Lab1_Conversions2019
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Southern Methodist University *
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Apr 3, 2024
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CEE 1331 Lab #1: Scientific Method / Unit Conversion
In today’s lab we will perform a simple observational experiment to demonstrate the concept of the Scientific Method. We will also learn how to convert from one set of units to another and how to apply this technique to solve practical meteorological problems. Applying the Scientific Method
The following activity is intended to help with your understanding of the scientific method. You will be starting with an observation and then formulating a “hypothesis.”
Step 1
: Observe the people in your lab class by looking at their height and shoe size. Based on your observations, write a hypothesis
that relates a person’s height to their shoe length. Hypothesis: __________________________________________________________________
Step 2A
: Conduct the Experiment
and collect data
by asking your fellow lab classmates for their height and shoe size. If height is only known in feet and inches, convert to centimeters by using 2.54 centimeters = 1 inch. Measure the length of the shoe in centimeters. Enter your data to record each person’s height in centimeters and shoe size in centimeters. Data table for recording height and shoe size.
Person
Height in cm
Shoe size in cm
Step 2B:
Create a graph in EXCEL by plotting the data from your table with the height
(dependent variable) in centimeters on the y-axis (vertical) and show shoe size
(independent variable) in centimeters on the x-axis (horizontal). Create a “scatter plot” graph in Excel and copy/paste it into this lab. The following short video explains how to make a graph with Excel and to draw a best fit line, also known as a trend line:
https://www.youtube.com/watch?v=eMEhjbhtfxQ
Step 3
: Conclusions
1.
Describe the pattern of data plots (dots) on your graph you created. For example, are they somewhat linear, or are they just randomly scattered all over the graph?
2.
Describe the relationship of height
to shoe size
from the evidence as suggested by your graph.
3.
According to your trend line, what is a reasonable estimate for the height of a person who wears
a shoe size that has a length of 25 centimeters? 4.
Summarize how accurately your graph predicts a person’s shoe size, given ONLY his or her height. 5.
Do you accept, reject, or should you modify your original hypothesis? Give the reason(s) for your
choice of accepting, rejecting, or modifying. 6.
Name 2 possible sources of error that might be in your experiment? Unit Conversions
In meteorology it is important to know how to convert from English units to the metric system, the system used in all sciences. For example, the common unit to measure length
in the English system is inches or feet, but in the metric system, the centimeter or meter is more commonly used. To convert from feet to meters or from inches to centimeters (or vice versa), we need to know the appropriate “conversion factors.” For example, we know that 1 meter = 3.28 feet. So, how would you convert 10 feet to the equivalent number of meters? You set up a conversion train
which allows you to go from one unit of measurement
to another by using the process of unit cancellation
in a sequence of “cars” in the “train.” Consider the following simple conversion train that converts 10 feet to an equivalent number of meters:
10 feet
X 1 meter
~ 3.05 meters
3.28 feet
Here you can see that the unit, feet
, in the numerator of the first car of the train cancels out when you multiply through by the units in the denominator of the second car, and you are left with only meters
for
your final answer. Note that the ~ symbol means “approximately equal to.”
Let’s do another one. How would you convert 60 miles mph to meters per second (written as mps or m/sec or m sec
-1
)? Before we begin, we need to know some more conversion factors. 5,280 feet = 1 mile
60 seconds = 1 minute
60 minutes = 1 hour Now we are ready to set up the conversion train. Keep in mind that whenever you see the word “per” in
a mathematical context, you can draw a dividing line. Thus, 60 miles per
hour is the same thing as writing 60 miles . Thus, our conversion train looks like the following:
hour
60 miles
X 5280 feet
X 1 meter
X 1 hour
X 1 minute
= 60 X 5280
~ 26.83 m/sec
hour
1 mile
3.28 feet
60 minutes
60 seconds
3.28 X 60 X 60
Notice that if you set up the conversion train correctly, the units that you don’t need cancel out, leaving only the units you do need. This is how you can tell if you have done the conversion correctly. Therefore, 60 mph is the same thing as approximately 26.83 meters per second.
Time for a tricky one! Let’s say you have an object that has a surface area of 10 square inches, or 10 in
2
. How many square centimeters (cm
2
) is this?
First, we need yet another conversion factor. 1 inch = 2.54 centimeters Now we are ready to do the conversion.
10 in
2
X ( 2.54 cm)
2
=
10 X 2.54 X 2.54
=
64.516 cm
2
(1 inch
)
2
1 X 1
Did you notice the tricky part? You had to SQUARE your conversion factor since you were dealing with a
surface area measured in square inches
rather than just a length measured in plain inches. If you did not
square your conversion factor, your units would not have fully canceled! Keep this in mind if you ever have to convert volumes
measured in CUBIC feet (ft
3
) or CUBIC centimeters (cm
3
) or whatever unit is being used. In other words, you would have to CUBE your conversion factor!
Unit Conversion Questions
Set up the appropriate conversion trains and answer the questions below. 1) A typical severe thunderstorm can grow to 50,000 feet above the ground. Using the conversion factors given in the introductory portion of this lab, how tall is this thunderstorm in meters
?
________________ meters
2) A violent EF-5 tornado can have a wind speed of 300 mph. Using the conversion factors given in the introductory portion of this lab, how many meters per second
(m/sec or m s
-1
) is this? ________________ m sec
-1
3) Assume that a typical puffy white cloud – called a cumulus congestus cloud - is contained within a volume of air that is 2 kilometers tall and 3 kilometers wide in the north-south direction and 4 kilometers wide in the east-west direction. This makes the volume of this cloud 24 cubic kilometers, or 24 km
3
. How many cubic feet
(ft
3
) does this cloud occupy? Watch out, this one is a little “tricky” !
The following conversion factors will be helpful:
1 meter = 3.28 feet 1000 meters = 1 kilometer
________________ feet
3
4) If the cloud in question #3 has one half of a gram (i.e., 0.5 grams) of water for every cubic meter the cloud occupies, determine how many grams of water are in the cloud, and then convert this mass of water to gallons of water
. The following conversion factors will be helpful:
1 meter = 3.28 feet
1000 meters = 1 km 453.6 grams = 1 pound
1 gallon of water = 8.35 pounds
________________ gallons
5) A tornado passed very close to a barometer in Tulia, Texas in April of 2007. Air pressure – which is essentially the weight of the air above you – is measured in units called millibars
(mb) or inches of mercury (Hg). The air pressure fell 194 mb as the tornado passed. How many inches of mercury
(Hg) would this be? Use 29.92 inches of Hg = 1013.25 mb.
________________ inches Hg
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