Buoyancy Background - University of Chicagoastro.uchicago.edu/~randy/YSI06_pdfs/ysi06.merged.fin… · · 2006-08-012006 Yerkes Summer Institute Buoyancy Background 1 Source: Buoyancy

2006 Yerkes Summer Institute Buoyancy Background 1

Source: www.geog.ucsb.edu

Buoyancy Background

Understanding buoyancy may sound pretty simple. You throw a stone in a pond, it

sinks. You throw a feather in a pond, it floats. But as we look closer and ask more

questions, buoyancy gets more complicated. Metal coins sink in water, so how can a metal

boat float? Does floating only apply to water, or can things float in other liquids, or even

air? Can something float or sink in outer space, where there is no clear up or down?

This summer we'll try to answer these questions. The practical

applications of this summer’s labs will range from

transportation to recycling to cooking to weather to how the sun shines. In

each lab you'll watch things rise and fall, and in every lab you’ll hear some of

the same words and concepts, such as density and pressure, used to explain

buoyancy. Although at first density and pressure may seem unrelated to

floating, whether something floats or sinks and how the motion takes place

actually depends entirely on these properties.

All of the labs this summer will deal with liquids or gases, and you'll likely hear

something about the substance’s “pressure.” Pressure is the amount of push

something exerts on every piece of surface it touches, or force per area. When we

talk about the pressure of a liquid or gas, it is useful to think of how much force that

substance would be putting on a flat surface, like a piece of paper or the side of a box.

However, there is pressure in the liquid or gas whether or not there is a solid surface to

push on! The pressure still exists because the particles that make up the gas or liquid are

moving around, bouncing off of and pushing on the other particles in the substance.

Keep in mind that there's a difference between the “random motion” of particles bouncing around in a

fluid, which happens in every direction with no preference for going one particular way, and “bulk

motion,” where the gas or liquid all moves together. Pressure is caused by random motion. Pressure,

in turn, causes bulk motion. One region might have a higher pressure than another, and the stuff in

between the higher and lower pressure spots will be pushed, as a whole, toward the lower pressure

area. When a weather report shows a high pressure center and a low pressure center, you can know

which way the wind must be blowing: the air must be pushed from the higher pressure toward the

lower.

You can think of random motion and bulk motion like people in a big

crowd at a party. The people will all be moving about, bumping into

different people. The more people in the room or the faster the

people are moving, the more you'll feel pushed about. That's random

motion. If a door opens and lets the party expand into another room

as well, what will happen? A lot of people will move together into

the new empty space where they can have a bit more elbow room.

That's bulk motion. Once enough people have moved into the new

room, the crowd won't move all together any more and will just go

back to milling about, with the occasional person moving from one room to the other. Equilibrium has

been reached, and the people's motion is once again all random motion.

Source: utahresort.com

Source: bowen2.com

2006 Yerkes Summer Institute Buoyancy Background 2

Source: poliforma.org

Density is also an important concept with which to be familiar. Basically, density is “how much stuff

per unit volume.” With pressure we talked about area, where each piece of surface had a force on it,

but with density we're talking about volume, which means a three-dimensional space. Most

commonly, especially in this Institute, we'll use density to mean mass density,

or how much mass per unit volume. (You could also use density to mean the

number density of something, or how many items there are in a unit of

volume. Or, you could talk about charge density, or the amount of electric

charge per unit volume. But here we’ll be dealing with mass density.)

Although the density of something is related to its mass, density and mass are

not the same thing. A bigger object might not have a larger density than a

smaller one. For example, a jumbo-sized marshmallow and a mini

marshmallow have the same density, but the larger one has more mass because

it has a bigger volume. As another example, consider a marshmallow and a

peppermint hard candy: the marshmallow is bigger than the hard candy, but the

marshmallow has a lower density than the candy, even though it is bigger.

Recall the party example we talked about for pressure. The number density in that case would be the

number of people per cubic foot of the volume of the room. If more people come to the party, the

density goes up because there are more people, but the same volume available to hold them. When the

second room opens, even with the same number of people at the party, the density has gone down

because the same number of people spread out more into the bigger total volume.

The reason we deal with these more complicated quantities of density and pressure, rather than just the

more familiar ideas of force and mass, is because when we deal with fluids, as we will for much of this

Institute, the total amount of force or mass can be difficult to measure. It’s hard to measure the total

mass of the air in the atmosphere because there's so much of it, and you can never “get a hold” of all of

that air. But you can more easily measure the air pressure or capture a small volume of air and

measure its mass, and from that you that you know the density and pressure of all the air.

Understanding buoyancy – why things sink or float – is a very important part of understanding the

flow of air and water in general. As you can probably imagine, such fluid flow is important for all sorts

of engineering applications. What you will learn over the next week is key if

you want to figure out how best to build a heating or air conditioning system

for a building or supply running water to a city. It

explains why fish can survive the winter in a

frozen-over pond, and how submarines can control

how deep they go. It also explains why clouds

form where they do in the atmosphere, and how we

can learn about weather on distant other planets

without actually going there ourselves. So enjoy,

and with any luck this week you may take quite a

ride... literally.

Source: ooer.com

Source: pfa.org

Density =

2 lb/ft3

2006 Yerkes Summer Institute Does It Float? 3

A

A A

(Robert Friedman & Sarah Hansen)

INTRODUCTION

We all know what floating is; floating is the opposite of sinking, it is the rising of one

object or substance inside another. If you float to the top of some substance, you can

rest right on the surface, like a boat on water.

But why do things float? As you will learn in other labs this week, floating depends

on the balance of upward-pushing forces (e.g. buoyant force) and downward

pushing forces (e.g. force of gravity). But it really all comes down to something simple: density. The

relative density of two things tells you which one can float on the other. It doesn’t matter in which

states the substances exist (i.e. solid, liquid or gas), or how much of them there is; it only matters what

the density is.

Let’s say we want to know if a particular solid A will float, sink, or hang perfectly in the middle of a

particular fluid B. There are three options:

� If A is more dense than B, then A will sink in B.

� If A is less dense than B, then A will float on B.

� If A and B are the same density, then A will be suspended

in B, neither floating nor sinking (this behavior is often

called being “neutrally buoyant”).

When you float in the pool or in the lake, you float because you are less

dense than the water. Maybe you have to hold your breath to help you float

– that’s because holding that air in your lungs makes you on average less

dense than when you aren’t holding your breath. A submarine takes

advantage of this technique to float or sink by taking in or letting out air as

need to adjust its average density to the right level.

In this lab, we’ll demonstrate the principle that density governs

buoyancy. We will measure the density of several different liquids and

show that with just this information we can predict in what order the

different substances can be floated on top of each other.

We can also take advantage of the density-buoyancy relationship to

measure density by turning it around: we can use knowledge about what

Source: www.fas.org

Source: planetlava.com


PRECISE PRECISE PRECISE PRECISE vs.vs.vs.vs. ACCURATE ACCURATE ACCURATE ACCURATE

Aren't they the same thing? Well, no. There is a substantial (and important) difference between precision and accuracy.

Accuracy Accuracy Accuracy Accuracy is how close something comes to an accepted standard. Precision Precision Precision Precision means how fine the divisions or segments are and how repeatable the results are. Here is an example.

Suppose you have a heater that controls the temperature of water in a tray. Suppose also that this heater has markings on it so that you can set the temperature you desire. You set the temperature for 75 degrees F and let the temperature stabilize. You measure the temperature of the water with a good thermometer and find that it is actually exactly 78 degrees. Your heater isn't very accurate.

Now suppose you leave it at the 75 degree setting and turn it off. The next day you turn it on again and let the temperature stabilize. Measuring the water temperature again you find it is 78 degrees. You repeat this process a few times per day over a few days and find that at the 75 degree setting it always heats the water to exactly 78 degrees. Your heater is very precise.

Inaccurate & imprecise Precise but inaccurate Accurate but imprecise Accurate & precise

substances can float on to estimate their densities. For example, simply by knowing that oil floats on

water, you can say that oil must be less dense than water. If there was another liquid in which oil

would sink then you could also say that the density of oil must be greater than the other liquid. Thus,

you could determine limits on the possible density of oil; less than water, greater than whatever else.

So why care? Well, this idea – that we can learn something about properties of

different substances simply by observing their behavior in relationship to each

other – is a key technique used in science every day. Astrophysicists who

study other planets try to figure out what chemicals are present on those other

worlds (especially important if you want to know if there is life on other

planets!). One way that this research can be done is by observing what the

properties (including density) of visible substances are. Finding a way to do

such investigation without having a sample of the substance is crucial, as we

do not have very many opportunities for travel to other planets!

Understanding the relationship between density and buoyancy and finding different

techniques for measuring density also has important Earth-bound applications. For

example, how do you think that different materials are separated for recycling once they

are collected? Most commonly, recycling plants separate different kinds of materials by

taking advantage of their different buoyancies in different liquids. By using the same

techniques that we will use in this lab, it is possible to reprocess used material into new

Saturn, from nasa.gov

Source: www.npl.co.uk


products rather than letting it go to waste.

Another theme of this lab will be the importance of quantifying

how well you know something. We always want to make

measurements that are both precise and accurate (see sidebar),

but it is important to be able to say how well we’ve succeeded.

Scientists express their confidence in their results by always

including an estimate of their uncertainty on all data. On a plot,

the error estimate is shown by always putting “error bars” on

every plotted data point. In a data table, the uncertainty is stated

by writing the data in the format of “answer +/- uncertainty” so

that someone can immediately see how good the results are. If

someone tells you the results of an experiment but does not tell

you the uncertainty, they’ve only given you half of an answer –

don’t be satisfied! Error bars tell you how confident you can be

that the result is a good one, and are just as important as the

answer itself.

CHALLENGE I:

STACKING LIQUIDS Your goal for this part of the lab is to make a tower of different

liquids stacked on top of each other. There is one particular

property of the liquids that will determine which will float on top

of the other – the density. You and your partner will be

responsible for accurately measuring the density of one of the

liquids, and then working with the whole group’s data, you will

predict the order in which to layer the liquids so that they will

remain buoyant and not mix. Finally, you will test this prediction

by seeing if you can get the liquids to stack up. It is very

important that your density measurement be as accurate as

possible since everyone will be using your measurement for their

predictions.

PART 1: PLANNING

In order to measure the density of your test liquid accurately and

precisely, you need to make several separate measurements of its

density and then average those

measurements to get a final answer. To

make these measurements you will use

a graduated cylinder and a scale.

Talk with your partner about how you

think the best way to make these

measurements will be. [Hint: what two

Errors vs. Errors vs. Errors vs. Errors vs. MistakesMistakesMistakesMistakes

Aren't they the same thing? Well, no. There is a substantial (and important) difference between errors and mistakes. Well at least in Science, maybe not in baseball.

ErrorsErrorsErrorsErrors are fundamental limits on how precise or accurate your measurement technique is. MistakesMistakesMistakesMistakes are sloppy or unintentional actions.

As an example, imagine measuring the temperature of a liquid again. If you didn’t put the thermometer all the way into the liquid, or the wrong end of it in, that would be a mistake. You weren’t properly using the thermometer. In this case you might measure the cold water at 65 degrees.

On the other hand, if the thermometer only had ticks every 10 degrees, it would be hard to measure the temperature any better than in steps of about 10, you’d only be able to measure 70 or 80 degrees. If the temperature was in between 70 or 80, it would be hard to tell where in between. So, you might say the temperature of the liquid was 75 degrees and the error on your temperature measurement was something like +/- 5deg .


Record Record Record Record your ideas!your ideas!your ideas!your ideas!

Record Record Record Record your your your your datadatadatadata!!!!

Record your Record your Record your Record your calculatiocalculatiocalculatiocalculationsnsnsns!!!!

EQUATION INFOEQUATION INFOEQUATION INFOEQUATION INFO

Density is the ratio of Density is the ratio of Density is the ratio of Density is the ratio of mass to volume of amass to volume of amass to volume of amass to volume of a substance. That is,substance. That is,substance. That is,substance. That is,

MASSMASSMASSMASS VOLUMEVOLUMEVOLUMEVOLUME

DENSITYDENSITYDENSITYDENSITY ====

quantities do you need to determine in order to calculate the density?]

As you discuss, consider the following questions:

? How many sets of measurements do you need to make to get a good average?

? What problems could arise?

? What could make the measurements difficult to make accurately?

? What errors will you have to watch out for?

In your lab notebook, write down:

• what liquid you are testing

• what your procedure will be to determine the density of your test liquid, including what

quantities you will measure, how many sets of measurements you will make, and exactly

what you will do to make the measurement

• at least five possible sources of difficulty in making the measurement accurate or precise

• what you will do to minimize the error due to each difficulty you mentioned above

As a group, we will discuss the procedures that each pair came up with. Maybe you will get some ideas

from that discussion about how you could refine your procedure to get the best results. In your lab

notebook, make any adjustments to your procedure that you feel will be necessary.

PART 2: TAKING DATA

Review your final lab procedure with one of the lab instructors,

and then go for it – put your technique into action!

In your lab notebook, make a data table and fill it in with all the

measurements that you take. For each measurement, make sure

to include an estimate of how well you think you make made it –

that is, include an estimate of your uncertainty – both in units and fractional – for

every measurement. (See Reporting Errors on the next page.)

In your lab notebook, write down

the equation that you will use to

determine the density of the test

liquid. For each set of

measurements, use that equation to

calculate the density, and record the result. For each set of

measurements, use your recorded error estimates and the density

equation to determine how much uncertainty there is on each

measurement of density.

(outreach.rice.edu)


Plot Plot Plot Plot your your your your

resultsresultsresultsresults!!!!

REPORTINGREPORTINGREPORTINGREPORTING ERRORS ERRORS ERRORS ERRORS You can report your error in two wayYou can report your error in two wayYou can report your error in two wayYou can report your error in two wayssss

UNIT – give errors in actual units

EXAMPLE:

MASS = 2g ±±±± 0.2g

VOLUME = 40mL ±±±± 2mL

FRACTIONAL – give errors as percentage

EXAMPLE:

MASS = 2g ±±±± (0.2g/2g * 100)%

= 2g ±±±± 10%

if there is 0% error, then you are 100% sure!

Fractional errors are great to work with because they are easy to pass on. To find the fractional

error for the density, you can just add the fractional errors for the mass and volume

measurements together to get a total error … nice and easy.

DENSITY =

EXAMPLE:

DENSITY = = ± (10 % + 5%) = 5 g/mL ± 15%

MASS

VOLUME ± SUM of FRACTIONAL ERRORS

40mL ± 5%

2g ± 10% 2g

40mL

PART 3: ANALYZE YOUR DATA

In your lab notebook, make both of the following plots:

(Make sure to clearly label the title, axes and units in your plots and

use a full sheet of paper for EACH graph!)

Mass vs. Volume Plot: Density Revealed

• Y-axis: put mass

• X-axis: put volume

• For each set of measurements, mark a point for the volume and the mass. Include error bars!

The mass bars should be vertical, the volume error bars horizontal. (Note: error bars for plots

are drawn with units not fractional errors.)

Density Plot – See the Precision

• Y-axis: put density

• X-axis: put the measurement number (i.e., was it the 1st, the 2

nd, etc)

• For each density measurement, put a point on the plot, and put error bars on the point.

Take a look at your plot – what is the average density? Draw a horizontal line on the plot


Record Record Record Record your your your your


Record your Record your Record your Record your predictionspredictionspredictionspredictions!!!!



representing where the average value of the data lies. How much is the uncertainty on that average? In

a different color, draw horizontal dotted lines above and below the average value

that represent the upper and lower bounds on what you think the density could be.

In your lab notebook, write the name of the liquid and its average density,

including your error estimate. This is your final result!

PART 4: USE YOUR RESULTS TO MAKE A PREDICTION

Now – let’s put it all to the test. We’ll combine the information from all the pairs to predict what order

the liquids should float in. In your lab notebook, write the results from each group so that you have a

record of all the data.

In your lab notebook, write what order you think the liquids will layer in,

starting with the liquid that will be at the bottom and ending with the liquid

that you think will be at the top. Write down why you predict this order –

what is it about the data that suggest that this is the correct order?

PART 5: TEST YOUR PREDICTION

To make the tower of liquids, you will need:

• A container

• Samples of each liquid

Going according to your prediction, put about 1” of the liquid that you think will be the one at the

bottom into your container. Then, pouring carefully, put in about 1” of the next liquid. Continue until

you have put in all the liquids in order, pouring slowly and gently to avoid mixing the layers.

Did it work? If you were right, the liquids should have layer nicely on top of each other. If you were

wrong, one or more liquids would have mixed as a more-dense liquid sank down through a less dense

liquid.

In your lab notebook, make a sketch of your tower of liquids, indicating which layer

is which liquid.


TRICKS OF THE TRADETRICKS OF THE TRADETRICKS OF THE TRADETRICKS OF THE TRADE Plastic items are made by Plastic items are made by Plastic items are made by Plastic items are made by machines that form machines that form machines that form machines that form melted plastic into a melted plastic into a melted plastic into a melted plastic into a desired shape. The plastic desired shape. The plastic desired shape. The plastic desired shape. The plastic cools and holds that cools and holds that cools and holds that cools and holds that shape. To have the plasticshape. To have the plasticshape. To have the plasticshape. To have the plastic----melting machines work melting machines work melting machines work melting machines work properly, the plastic must properly, the plastic must properly, the plastic must properly, the plastic must be in small pieces to melt. be in small pieces to melt. be in small pieces to melt. be in small pieces to melt. So plastic recycling So plastic recycling So plastic recycling So plastic recycling companies, which buy companies, which buy companies, which buy companies, which buy used plastic and then used plastic and then used plastic and then used plastic and then process it so that it can be process it so that it can be process it so that it can be process it so that it can be made into new products, made into new products, made into new products, made into new products, need to not only separate need to not only separate need to not only separate need to not only separate the different kinds of the different kinds of the different kinds of the different kinds of plastic, butplastic, butplastic, butplastic, but also chop it up also chop it up also chop it up also chop it up into very small pieces so into very small pieces so into very small pieces so into very small pieces so that plastic that plastic that plastic that plastic manufacturing manufacturing manufacturing manufacturing companies will want to companies will want to companies will want to companies will want to buy it from them. The buy it from them. The buy it from them. The buy it from them. The plastic we are using has plastic we are using has plastic we are using has plastic we are using has already been through a already been through a already been through a already been through a recycler’s “shredder.”recycler’s “shredder.”recycler’s “shredder.”recycler’s “shredder.”

CHALLENGE II:

DENSITY OF WEIRD-VOLUME SOLIDS

In this part of the lab, your goal is to do what plastic recycling

companies do – figure out how to tell which kind of plastic is which.

Specifically, the group’s task is to determine the density of several

different kinds of plastics, and figure out what the best method for doing

so is. You need to propose two different methods for measuring the

density of one kind of plastic and then carry out the experiment both

ways. You will have to use your result to decide what kind of plastic

your sample is. We will then compare the results from all groups. Keep

in mind what your experiences in the first part of this lab were –

they may help you out now! Throughout your data collection in

this part of the lab, it will be important to keep track of your

error estimates because at the end of the lab you will need to

decide which of the two methods you used is the better one for

measuring the density of plastic.

Tip: The test samples of plastic that you will use consist of

small pieces of the material. Their shapes may make measuring

their volume tricky!

PART 1: PLANNING

In this part of the lab, you need to come up with two different

procedures for making the density measurement. At least

one of your procedures must include making several separate

measurements of the test sample’s density and averaging those

measurements to get a final answer. In the end, we’ll figure out

which procedure gives better results by examining the accuracy

and precision of each.

You will have everything we used in the morning available for

your use in this part (graduated cylinders, liquids, scale….).

Talk with your partner about how you can make these

measurements. [Hint: use what you know!] Consider the

following questions:

???? How many sets of measurements do you think you need

to make?

???? What problems could arise with your procedures?


Record Record Record Record your your your your plansplansplansplans!!!!


???? What could make the measurements difficult?

???? What errors will you have to watch out for?

???? What will the limiting factors be for the accuracy of each procedure?

???? Which procedure do you think will be better?


• what your procedure #1 will be to measure the density of the plastic

sample, including what quantities you will measure, how many sets of

measurements you will make, and exactly what you will do to make the

measurement

• what your procedure #2 will be to measure the density of the plastic

sample, including what quantities you will measure, how many sets of

measurements you will make, and exactly what you will do to make the

measurement

• for each procedure, list at least five possible sources of difficulty in making the measurements

accurate and precise

• what you will do to minimize the error due to each difficulty you mentioned above

• Which procedure you think will be better, and why you think that [hint: what is the most

significant source of uncertainty in each procedure?]

As a group, we will discuss the procedures that each pair proposes. Maybe you will get some ideas

from that discussion about how you could refine your procedures to get the best results. In your lab

notebook, make any adjustments to your procedure that you feel will be necessary.

Review your final lab procedures with one of the lab instructors, and then go for it – put your

techniques into action!

PART 2: TAKING DATA

In your lab notebook, make two data tables – one for each procedure you will

follow.

Follow your procedure #1, and fill in the table with all the

measurements that you take. For each measurement, make sure to

include an estimate of how well you think you make made it. That is, include an

estimate of your uncertainty – both in units and fractional – for every measurement.

Then, do the same for procedure #2.


WHAT’WHAT’WHAT’WHAT’SSSS THAT THAT THAT THAT SYMBOL??SYMBOL??SYMBOL??SYMBOL??

PETEPETEPETEPETE (Polyethylene (Polyethylene (Polyethylene (Polyethylene Terephthalate)Terephthalate)Terephthalate)Terephthalate) 1.38-1.39 g/mL Two-liter beverage bottles, mouthwash bottles, boil-in-bag pouches.

HDPEHDPEHDPEHDPE (High Density (High Density (High Density (High Density PolyethylenePolyethylenePolyethylenePolyethylene) 0.96 g/mL Milk jugs, trash bags, detergent bottles.

VVVV (Vinyl (Vinyl (Vinyl (Vinyl ---- sometimes sometimes sometimes sometimes seen as PVC, for polyvinyl seen as PVC, for polyvinyl seen as PVC, for polyvinyl seen as PVC, for polyvinyl chloride)chloride)chloride)chloride) 1.15-1.35 g/mL Cooking oil bottles, packaging around meat.

LDPELDPELDPELDPE (Low Density (Low Density (Low Density (Low Density Polyethylene)Polyethylene)Polyethylene)Polyethylene) 0.92-0.94 g/mL Grocery bags, produce bags, food wrap, bread bags.

PPPPPPPP (Polypropylene (Polypropylene (Polypropylene (Polypropylene)))) 0.90-0.91 g/mL Shampoo bottles, straws, margarine tubs, diapers.

PSPSPSPS ((((PolystyrenePolystyrenePolystyrenePolystyrene)))) 1.05-1.07 g/mL Hot beverage cups, take-home boxes, egg cartons, meat trays.

OTHER OTHER OTHER OTHER All other types of plastics or packaging made from more than one type of plastic.



PlPlPlPlot ot ot ot your your your your datadatadatadata!!!!

PART 3: ANALYZE YOUR DATA

In your lab notebook, make four plots:

(Make sure to clearly label the title, axes and

units in your plot)

PROCEDURE #1: Density Plot – See the

Precision


• X-axis: put the measurement number (i.e., was it the 1st,

the 2nd, etc)

• For each density measurement made using procedure #1,

put a point on the plot, and put error bars on the point.

PROCEDURE #2: Density Plot – See the Precision


• X-axis: put the measurement number (i.e., was it the 1st,

the 2nd, etc)

• For each density measurement made using procedure #2,

put a point on the plot, and put error bars on the point.

Take a look at your plots – what is the average density on each?

Draw a horizontal line on each the plot representing where the

average value of the data lies. How much is the uncertainty on

that average? In a different color, draw horizontal dotted lines

above and below the average value that represent the upper and

lower bounds on what you think the density could be.

In your lab notebook, record which sample you

have and its average density as measured with

each procedure, including your error estimate.

Do the answers from the two different

procedures agree?

Take a look at the sidebar: what kind of plastic

do you think you have?

In your lab notebook, record the name and number of the kind

of plastic that you have determined you have.

We will compare everyone’s results and find out which

procedure produced the most accurate and precise answers, and

we’ll think about why it is that some procedures worked better


Record Record Record Record your your your your ideasideasideasideas!!!!

than others for measuring the density of the plastic samples, and how our techniques can be improved.

In your lab notebook, answer the following:

???? Which procedure worked best?

???? How did you decide which was best – that is, what do you really mean

by “best?”

???? Did the results of the two procedures agree? If not, why might that be?

???? What issues caused the results to be uncertain?

???? Which issue caused the most uncertainty?

???? What could we do in the future to make even better measurements?

IN CONCLUSION…

In this lab, we explored a few different techniques for determining an object’s density, and discussed

some different applications where density and buoyancy tricks come in handy. In your lab notebook,

write a paragraph summarizing what you did in this lab and what you have learned about

density and buoyancy.

2006 Yerkes Summer Institute Convection 13

Source: www.balmer.com

Source:http://www.physics.

brocku.ca/courses/1p93

Convection (Walter Glogowski, Chaz Shapiro & Reid Sherman)

INTRODUCTION

You know from common experience that when there's a difference in temperature between two places

close to each other, the temperatures tend to even out over time: the hot part cools and the cool part

warms. A fire can warm a whole room, not just the air right around it. You

close your doors and windows in the winter because the heat wouldn't stay

in your building if you left them open. So heat can obviously get

transferred from one place to another. But how does this process happen?

First we must picture what heat is: heat is the energy in the "random

motion" of something's atoms (types of motion are described in Buoyancy

Background). The atoms in a glass of hot water are moving around more

quickly than the atoms in a glass of cold water. When water is hot enough,

the atoms move so fast that they "escape" to become a gas (steam, a.k.a. water

vapor), and when water loses enough heat, it becomes a solid (ice) whose atoms barely move at all -

they simply jiggle in place. So when we talk about heat "moving" we're really talking about energetic

atoms in one place transferring some of their random motion to atoms in another place.

Then how does heat move? A simple way is for a fast particle to

bump a nearby particle, transferring a little energy. That bumped

particle will then bump into another one, and so on, until the heat

energy (the motion of the particles) has been spread out. This

process of energy being transferred by nearby particles bumping

is called CONDUCTION, and it can happen in solids, liquids or

gasses.

However, FLUIDS (meaning liquids and gasses - things that can

flow) have another important way of moving heat energy around. If

one part of a fluid is hotter than another part, and if all the hot (fast

moving) atoms get moved to a different place in the fluid, then their heat has moved with them. This

process is called CONVECTION: energy being transferred by "bulk motion" of particles

through a fluid (types of motion are described in Buoyancy Background). Convection cannot happen

in a solid because, like the bricks in a wall, the atoms in a solid cannot move far from where they are.

In liquids and gasses, however, the particles are free to move about (which is why a fluid can change

its shape to match its container).

If one part of a fluid is heated, where will the hot part go? For reasons that you will learn about in the

Lighter Than Air day lab, heated gas or liquid tends to rise, while cooler stuff will sink. The heated


http://www.rit.edu/~andpp

h

http://www.rit.edu/~andpph

Record your Record your Record your Record your predictionspredictionspredictionspredictions!!!!

Record your Record your Record your Record your observationsobservationsobservationsobservations!!!!

substance rises, moving farther away from the heat source and spreading out. In

doing so, the heated fluid gives its heat to the surrounding fluid, thereby cooling

off.

When the heated fluid rises, something has to take its place. It can't happen that

everything rises, because that would leave empty space at the bottom. As the

warm material rises, some cool fluid from the top sinks and moves into the

vacated space at the bottom. The cool fluid then gets heated by the heat source

and repeats the cycle. So the whole picture is that warm material will move

away from the heat source and warm up the cooler areas while cool fluid will

move toward the heat source and get warm. In this way the heat from the heat

source gets transferred throughout the fluid by convection.

PART I: WATER & FOOD COLORING

In this demonstration, we will begin our exploration of the close relationship between temperature and

fluid motion. We will first make predictions about what will happen, and then your job will be to

watch the demonstration closely and record your detailed observations.

We will fill a fish tank with tap water. We will then fill two beakers with water, one with warm water

and one with cold. We will add colored dye to each beaker. If we place the beakers in the fish tank,

what do you think will happen?

In your lab notebook, write your predictions for:

???? What do you think will happen right away to the water in each

beaker?

???? What do you think will happen over a long time?

???? What would be different if the warm beaker water is just a little

warmer than the water in the rest of the tank, than if the beaker water was a lot warmer than

the tank water? Why?

Now, watch as the experiment is

carried out, and record your

observations in your lab

notebook. Make a sketch of the

experiment. Did what you think

would happen actually happen?


Source: preparedpantry.com

Record your Record your Record your Record your observations!observations!observations!observations!

Record Record Record Record your your your your data!data!data!data!

!!! WARNING !!!

For this experiment we will be working with hot objects. The hot plate, breadpan and oil will all get

very hot - take care not to touch any heated surfaces or you may be burned!!

DO NOT TOUCH THE HOT PLATE, BREAD PAN, OR OIL WHEN IT IS HEATED! BE CAREFUL: ITEMS WILL REMAIN HOT EVEN WHEN THE HOT PLATE IS TURNED OFF!!

PART II: OIL & THYME

The idea in this section is to make your own convection cell and study it – see how it moves and what

makes it move the way it does.

Materials:

Pyrex bread pan 2 clamps

Vegetable oil 2 thermometers

Thyme Stopwatch

Hot Plate Ruler

Metal block Ring stand

Directions:

Fill the breadpan about halfway with

vegetable oil and mix in some thyme. Be

sure to stir in thyme so that it is suspended

throughout the oil rather than all being at

the top or bottom. Place the metal block

on the hot plate and the breadpan on top

of the block so that only the center of the

bottom of the pan gets heated.

1) The pieces of thyme will follow the oil

as it moves. Watch the motion of the fluid

as the bottom gets heated.

In your lab notebook, record

•••• What do you observe? Sketch it!

•••• How does the motion change as time goes on?

•••• Draw a picture in your lab book tracing out the motion.

2) Now attach the thermometers with the clamps to the ring stand in such a way that one will measure

the temperature of the oil closest to where it is being heated and the other will measure the oil at the

edge, as far away from the heat source as can be.

3) Using a ruler and a stopwatch, measure the speed that a piece of thyme moves

across the pan. While you are measuring the speed, take a measurement of both

thermometers. Record the speed, the two temperatures, and the temperature

difference between the thermometers in your lab book.

4) Do not continually heat the oil, but occasionally turn the hot plate off and on,

so that you are sometimes taking measurements while the oil is being heated and sometimes while it is

not. (Note: it will still be hotter than room temperature because it takes a while to cool off.) Also, once

or twice, stir up the oil, wait for it to settle for a couple of seconds, and take a measurement.


Plot Plot Plot Plot your your your your datadatadatadata!!!!

!!! WARNING !!!

For this experiment we will be working with sunlight. The sun is a very bright source of

light and can be very dangerous to your eyes.

DO NOT STARE DIRECLY AT THE SUN! DO NOT LOOK THROUGH THE TELESCOPE AT THE SUN WITHOUT A SOLAR FILTER!

Graphing: Now make three graphs in your lab notebook.

• In the first one, put the temperature measured at the center of the pan on

the horizontal axis and the speed of the oil's motion on the vertical axis.

Then for each of your measurements, plot a data point. When you have

plotted all the points, look at the graph. Do you notice a clear trend to

the points?

• For the second graph, do the same thing, but instead of putting the temperature at the center of

the breadpan on the horizontal axis, put the temperature at the edge.

• In the third graph do the same again, but the horizontal axis will be the temperature difference

between the center and the edge.

???? Which of the three graphs shows the strongest connection between the value on one axis and

the value on the other?

PART III: CONVECTION IN THE SUN

We will use a solar telescope to take pictures of the surface of the sun. We

will put a filter on the telescope so that we only see light from a specific

temperature-sensitive process happening in the sun.

NEVER LOOK AT THE SUN THROUGH A TELESCOPE

WITHOUT A SOLAR FILTER!!

The filtered image of the sun will show us a general map of the temperature of the surface of the sun.


• A description & sketch of what you see.

• How does this relate to convection?

• Does it look like a convective cell?

In the convective cells we looked at earlier,

there was a heat source at the bottom of some

fluid, and hot stuff rose while cool stuff sank.

How is that related to what in going on in the

sun?


Source: http://apollo.lsc.vsc.edu/

http://www.astro.su.se/

In your lab notebook, answer the following:

???? In the sun, where is the heat source?

???? In what direction would “rising” or “sinking” movements be?

???? Can you think of an analogy of where we could see convection from a similar perspective as

we see the convection in the sun?

PART IV: CONVECTION ALL AROUND US

Here are a few more places where convection plays an important

role:

Weather

As you probably know, the reason the earth is warm and

comfortable for life rather than being an isolated ball of ice is that

we are close to the sun. However, the actual heating of the air

takes place almost entirely from sunlight absorbed by the earth

and then released into the air as heat (infrared radiation). So the

heat source of the atmosphere is the ground, at the bottom of the

atmosphere, and not above us in the sky. That's why the air tends

to get colder higher in the atmosphere. Mountains have snow at

their peaks, not at their bases.

But, we know that hot air rises. So with a heat source at the bottom of a large amount of air,

convection often forms in the atmosphere, just as it did in the breadpan of oil and thyme.

As warm air rises from the ground, if often carries with it a large amount of water vapor. This situation

happens because the water is evaporating at the ground as well, and humid air (air with a lot of water

in it) is lighter than dry air. When the air rises to where it is cool, the water vapor condenses into little

droplets. Water condensing high in the atmosphere in this way is how clouds form. Clouds are the

peaks of gigantic convective cells! You will have a chance to further explore clouds in the night lab

Weighing Clouds.

Cooking

What happens when you put a pot of water on the stove? The bottom

of the pot gets heated very quickly, and that heats the water at the

bottom of the pot. The hot water will rise to the top, letting cooler

water take its place at the bottom of the pot, where it will get heated.

Convection cells form in the water as the water at the bottom gets

heated from the flame and water at the top loses some heat to the air

above it. This convection is why when you boil a pot of liquid, the

liquid seems to be bubbling. You are seeing the tops of convection

cells.

You also may have heard of “convection ovens.” The name is actually a little misleading, since


Source:kicp.uchicago.edu/edu

cation/explorers/2002winter-

YERKES/

regular ovens use convection as well. In a regular oven, the heat source is at the bottom, causing the

hot air to rise; new air then is next to the bottom, gets heated, and rises. Convection will work to heat

all the air in the oven, but it does not do it very efficiently, and most of the hot air stays at the top of

the oven. Thus, you have to pay attention to where in the oven you put your food, because the

temperature is different in different parts of the oven. A convection oven has fans in it that basically

force even more convective air currents than would happen naturally. These currents even out the air

temperature faster and get the hot air all over the oven rather than just at the top.

Clothing

You know that in winter time you don't want to go outside without much clothing

on. However, the reason you feel cold is much more complex than just the air

around you being cold. After all, air is a terrific insulator, and does not carry

much heat away from your body. In newer, more expensive windows, there will

be two panes of glass with a little pocket of air between them because that air

prevents heat from leaving your house. So why doesn't the air around you prevent

you from getting cold outside? Because as soon as your body warms up the air

around you, that air rises and lets new, cold air move in. Your body acts as a heat

source for convection in the air, and loses heat much more quickly that way!

In fact, the reason clothes make you warm is that they trap air next to your body.

When your body heats the air around you, instead of rising and leaving you with

new, cold air to heat, the warm air gets stuck where it is, forming a warm pocket

around you. Down feathers are very warm because they trap lots of air.

The Rest of Summer Institute

Why are we talking about convection at this Summer Institute? What does the transfer of heat

throughout a fluid have to do with measuring density by floating objects in liquid or building hot air or

helium balloons? Well, one of the main things we will discuss in this lab is that hot gas or liquid will

rise. Hot fluid rises because it has a lower density than the cooler material around it. Things of low

density float on things of high density, as you will study in the Does It Float? day lab. The hot air

balloon lab, Lighter Than Air, also is closely connected to convection. Convection explains how the

air in the balloon gets hot, since hot air balloons put the heat source at the bottom of the balloon and let

convection do the work in moving the hot air around and warming the whole balloon. You can also

think of the entire balloon as a small package of air in a convective cell. As it heats, it rises up into the

atmosphere, and as it cools by releasing its heat into the air around it, it falls back to the ground.

IN CONCLUSION…

In this lab, you became an expert in convection and its effects, and discovered how convection is

useful in your everyday life and in other labs at this Summer Institute. In your lab notebook, write a

short paragraph summarizing what you learned about and did with convection in this lab.

2006 Yerkes Summer Institute Lighter Than Air 19

Lighter Than Air:Lighter Than Air:Lighter Than Air:Lighter Than Air:

Why Do Balloons Float? Why Do Balloons Float? Why Do Balloons Float? Why Do Balloons Float? (Randy Landsberg, Bill Fisher & Dan Robertson)

INTRODUCTION

We are all familiar with balloons. They are a common sight at birthday parties and other fun events.

But there is much more to balloons then just that. Coming in a range of

shapes and sizes, balloons have vital applications in all walks of life, from

flying machines to planetary exploration, medicine to meteorology; we use

balloons for more things then meets the eye.

But what makes some balloons float, while others do not? In this lab we will

investigate the phenomena of buoyancy, and examine the relationship of

buoyancy to floating objects. We will explore what a lazy afternoon floating

in the pool has in common with a hot air balloon. Some questions that we

will tackle include:

???? We are all familiar with the idea of floating on water, but why do

things that float in water not float in air?

???? How does the density of an object determine what it will float in?

???? How can we take advantage of floating to do science?

To answer these questions, this investigation will have three parts. In Parts I and II, we will investigate

the effects of heat on density and floating. In Part III we will explore the use of helium for floating.

BACKGROUND

Why does a rock sink when thrown into a lake but a piece of Styrofoam

floats?

Why do hot air and helium balloons rise?

What does this have to do with Archimedes?

Floating in air is not a common experience for humans but floating in water, or at least seeing things

float in water, is. The physics of floating in both air and water is similar because both air and water

behave in similar ways - both are fluids. A fluid is a substance that flows and conforms to the shape of

a container that holds it (for example, if you pour water, a fluid, into a bucket, the water will take the

shape of the bucket, but if you put a rock into a bucket the rock stays the same shape).

Source: Robert Friedman


ARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLEARCHIMEDES’ PRINCIPLE When a body is fully or partially submerged in a fluid, a buoyant force Fb from the surrounding fluid acts on the body. The force is directed upwards has a magnitude equal to the weight, m x g, of the fluid that has been displaced by the body (Fundamentals of Physics 6th ed, Halliday, Resnick & Walker p. 330 )

When do things float in fluids? What is going on that makes floating happen? Something will float in

a fluid when the force from the fluid pushing up is greater than the force pulling down. Generally

things float when they are less dense than the fluid by which they are surrounded.

The downward force an object feels (Fg) is from gravity, and is equal to the weight of the object.

[Technically Fg depends on the mass (m) of the object and the local gravitational force (g) pulling on

that mass, but g is essentially constant on the earth.] The downward force depends on how much ‘stuff’

there is in the object. A kilogram of rock and a kilogram of Styrofoam feel the same downward force,

even though one is much denser and smaller then the other. Two kilograms of anything feels twice the

downward force as one kilogram of anything. We can express the downward force on an object as:

Downward force = Fg = mass of object (m) x gravitational strength (g) = weight of object

The buoyant force pushing up (Fb) is determined by how much fluid the object displaces. The amount

of displacement depends on the object’s volume. A bigger object displaces more fluid. Think about

taking a bath. What happens to the water level when just your foot is in the tub compared to when you

sit in the bath? The buoyant force (Fb) depends on the weight of the fluid displaced by the object. In

other words, the volume of fluid that has been pushed aside by the object pushes up with a force that is

equal to how hard gravity pulls the fluid down.

Upward force = Fb = mass of fluid displaced (m) x g = weight of fluid displaced

Net lift is equal to the upward buoyant force minus the downward gravitational force:

Lift = Fb - Fg

So, just by comparing the upward and downward forces, you can tell if something will be buoyant.

That is, if Fb is bigger than Fg, then the object will float.

Fb

Fg

Floating Fb > Fg

Fb

Fg

Sinking Fb < Fg


Buoyancy Example: Under Water Soda Bottle Balloon

(from http://www.howstuffworks.com/helium.htm/printable)

Let's say that you take an empty plastic 1-liter soda bottle, sealed tightly. Tie a string

around it like you would a balloon, and still holding it, dive to the bottom of a

swimming pool. Since the bottle is full of air, you can imagine it will want to rise to

the surface. If you sit on the bottom of the pool holding the string, it will act just like a helium balloon

in air. If you let go of the string the bottle will quickly rise to the surface of the water.

This soda bottle "balloon" wants to rise in water because water is a fluid, and the 1-liter bottle is

displacing one liter of that fluid. The bottle and the air in it weigh very little (1 liter of air weighs about

a gram, and the bottle is very light as well). However the liter of water it displaces weights about 1,000

grams (2.2 pounds or so). Because the combined weight of the bottle and air is less than the weight of

the water it displaces, the bottle floats. This behavior is the law of buoyancy.

Buoyancy Example: Helium Flotation

(from http://www.howstuffworks.com/helium.htm/printable)

Helium balloons also work by the law of buoyancy. In this case, the helium balloon that you have is

floating in a "pool" of air (in a swimming pool you are standing in a "pool of water" perhaps 10 feet

deep - in an open field you are at the bottom of a "pool of air" that is many miles deep). The helium

balloon displaces an amount of air (just like the empty bottle displaces an amount of water). As long as

the weight of the helium plus the balloon fabric is lighter than the air it displaces, the balloon will float

in the air.

It turns out that helium is a lot lighter than air. Though the difference is not as great as that between

water and air (a liter of water weighs about 1,000 grams, while a liter of air weighs about 1 gram), it is

still significant. Helium weighs 0.1785 grams per liter. Nitrogen weighs 1.2506 grams per liter. As

nitrogen makes up about 80 percent of the air we breathe, 1.25 grams is a good approximation for the

weight of a liter of air.

Therefore, if you were to fill a 1-liter soda bottle full of helium, the bottle would weigh about 1 gram

less than the same bottle filled with air. That doesn't sound like much, but in large volumes the 1-

gram-per-liter difference between air and helium really adds up. That is why blimps and balloons are

generally quite large - they have to displace a lot of air to float!


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PART I: HOT AIR AND DENSITY,

OR, CAN GARBAGE BAGS FLY?

In this part of the lab we will investigate what happens when air is heated, and

how this can make things float.

In your lab notebook, describe what you think happens to air when it is heated.

What changes?

What might one observe?

Solar Bag

In this outdoor activity we will use sunlight to heat the air inside a “solar bag”. A solar bag is

essentially a super-sized plastic bag that is 50 feet long.

Materials: Solar Bag, strong string, & sunshine

Step 1 – fill the bag with air – this is a challenge for the group

Step 2 – seal the bag & connect a tether, a long line of string

Step 3 – place the bag in sunlight and observe what happens

Step 4 – Record you observations in your lab notebook

Step 5 – Try to explain what happened

Demonstration: What happens when air is heated? (The instructor will perform this demonstration. Your job is to observe and record what happens.)

The solar bag provided an example of what can happen when air is heated. In this demonstration we

will explore in more detail what happens to air when it is heated up.

Materials: Erlenmeyer flask, stopper, stopper w/ hole, tubing, beaker, thermometer, hot plate &

balance

Does heating air make it heavier?

Does heating air change its volume?

Does heating air change its density?

(If you were at YWI 2005, think

about the kinetic theory of gases lab)

In your lab notebook, sketch a picture of both parts of the demonstration.

Describe what was done in each part and what conclusions the group made

about the effect of heating air on its mass and its volume.

???? What can you conclude about the density of hot air vs. cool air?

???? What can you say about the volume & density of the air inside the

solar bag before and after it was in the sunshine?

???? Can you relate this behavior to Archimedes principle?


Source: wikipedia.com Record Record Record Record your ideas!your ideas!your ideas!your ideas!

PART II: BUILDING PAPER BALLOONS

Earlier in the week, if the

weather cooperated, you

witnessed the launch of a

modern hot air balloon. In

this portion of this lab we

will build our own hot air

balloons out of paper. As odd as a paper

balloon may sound, it is actually similar to

some of the very first hot air balloons ever

launched (see sidebar).

Though our paper balloons will be a bit

smaller than both modern and historic hot air balloons, they will operate on the same principles. The

key is to fill the balloons with something lighter, or more properly less dense, than the surrounding air.

We are so accustomed to swimming in air we forget that it is made of atoms and molecules (mostly

nitrogen molecules, N2), that have mass. This fact means that when the air molecules are displaced by

an object, they push back with a buoyant force equal to the mass of the volume air pushed aside.

Materials:

• 12 small sheets thin tissue paper

• Glue

• Stapler and staples

• Rulers

• Wire

• Newspaper

• Scissors

• Section patterns

• Heat source (e.g. camping stove)

Questions to discuss with your group:

What do you think is important in designing and making a good hot air balloon?

Are there things to avoid? Why?

Construction Instructions:

1. Join sheets together on short edge, overlap edges 1cm and glue (use as

little glue as possible). Run a thin continuous line and allow glue to dry

before you go on. Sheets need to be ~47x51cm

2. Fold the sheets lengthwise, and then stack one on top of the other. Make

certain that all the folded edges line up evenly.

3. Making sure they stay aligned, staple the stacked sheets together along

the three unfolded edges (see view B)

THE FIRST BALLOON FLIGHTTHE FIRST BALLOON FLIGHTTHE FIRST BALLOON FLIGHTTHE FIRST BALLOON FLIGHT

The first recorded manned flight of a hot air balloon took place in Paris on November 21, 1783. The balloon, made of paper and silk , was designed by Joseph and Etienne Montgolfier, brothers whose family owned a famous paper company. The flight of “Seraphina” lasted about twenty minutes, reached a height of about 500 feet, and landed a few miles outside of Paris.




4. Place pattern on top and trace on with a magic marker.

5. Carefully cut out the pattern with sharp scissors.

6. Lay out one of the folded sections on a sheet of

newspaper. Run a thin continuous line of glue

about 1 cm from the right hand side (see View C).

7. Place another folded section on top of the first (View D)

8. Repeat and continue until all six sections are glued together. Put newspaper

between the folds to keep them from sticking together.

9. When completely dry, carefully remove the

newspaper. Run a line of glue on one of the last edges. Connect that

edge with the other free edge. (see View E).

10. Measure the circumference of the bottom opening. Cut a piece

of wire 5 cm longer and bend it into a circle the size of the opening

and twist the overlap

11. Fold up the bottom 3 cm of the balloon. Place the wire inside the fold,

and glue the fold over the wire. (View F)

12. Reinforce the top of the balloon by gluing a 10 cm (diameter) circle on

the top.

13. Repair any breaks or tears with

patches of tissue paper and glue.

Getting to Launch:

Once the balloons are assembled, weigh each balloon and record

the weights.

Then, carefully carry the balloons one at a time to the launch pad.

Time each flight and try to gauge how high the balloons fly.

Record & discuss your observations of the launches:

•••• successful or not

•••• duration of the flight

•••• approximate maximum height

•••• other observations


Photo credit: wikipedia.com

MODERN HOT AIR BALLOONS

Typical Height: 80’ tall

Typical Girth: 50’ across

Typical Inflated Volume: 78,000 cubic feet

(or about 2,200,000 liters)

Typical Weight of Air Contained: 2 ½ tons

(or about 2,270 kg)

The world’s record for altitude in a hot air

balloon is 64,997 feet.

The baskets that hang from hot air balloons

are all made by hand.

DO THE CONVERSIONDO THE CONVERSIONDO THE CONVERSIONDO THE CONVERSION

Cubic feet to liters: 28.317 liters/cubic foot

Liters to cubic feet

0.03531 cubit feet/liter

Thinking About It…

The picture below on the left is of a hot air balloon, with greatly oversized air molecules, before

heating. Using the same idea of oversized air molecules, sketch in your lab notebook what a similar

air balloon would look like after heating.

How Does It Compare?

Compare your balloon to a typical modern hot air balloon.

???? How many times bigger do you think a modern hot air

balloon is compared to yours?

Before heating After heating

?


RecordRecordRecordRecord your ideas!your ideas!your ideas!your ideas!

PART III: SCALING UP FROM PARTY BALLONS

TO SCIENTIFIC PAYLOADS

How many helium filled balloons do you think it would take:

???? To lift you? ???? To lift as much as a modern hot air balloon? ???? To lift a big telescope?

Take a guess for each question and record your guesses in your lab notebook.

In this part of the lab we will explore how good your guesses were, and how scientists determine the

right size balloon to use for their experiments.

Introduction:

Helium filled balloons are commonly seen at festivities and celebrations. In

addition to being used for entertainment purposes, helium filled balloons play an

important role in many areas of scientific research. For example, “small” six to

eight foot diameter weather balloons are frequently launched to acquire many

different types of metrological data. At the South Pole, balloons are launched to

monitor the amount of ozone in the atmosphere (see photo). These balloons

provide information that other methods such as satellite remote sensing cannot,

e.g., the amount of ozone at specific altitudes.

The beauty of a helium balloon as a launch vehicle is that it is simple, has no

moving parts, and is relatively inexpensive. They can also go places where

humans might not want to. Typical weather balloons contain a small radio

transmitter, which is used to send the data back to the researchers.

Much bigger helium balloons are used for larger research projects. Researchers at

the University of Chicago use simple balloons for some of the most sophisticated

experiments in modern physics. For example, Professor Stephan Meyer flew a

telescope named TopHat over Antarctica in the austral summer of 2000-2001.

This telescope was designed to look at light from the infant universe, microwave

photons that had traveled for about 14 billion years and hold physics secrets of

the early universe. As the name suggests, the TopHat telescope sat on top of the

balloon rather than hanging underneath it. The reason for this funny geometry is

that the experiment was so sensitive that the thin fabric of the balloon itself

would have gotten in the way, making it an unwanted source of error (the small

balloon in the photo was detached after launch). This summer, Professor Dietrich

Muller flew a cosmic ray detector experiment called TRACER (Transition Radiation Array for Cosmic

Energetic Radiation) in the Arctic over Sweden.



Supplies/Resources:

• 11 inch Diameter Latex Balloons

• Helium Tank with Low Pressure Regulator (ask an instructor for help using this)

• String

• Paper Clips (many)

• Balance

• Set of Metric Masses (10gm, 20gm, 100gm, 200gm, 500gm, 1,000gm)

Experimental & Computational Challenges:

# 1 - The Power of Averages Part I (paper clip)

• Determine the weight of one (1) paper clip

• Weigh ten different paper clips, one paper clip at a time, determine the average weight

• Weigh ten paper clips and determine the average weight by dividing by 10

• Compare your results to other groups & estimate the error in the weight

In your lab notebook, make the following data tables and fill them in:

Trial Weight One paper clip (g)

1

2

3

4

5

6

7

8

9

10

Average

Group Weight 10 paper clips (g) Weight one paper clip (g)

Average

# 2 - Determine how much mass one balloon can lift. • Describe the method that your group develops – be sure to account for everything!

• Compare your results to those of the other groups.

# 3 - Determine how much mass 2 balloons can lift. • Describe the method that your group develops.

• Compare your results to those of the other teams.


# 4 - Determine how much mass 10 balloons can lift. • Describe the method that your group develops.

• Compare your results to those of the other teams.

# 5 - The Power of Averages Part II (balloon lift)

• Pool the class data to determine the lift in terms of number of paper clips for:

• One balloon

• Two Balloons

• Ten Balloons

• In each case calculate the lift of one (1) balloon based on the average.

In your lab notebook, make the following data tables and fill them in:

Group Lift 1 balloon (#paper clips) Lift 1 balloon (g)

Average

Group Lift 2 balloons (#paper clips) Lift 2 balloons (g)

Average

Group Lift 10 balloon (#paper clips) Lift 10 balloons (g)

Average

# 6 - Calculate and then test how many balloons are needed to lift a 20 gram mass.

(Share balloons with other groups for the test)

• Compare your calculation to the experimental results

# 7 - Based on your previous results, calculate how many balloons would be needed to lift

yourself. (Note: there are about 2.2 kg in a pound)

• Show all calculations in your lab notebook.

• Describe you calculation and any assumptions made.

• Compare this answer to your guess at the start of the lab.


TOPHAT TELESCOPE

Balloon volume: 56,800 ft3 at sea level

Balloon volume: 28.4 million ft3 at float

(at float altitude: 1/500 pressure of sea level)

Inflated Height: 335 ft.

Inflated Diameter: 424 ft.

Balloon Weight: 3,600 lbs.

Float Altitude: 118,000 to 130,000 ft.

Top Package Weight: 200 lbs.

Bottom Gondola Weight: 1,500 lbs.

Free Lift: about 10%

HELIUM VOLUMESHELIUM VOLUMESHELIUM VOLUMESHELIUM VOLUMES

TopHat held 56,800 cubic feet at sea level

28.4 million cubic feet at float. An 11-inch diameter balloon holds between 0.4 and 0.5 cubic feet of helium at sea level.



# 8 - Based on the description of the TopHat telescope below, calculate how many helium filled

party balloons would be needed to lift the TopHat telescope. • Describe your calculation & record it in your lab notebook.

• Compare your results to your initial guess.

# 9 - Compare the number of balloons that you calculated were

needed to lift TopHat and the actual volume of helium used for

the TopHat balloon. • Show your comparison calculation.

• Comment on the difference between sea level and float

volumes.

• Calculate the buoyant force (Fb) on the TopHat balloon

(Useful info: there are about 28.3

liters/cubic foot and air weighs

about 1.25 grams/liter (at sea level

and ambient temperature). )

# 10 – Determine how much all the balloons in the lab can lift

• Count all the inflated balloons for the entire group.

• Calculate how much they can lift (show your calculations in your lab notebook).

• Test your prediction.

IN CONCLUSION…

Well, now you should be experts in getting things to float in the air! We have used a couple different

techniques for ensuring floatation, and with each method employed key concepts that come up in other

labs as well. In your lab notebook, write a short paragraph summarizing what you did in this lab

and what you learned about floating in air.


APPENDIX: USEFUL INFORMATION

(Source:http://www.ce.utexas.edu/prof/kinnas/319LAB/Book/CH1/PROPS/GIFS/densair.gif)

Standard Temperature and Pressure: 20 °C and 760 mm Mercury

•••• Weight of air per liter at STP = 1.20 g/l

•••• Weight of helium per liter at STP = 0.18 g/l

•••• Net lift per liter of helium at STP = 1.03 g/l

A typical balloon should provide from 4 to 5 mm of overpressure and reduce lift to .9935 of these

figures.

VOLUMES

• Sphere: (4/3) π r

3

• Cylinder: π r2 h

Documents

Buoyancy Background - University of Chicagoastro.uchicago.edu/~randy/YSI06_pdfs/ysi06.merged.fin… · · 2006-08-012006 Yerkes Summer Institute Buoyancy Background 1 Source: Buoyancy