"Physics Floats My Boat

Transcription

1 "Physics Floats My Boat A Modeling Approach to Teaching Archimedes Principle & Buoyant Force Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes of Syracuse Introduction Using the activities and methodology listed in this handout, which is influenced by the Arizona State University Modeling Instruction Program in Physics, students will apply their knowledge of forces to determine the concept of a buoyant force, quantify the relationship between the buoyant force and the volume of displaced, and finally arrive at Archimedes' Principle. Students will then apply their newly formulated model of buoyancy to activities, projects, and performance assessment challenges. The entire investigation of buoyancy culminates with a large- scale project called the Cardboard Boat Regatta. In this project, students build cardboard boats to hold themselves and they race their boats in a body of water (pool, pond, or lake.) It is critical to note that the teaching of the buoyancy concept should follow a discussion of forces and a discussion of density. Students should be able to draw force diagrams or identify the forces acting on an object prior to investigating buoyancy, have a familiarity with the difference between mass and weight, as well as understand a relationship between density, mass, and volume. The activities are appropriate for upper elementary grades all the way through high school. Depending on the resources available in your classroom, these activities can be modified to be appropriately high- tech, or they can be done in a low- tech version with most of the listed materials and directions.

2 Differentiation Any of the listed activities, projects, or labs can be adapted for any grade. Explanations can be limited to qualitative analysis or conceptual understanding for lower grades. Calculations can be included and tailored to the level of the learner. Guidelines and expectations can be modified to be appropriate for the level of the learner in activities, projects, or challenges (performance assessments)

3 Application of Force: Buoyancy Foreword: These activities are applications of the force concept. They should be done only after an introduction to forces, force pairs, and normal force is completed. Instructional Goals: Students will Observe when the buoyancy force is equal to the force due to gravity, the object floats Observe when the buoyancy force is less than the force due to gravity, the object sinks Develop a qualitative buoyancy model (relationship between displaced water and loss of weight) Develop a quantitative buoyancy model (Archimedes' Principle). Apply Archimedes' Principle to calculate the weight needed to sink a barge to a predetermined depth. Sequence: Activity 1 - Apparent Loss Lab Worksheet 1 Activity 2: The Boat Lab Extension Activity: Mini- Boat Challenge Performance Assessment Cardboard Boat Regatta Project

4 Activity 1: Apparent Loss Lab Launching Demonstrations QUALITATIVE: Suspend an object from a rubber band. Showing students the stretched rubber band, lead them into a discussion of the tension force on the rubber band as result of the weight of the object. Gradually lower the object onto a table or other surface, illustrating that the stretch in the rubber band changes. Direct the discussion into a focus on the change in the tension of the rubber band and a force that must be in the upward direction on the object. The amount of force provided by the surface in the upward direction on the object can be connected to the loss of stretching in the rubber band. This demonstration allows students to get a sense of "normal force" as well as relate that upward force to a change in the rubber band tension. They should see that the more upward force provided by the surface, the less tension there is in the rubber band; furthermore, the more force provided by the surface, the more decrease in tension. Help students to conclude that the "loss of tension" is equal to the upward force provided by the surface. QUANTITATIVE: Repeat the same demonstration but this time with a spring scale instead of rubber band. This allows students to calculate the amount of force provided by the surface in the upward direction. Have students record the reading on the scale with differing amounts of upward force provided by the surface. That is, as you slowly lower the object onto the surface, pause and record the spring scale reading. By subtracting from the initial reading on the scale (the actual weight of the object) students can find the change in weight, which is equal to the upward force provided by the surface. LIQUID "SURFACE" DEMO: Repeat the same demonstration with an object (a full diet soda can works well) hanging from the rubber band (or a rope/string) for students to see a connection between the loss of stretch in the rubber band and the submerging of the object into water. Ask them to compare and contrast this demonstration with the previous demonstration. Ask them to make observations about the demonstration. They should note that the water level rises and the object submerges by a measurable amount. Ask students what could be done to determine the amount of force provided by the water. Lead students to approach determining the upward force provided by the water as was done for the surface earlier. Students should measure the volume of water displaced by the submerged object and the change in scale reading (apparent loss of weight) to then determine the relationship therein. Students can graph their data to determine a mathematical model to explain the relationship (this depends on the students' level.)

5 Apparatus Ring stand Spring scale or a centigram balance (hanging pan) Water Salt water Spill can Graduated cylinder Kilogram masses Pre- lab Discussion Previously we have seen an apparent loss of weight in the form of a decreased stretch from a rubber band. Remind the students that the stretch in a rope, rubber band or spring scale will result in equal, but opposite forces. A qualitative discussion would lead students to see believe that the liquid, like the surface in prior demo, provides a force on the object to decrease the amount of stretch of the spring scale. In this lab, we will quantify the amount of lift on the object from the liquid. The mass of the volume of water displaced by the submerged object will equal the apparent loss of mass of the submerged object. The density formula, D = m/v, will be utilized to find the mass of the displaced liquid. Apparent Loss Lab: Performance Notes For this lab the following information will need to be collected: Density of each liquid Weight of the object in air Weight of the object in water Difference in these weight measurements Volume of water displaced Find the weight of each object in the air Completely submerge the object into the liquid and find the weight of the object in the liquid. Repeat for each of the liquids. For each object, in each different liquid, find the difference between the weight in the air and the weight in the liquid. Fill a spill can with the liquid. Place a graduated cylinder so that it will collect the "runoff" liquid as the object is slowly placed into the spill can. Calculate the mass of the displaced liquid using the density formula Using the equation from the Comparing Weight and Mass lab, calculate the weight of the displaced liquid. Compare the weight of the displaced liquid to the apparent loss of weight for the submerged object.

6 Post- lab discussion Lead a discussion of this lab to engage the idea that the weight of an object can have an apparent alteration. How does the weight of the displaced liquid compare to the apparent loss of weight of the object? How does the mass of the displaced liquid compare to the apparent loss of mass of the submerged object? How can you justify that the object did not truly lose mass? Archimedes' Principle can be cited as the reason for the apparent loss of weight for the submerged object. The weight of the displaced liquid is equal to the apparent loss of weight of the object. What does the liquid do to cause this apparent loss of weight of the object? How can you explain that the liquid is responsible for the apparent loss of weight? Discuss with the class and lead them to state that the liquid is providing a lift, or push, on the object. This push would be called the Buoyant Force. Continue a discussion to engage the idea and explain that in order for it to be a force, it must have units of force (N) and based on the measured quantities obtained from the experimental relationships derived, an equation can be arrived at as follows: Buoyancy (apparent loss of weight) = Density liquid * Volume liquid displaced * g where g = 9.8m/s 2 ~ 10m/s 2 This should allow students to see that the unit analysis (kg/l x L x m/s 2 = N) and thus the Buoyant Force is indeed a force. Have the students draw force diagrams for each object, both in the air and in the liquids.

7 Application Activity #2: The Boat Lab Apparatus - "Titanic Revisited", Boat Lab Aluminum foil cut into a 30cm x 30cm piece per student Tank of freshwater Washers, slotted masses, coins, or marbles, etc. as payload Pre- lab discussion - Boat Lab We have seen when the weight (force of gravity) is greater than the buoyant force an object will sink. Lead students to use a force diagram to justify this idea. LAB PERFORMANCE NOTES - Boat Lab o Design a boat made of only aluminum foil, which will hold the most weight in a tank of freshwater. o Make diagrams and plans for the boat, which includes dimensions of all sides. o At the moment of the boat launch, place the foil boat into the tank and begin adding payload objects until the boat sinks. o Record observations for how your boat reacted to the increased weight o Dry the payload objects and determine the maximum weight each boat held. Post- lab discussion - Boat Lab Discuss the outcome of the lab. Probe for answers to why some designs worked and some did not. Ask students of both successful and not- so- successful boats to describe their structural techniques in building the boat. Have students refer to the model of Buoyancy found in the Apparent Loss of Weight Lab: Buoyancy (apparent loss of weight) = Density liquid * Volume liquid displaced * g where g = 9.8m/s 2 ~ 10m/s 2 Discuss how the buoyancy of the boat in the water could have been calculated. Compare the amount of weight that the foil boats held in freshwater to the theoretical payload capacity in salt water or alcohol. Review the concept of adding forces that act in the same direction. Discuss how the liquid is pushing up on the boat and the boat itself is being pulled down. As long as the buoyant force is equal to the weight, the boat will remain afloat. Adding the payload to the boat increases the weight and causes the boat to ride lower and displace more water. As more water is displaced, the buoyant force increases. When the weight becomes greater than the buoyant force, the object will sink.

8 Extension Activity - Mini Boat Challenge The Challenge: Students must build a boat made only of aluminum foil (a 30cm x 30 cm piece), 10 Popsicle sticks and Elmer's Glue that will float with at least 500 grams of mass in a tank of water. The minimum mass that the boat must hold is 500 grams, but more mass can be added to find out which boat holds the most mass before sinking. NOTES: 1. The Popsicle sticks will provide more rigidity and strength to the boat. 2. The Elmer's Glue dissolves in water; therefore, students who use too much glue will develop structural flaws as the glue dissolves. 3. A comparison between the boats made only with aluminum foil against boats made of foil with added support could be made. 4. Using this extension activity, students have been able to create boats that have held as much as 2100 grams!

9 Performance Assessment - Make a barge sink to the marked water line Apparatus - Lab Practical 1 metal container (candy tin or tea canister) o Painted a line around it to represent the depth to which you want the barge to sink Tank of water Set of masses (could be miscellaneous objects, e.g., pennies, washers, or lab masses) Pre- lab/performance - Lab Practical Directions Students must add a calculated weight to the barge prior to placing the vessel in the tank. The barge will sink to a certain line that has been painted around the vessel. Students are graded according to the number of attempts it takes to get the barge to sink to the desired water line (e.g., first attempt is a success = A; 2nd attempt = B, etc.) Post- Lab - Lab Practical Students must create a summary of their calculations and method for solving the problem of getting the boat to sink. This can be presented to the class for students to demonstrate their understanding and reasoning; presentation allows the teacher to ask questions of the students to assess their understanding or clear up misconceptions.

10 Culminating Application Project - Cardboard Boat Regatta Goal: To use physics principles to design and build a cardboard boat that can be paddled by two students across the school pool and back. Permitted Materials: Corrugated cardboard Utility knife Straight edge Tape (of any kind) Wood glue Acrylic latex caulk Creasing tool Clamps For more details of the project and resources for holding a cardboard boat regatta at your school, please see the links on the presentation resources page.