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Density ConfusionCan it be cured?

Lynn A. Melton

University of Texas at Dallas

Mini-CAST

January 22, 2011

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One Concept, One Demo,One Lesson!

When you do a density lesson,

what do you want your students to learn?

Note: Presentation and instructions can be found

at http://www.chemchapterzero.com

Concepts Related to Density

• Eureka!

• Properties

• Per

• Algebra and Units

• Buoyancy and Archimedes Principle

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Concepts Related to Density

• Eureka!– Archimedes, King’s gold crown, bath tub,

water sloshes over, runs down the street naked shouting “Eureka”

– Concepts: density and measure volume by displacement

– Nearly impossible to do as a demo (iron crown versus lead crown)

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Concepts Related to Density

• Properties– “I put density at the first of the year because I

want students to learn that stuff has properties.”

• Concept: Density is just a property, just like color, hardness, sheen, taste ….

• Easy and safe to do

• Impact?

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Concepts Related to Density

• Per (slide A)– It’s not the mass and it’s not the volume, it’s

the mass per volume!”– Problem: Kids have a lot of difficult with PER

(mass, volume, density), or (distance, time, speed), or (heat, amount of substance, temperature)

– Concept: something PER something else

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Concepts Related to Density

• Per (slide B)– It’s not the mass and it’s not the volume, it’s

the mass per volume!”– Concept: intensive property (density) versus

extensive properties (mass, volume)

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Concepts Related to Density

• Algebra and Units– “The density equation, density = mass/volume,

is the simplest equation I can find to review or test them over algebra. I use it at the beginning of the course to get them into the swing of the math we will need in the course.

– “…And, this is a good time to start them on using units properly (grams, ml’s, grams/ml).”

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Concepts Related to Density

• Buoyancy and Archimedes Principle– Things sink or float depending on whether they

are more buoyant.– There are lots of neat demos – wood floats, iron

sinks, Cartesian divers are fun!– Concept: We usually explain these demos in

terms of “buoyancy”, “buoyant force” , etc.– Density Confusion: What is “buoyancy”?

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Archimedes Principle

• "Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object." -- Wikipedia

• “If the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink.” -- Wikipedia

• Is there a force called “buoyancy”?

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Archimedes Principleand Buoyancy

• In every sink or float demo, there is no separate physical principle or law called “Archimedes Principle”.

• “Buoyancy” is the balance between two gravitational forces.

• Concept: It’s all GRAVITY! Get rid of the “b” word.

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Archimedes Principle,Buoyancy and Unteach

• Melton tries an “unteach”.

• He is going to try to get you to voluntarily give up the words “buoyancy” and “buoyant force” and switch to words such as “difference of two gravitational forces”.

• This is tough—– wife’s birthday

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Archimedes Principleand Buoyancy

• Melton Demo #1: Drop an object.

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Archimedes Principleand Buoyancy

• Melton Demo # 2: Two weights suspended over a pulley

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Archimedes Principleand Buoyancy

• Melton Demo #3: Put water in a plastic cylinder, then put a reasonably close fitting dowel in the water. Dowel goes down and water goes up.

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Lower an Object into a Liquid

Object goes down and liquid goes up

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Sink or Float?Gravitational Potential Energy

• I can do the argument in terms of balancing forces, but it is much easier to use the gravitational potential energy.

• You probably will not use this material directly with your (middle school) students, but it will inform your thoughts and your answers.

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Sink or Float?Gravitational Potential Energy

• PE = mgh– m is mass– g is the “acceleration of gravity”– h is the height

• Drop an object!– The object experiences a force that acts to

reduce its gravitational potential energy.

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Sink or Float?Gravitational Potential Energy (GPE)

• GPE = mgh

• Students probably need help understanding what this equation means.– More mass results in greater GPE– The same mass moved higher results in greater

GPE

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Sink or Float?Gravitational Potential Energy (GPE)

• GPE = mgh

• With the string over a pulley, one object moves up ∆h and one object moves down ∆h.

• ∆GPE = [m1g∆h] + [m2g(-∆h)]

= [m1 – m2]g ∆h

If m2 > m1, ∆GPE < 0, and m2 goes down.

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Archimedes Principleand Buoyancy

• Melton Demo #4: Rearrange a stack of disks, and determine whether the gravitational potential energy goes up or down.

Sink or Float?Gravitational Potential Energy

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Suppose that we place a stack of disks in a glass of water.

Sink or float?

Which glass has the least gravitational potential energy?

start end

Sink or Float?Gravitational Potential Energy

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Suppose that we place a stack of disks in a glass of water.

Sink or float? Blue disk went up and tan disk went down.

Which glass has the least gravitational potential energy?

start end

Sink or Float?Gravitational Potential Energy

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∆GPE = m(blue)g(∆h) + m(tan)g(-∆h) = [m(blue) – m(tan)] g∆h

If m(tan) > m(blue)], ∆GPE < 0, and tan sinks.

If m(tan) < m(blue), ∆GPE > 0, and tan does not sink. It floats.

∆h

start end

Sink or Float?Gravitational Potential Energy

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The tan and blue disks have the same volume, since water is incompressible. “Lighter with the same volume” is the same as “less dense”. “Heavier with the same volume” is the same as “denser”.

Note: We have introduced “density” AFTER the gravitational potential energy concept has been introduced.

∆h

Sink or Float?Gravitational Potential Energy

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We just used an argument based on gravity to reason that objects whose density is less that the density or water will float [and objects whose density is greater than the density of water will sink.]

Can we leave “buoyancy” behind and teach with gravity?

∆h

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Vocabulary

• density (mass/volume)

• specific gravity = density of material/density of water (no units)

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Useful Links(must be in Slide Show mode)

• Specific Gravity of wood

• Specific Gravity of materials

• How submarines work (has nice interactive figure)

• Submarine simulator

Submarine Demo

• Use a submarine demo to drive home to students that changing the amount of air in the support shell (and therefore driving water out of the support shell) can change the mass of the submarine so that the mass of the submarine is less than the mass of the water displaced.

• Everything is visible in this demo.01-22-2011 29

Cartesian Divers

• Write a paragraph to explain why Lynn Melton rants about the popularity of Cartesian diver demos?– Hint: The cause of the effect is not visible.

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Does anybody care about density?

Fig. D.1 – Rising current separator for the separation of lead and plastics from car batteries. Here the plastics float out to a dewatering screen.

www.femp.org/info/Recycling/7_DensitySeparation/Density%20separation.doc

Take Home Concept

• If you are a density confuser, you don’t understand the gravity of the situation.

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