Buoyancy Background - University of...
Transcript of Buoyancy Background - University of...
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
2006 Yerkes Summer Institute Does It Float? 4
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
2006 Yerkes Summer Institute Does It Float? 5
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 .
2006 Yerkes Summer Institute Does It Float? 6
Record Record Record Record your ideas!your ideas!your ideas!your ideas!
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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)
2006 Yerkes Summer Institute Does It Float? 7
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
2006 Yerkes Summer Institute Does It Float? 8
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resultsresultsresultsresults!!!!
Record your Record your Record your Record your predictionspredictionspredictionspredictions!!!!
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resultsresultsresultsresults!!!!
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.
2006 Yerkes Summer Institute Does It Float? 9
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?
2006 Yerkes Summer Institute Does It Float? 10
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???? 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?
In your lab notebook, write down:
• 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.
2006 Yerkes Summer Institute Does It Float? 11
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.
Record Record Record Record your your your your
resultsresultsresultsresults!!!!
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
• Y-axis: put density
• 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
• Y-axis: put density
• 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
2006 Yerkes Summer Institute Does It Float? 12
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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
2006 Yerkes Summer Institute Convection 14
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?
2006 Yerkes Summer Institute Convection 15
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.
2006 Yerkes Summer Institute Convection 16
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.
In your lab notebook, write down:
• 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?
2006 Yerkes Summer Institute Convection 17
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
2006 Yerkes Summer Institute Convection 18
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
2006 Yerkes Summer Institute Lighter Than Air 20
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
2006 Yerkes Summer Institute Lighter Than Air 21
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!
2006 Yerkes Summer Institute Lighter Than Air 22
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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?
2006 Yerkes Summer Institute Lighter Than Air 23
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.
2006 Yerkes Summer Institute Lighter Than Air 24
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resultsresultsresultsresults!!!!
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
2006 Yerkes Summer Institute Lighter Than Air 25
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
?
2006 Yerkes Summer Institute Lighter Than Air 26
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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.
2006 Yerkes Summer Institute Lighter Than Air 27
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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.
2006 Yerkes Summer Institute Lighter Than Air 28
# 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.
2006 Yerkes Summer Institute Lighter Than Air 29
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.
Record Record Record Record your your your your
resultsresultsresultsresults!!!!
# 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.
2006 Yerkes Summer Institute Lighter Than Air 30
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