

*Assessment:* The professional development provider can assess students understanding through oral explanations and written observations and drawings.

**Explanation**

**What is the mass of 1 mL water?**

Students should have found that the mass was 1.0 g. There is likely to be some experimental error, but answers should be close to 1.0 g. This is important later when the mass of objects are determined based on the volume of water they displaced.

**What is the difference between mass and weight?**

Mass is the amount of matter a substance contains and is measured using a balance scale. Weight is a measure of the force of gravity and is measured using a spring scale. If the force of gravity changes, weight changes, but the mass remains constant. In this exercise, the weight of an object was calculated by multiplying the mass of the object by 0.01. The unit for weight is Newtons.

**What did you observe when you submerged your index finger in the water?**

The level of the water rose. This is a visual example of water displacement. At this point the discussion of the term displacement is appropriate. Displacement means that a substance was in one place but has moved to another - "dis - placed". All matter takes up space; consequently two things can't be in the same place at the same time. When an object is placed in water, it causes the water to move out of the way. The measure of the change in water from its original point to its new position is referred to as "displacement".

**What happens to the film canister as pennies are added?**

The film canister initially floats high in the water, but as pennies are added, it floats lower. It is important here to recognize that the volume of the canister did not change, but the mass did.

**What is the relationship of the weight of the water displaced to the buoyant force?**

The weight of the water displaced is equal to the buoyant force. The buoyant force is the difference in the pressure on top of the object, which is pushing it down, compared to the bottom of the object where the pressure from the water is pushing it up. When the finger was submerged in the water, it was visible to see that the water level went up, not down. As the weight of the canister increases, more of the volume of the container becomes submerged and more water is displaced. The markings on the container help the students to better estimate the volume of the canister submerged though there is still inherent error in the accuracy of the markings and the ability to read them. When the weight of an object is greater than the weight of the displaced water, the object sinks.

**What is the density of the canister at the point at which it sank?**

Density is the relationship of mass to volume. D = m/v

**Compare the density of the canister when it sank to the density of water, which is 1.0 g/mL.**

It should be noted that the density of the canister was greater than the density of water. This is also the reason the canister sank.

**If the density of another fluid was 2.0 g/mL, would the canister float or sink?**

The canister would float, as long as the calculated density was less than 2.0 g/mL

**Read the story of Archimedes and his discovery to students.**

*Assessment:* students' responses to key concepts.

**Elaboration**

- Show pictures of various types of boats - sailboats, barges, fishing boats, recreational boats, etc. and ask students to discuss the similarities and differences of the boats.
- Tell them that a block of steel sinks, yet ships made of steel float.
- Tell students that they are to create a "ship" using modeling clay so that it is capable of carrying the greatest amount of cargo (pennies) without sinking.
- Divide students into groups of appropriate size so that every member can contribute.
- Tell each group that you will be providing them with a specified mass of modeling clay from which they will design a boat hull for carrying a maximum load. Allow students to brainstorm together to develop two different hulls for testing.
- Before testing, tell students to provide explanations for the choices of their hulls and to hypothesize which of the two designs will hold the greatest cargo. Accept all reasonable explanations. Tell them to illustrate their hull designs.
- Instruct students to create a data table to record testing results and then allow them to test their crafts using the plastic container filled with water and pennies for the cargo.
- Ask groups to come together and report their findings.

Minimal math skills multiplication and division

Use of a calculator

- Learning Cycle
- Science Process Skills
- Inquiry

**NGSS Standards:**

- MS-PS1-3 Gather and make sense of information to describe that synthetic materials come from natural resources and impact society.
- MS-PS3-1 Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.

**Common Core Standards:**

- RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.
- RST.6-8.3 Follow preciesly a multistep procedure when carrying our experiments, taking measurements, or performing technical tasks.
- WHST.6-8.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes.

**National Standards:**

- Content Standard A: 5-8 Science as Inquiry
- Content Standard B: 5-8 Physical Science
- Content Standard G: 5-8 History and Nature of Science

**Ohio Standards:**

- Grades 6-8 Physical Science Benchmark D
- Grades 6-8 Scientific Ways of Knowing Benchmark A, B, and C
- Grades 6-8 Scientific Inquiry Benchmark A and B

It is a common experience that an object in water appears lighter than an object in air. In air, objects are affected by the force of gravity, but in water the object is affected by two forces: the force of gravity pulling it down and the buoyant force of water that pushes it upward. This upward force is a result of the *difference* in pressure exuded by the surrounding water between the top of the object and the bottom of the object. If the force is greater at the bottom, the object will float. If the force is greater at the top, the object will sink. Archimedes' Principle states that the volume of water displaced by an object is equal to the volume of the object submerged in the water. Different materials displace different amounts of water, which is why Archimedes was able to prove that the gold crown was not made of pure gold. Shapes of objects can influence the ability of an object to displace water. Boats are designed for various purposes, but displacement of water is critical to their ability to stay afloat. The mass of steel used to build a cruise ship would sink if it where a large block. By creating a shape that will allow for a large displacement of water to support the mass, a steel ship can float. (All ships must also have a sufficient amount of hollow area in the submerged portion of the structure for air. Remember, density is the relationship of mass to volume!)

References include:

- "Sink and Spill", Prentice Hall Physical Science Explorer. Prentice Hall, Inc., New Jersey.2001. pp.360-361.
- http://theory.uwinnipeg.ca/mod_tech/node67.html
- http://physics.weber.edu/carroll/Archimedes/principle.htm
- http://www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/PressureFluids/ArchimedesPrincipleMain.html
- http://www.cut-the-knot.org/pythagoras/bath.shtml
- http://www.crsep.org/PerplexingPairs/Jan.%2022.2003_Archimedes.pdf
- http://www.sciam.com/article.cfm?articleID=5F1935E9-E7F2-99DF-3F1D1235AF1D2CD1
- http://www.teachersdomain.org/sci/phys/matter/sink/index.html
- http://scifun.chem.wisc.edu/HomeExpts/cans.htm
- http://www.springboardmagazine.com/science/archimedes.htm

N/A

Floating and sinking are common experiences among children and adults, yet the concept of why an object floats or sinks is often misunderstood. Much of this results from an incorrect use or a lack of vocabulary. There is power in words and proper language helps communication. Through guided exploration and development of vocabulary, individuals can build a knowledge base. With this knowledge base, they can cooperatively work and effectively communicate with one another to develop solutions to new, related problems.

Ongoing throughout learning cycle.

**Grouping Suggestions:** Try to insure that all students have participated and expressed their ideas either verbally or through written comments. When working in pairs or groups try to make the groups as heterogeneous as possible being sensitive to specific needs of individuals.

**Pacing/Suggested Time:** Engagement - 5 minutes; Exploration - 40 minute session; Elaboration - 30 minute session; Explanation - 40 minute session