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Multiple Representations of Buoyancy

Meredith Weglarz, Jessica Oliveira, James Vesenka University of New England, Department of Chemistry and Physics

Abstract: A modeling lab exercise, based on multiple, quantitative, identical representations of buoyancy, has been developed and deployed in an introductory general physics laboratory for life science majors. The development of this activity is multifold.

• To provide life science majors with practical quantitative representational tools. • To provide fluids physics concepts in biologically-rich contexts. • To develop authentic assessments based on student preconceptions on fluids.

We describe the laboratory and preliminary assessment results designed in light of multiple representations (graphs, math models, diagrams, and verbal). The second generation of assessment is based on student explanations to a simple buoyancy problem. The student-generated responses have revised the assessment, several more iterations are in process. Introduction: The term "neutral buoyancy" can be used to describe the innate ability of all forms of marine life to compensate the buoyant force in aqueous environments as the move parallel to earth's gravitational field. Each species has their own unique mechanism for compensation, usually involving a swim bladder or oil filled liver. Some species can vent their swim bladder directly through the mouth, like humans breathing out in pool water to sink to the bottom (ref). Others (scientific name) vent through their blood system (ref), and still others (elastmobrachs? Sharks, skates, etc) balance the buoyant force of water using their oil filled liver (ref.). Nature examples of neutral buoyancy in air is less common and general limited to objects of much smaller size in which other forms of fluid interactions typically play more dominant roles (ref.). Historically Archimedes has been credited with developing the accepted conceptual quantitative formulism describing the buoyant force as equal to the weight of fluid displaced by an object (ref). Mathematically this relationship has been described as:

Fb = ρfluidgVobject

Where ρfluid is the density of the fluid medium, g is the gravitational field, and Vobject is the volume of fluid displaced by the object. Though simple and elegant this concept appears to be very challenging for students to apply because a variety of preconceptions. One preconception is based on conceptual misunderstandings of ρfluid (ref). Another of these preconceptions is that objects that sink do not experience a buoyant force (ref.). Even when objects float the particle model frameworks that could be applied to effectively predict buoyancy responses may be lacking (ref?). A case in point tying the latter two preconceptions together is to have student predict the force of air on an object (like a can) hanging from a string. The two most common responses by students are that the air either pushes down, or from all directions, on the object. Yet when asked what the sum force of water will be on the object students will choose "up" as the preferred (and correct) universal answer. The importance of providing student with an adequate framework for making sound predictions on physical principles has been under scrutiny. The Howard Hughes Medical Institutes

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recommendations for the next generation of health science workers recommends integrated physical science skills. For example, tying together the biological importance described in the first paragraph with the physical science description of the second paragraph. Our general physics sequence almost exclusively trains health science majors. In the laboratory sequence described below, based on modeling instruction (ref.) we systematically develop a multiple representational approach to buoyancy. This approach is supplemented with a multiple particle framework that provides students with conceptual foundation centered around a more rich understanding of what "density" of the fluid means and the importance of the gravitational field in driving. The biological importance of the concept is then tested out on a quantitative problem based on the classic Cartesian Diver experiment. The quantitative portion involves careful measurement of the air bubble inside a volumetric syringe (the "swim" bladder). A student generated assessment on buoyancy has been constructed through oral and written responses to a free response activity involving the following set up: A bucket of water and a plastic toy "kickball". Students are given two sets of questions to answer after being requested simply to submerge the ball in the water and describe what they feel and see.

Part 1: Take the object (an air filled plastic ball) and immerse it completely in the liquid (water) WITHOUT letting it "sink or swim". What do you observe happening? How would you explain your observations to a friend? How would you explain your observations to a First Grader? How would you explain your observations to a physics teacher?

After completing this task the students are then asked to turn the paper over and answer the following questions.

Part 2: Rank below how you believe you learn physics best? ___ Diagrams ___ Written or verbal explanations ___ Mathematical equations ___ Graphs Give an example of one of each for the problem you examine above (previous page).

The activity and problems are designed so that students are not biased in their responses by anything the facilitator says or the questions infer. The student responses are video taped and have been analyzed to extract common preconceptions about buoyancy in this context. One of the interesting findings is that each context appears to be different. The results of these interviews are currently being analyzed.

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+0.041 N FT

Fg

Appendix: Buoyancy Lab Timeline: First semester second lab, introduction to fluids Objective: To provide graphical, mathematical, diagrammatic, and written representation for the forces on an object immersed in a fluid. Materials: Force sensor, cylinders (or cubes) of different materials but identical sizes (hereafter identified as "dowels"), different fluids in beakers (e.g. water in beaker, oil in another beaker). Teacher notes: Please avoid "leading your witnesses". In particular do not use the following terms in the initial observation of activity until the students have mentioned them and as a class have decided on a reasonable operational definition: Term General definition Lab specific definition Symbolic definition

w/units "density" "stuff"/"space" mass density = mass/volume ρ=m/V

(kg/m3) "buoyancy" upward force due

to displaced fluid DO NOT DISCUSS MATH MODEL UNTIL END OF LAB DURING CONSENSUS

Fb = ρfluidgV (N)

"pressure" force/area P=F/A (N/m2 = pascals)

Other terms at discretion of instructor Observation: Ask students to observe a force measurement from a wooden dowel attached to a thin rigid plastic rod (weight of rod zeroed out in force measurement prior to mass attachment). Set sensor such that positive weight is recorded (up is positive) (figure 1).

Figure 1 Figure 2

Whiteboard prediction: Ask students what they predict will happen to the force measurement when the dowel is immersed in a fluid such as water. Discussion: Have students defend predictions made on whiteboard using any representation of their choice (force diagram, graph, math, written). Discuss operational definitions as needed.

Fg

-0.039 N

FT

Fb

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Observation: Dowel is immersed in fluid (Figure 2). Buoyancy force included for instructor's reference only. "Observables" "Measureables" Force is negative Weight = Fg = mg Dowel is immersed in liquid Tension = FT from sensor Does not appear to be "floating"? Density of fluid "ρ" Dowel is being pushed into liquid? Volume of dowel "V" Dowel is yellow, rough, many other non-useful attributes Other Winnow down "measureables" to independent (weight) and dependent (tension) variables. Since the focus of this lab is to develop a definition of buoyancy choose the volume of the dowels and density of the fluid to be constants. Problem statement: How does tension of the dowel immersed in the same fluid depend on the weight of the dowel in air. Prediction: Have students make a graphical prediction of tension versus weight on their whiteboard BEFORE starting any data collection. Example Results: Graphical

Figure 3 Mathematical: ΣF=Fb+Fg+FT=0 Equation 1 FT=-Fg-Fb Equation 2 FT = Fg - Fb Equation 3 Slope = 1 Equation 4 Intercept = -Fb Equation 5 "Sharp" students should be asked to compare their intercept result with the product of the fluid's density they used, the volume of the dowel and earth's gravitational field "g". Fb = ρgV= 0.062N

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Diagrammatic:

Figure 4 Instructor notes: N.B. Buoyant force is constant for same size dowel. Verbal: Have students defend their graphical, mathematical and diagrammatic data. Consensus: The intercept of weight versus tension represent a buoyant force on the dowels within the constraint of identical volumes and the same liquid. This buoyant force is fluid dependent (i.e. depends on the fluid density), the volume of the dowel (can be tested with different dowels) and the gravitational field the fluid and dowels are experiencing: Fb = ρgV Deployment: Students are to determine the volume of a Cartesian Diver at neutral buoyancy. Start by applying pressure on the capped bottle with Cartesian Diver inside. Discuss what happens at the instant the diver is not longer sinking or floating upwards (definition of neutral buoyancy). Video below:

Figure 5 1. Measure weight of empty, dry diver on a scale. Remind students about units and

calculation of weight only IF they first err. 2. Measure volume of trapped air inside a 1ml syringe at "neutral buoyancy". Remind

students about conversion to appropriate only IF they first err. 3. Using Fg = Fb = ρg(Vdiver+Vair), have students solve for volume of diver.

Fg FT

Fb

Fg

FT Fb ρfluid>ρdowel ρdowel>ρfluid