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Project Grant Team
John S. Pazdar Peter A. Wursthorn Project Director Principal Investigator Capital Comm-Tech College Capital Comm-Tech College Hartford, Connecticut Hartford, Connecticut
This project was supported, in part, by the Patricia L. Hirschy National Science Foundation Principal Investigator Opinions expressed are those of the authors Asnuntuck Comm-Tech College and not necessarily those of the Foundation Enfield, Connecticut
NASA - AMATYC - NSF
SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily
implemented to support student learning in courses ranging from prealgebra through calculus.
The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 8A Exploring Shuttle Preparations:
Crawler and VAB
LTA - SPINOFF 8B Unit Analysis
LTA - SPINOFF 8C Pressure and Volume
LTA - SPINOFF 8D At What Cost? High Versus Low Pressure
K - Bottles for the Space Shuttle
Johanna Halsey - AMATYC Writing Team Member
Dutchess Community College, New York
Virginia Lee - AMATYC Writing Team Member
Brookdale Community College, New Jersey
Michael Haddad - NASA Scientist/Engineer
Kennedy Space Center, Florida
SPINOFF 8B
Unit Analysis
Converting from one unit of measurement to another or from one rate to another is a necessary and critical part of scientific work. You may have used simple divisions or multiplications to change units before, or you may have used proportions. Another method that is often quicker and easier is called unit analysis. Unit analysis involves using simple equations that relate different types of measurements. For example, you know that:
12 inches = 1 foot 16 ounces = 1 pound 60 seconds = 1 minute
- Write two other equations that you know:
These equations can be manipulated to produce equations that are equivalent to 1. Take the equation 12 inches = 1 foot, and divide both sides by one foot. This will produce:
12 inches 1 foot
1 foot 1 foot
Since the right side of the equation involves dividing a quantity by itself, we know we can rewrite the equation as: 12 inches 1 foot
We often call the fraction
12 inches 1 foot
a unit fraction , indicating that it is actually equivalent to 1.
You could just as easily have divided both sides of the equation, 1 foot = 12 inches, by 12 inches, and produced the equation: 1 foot 12 inches
The equation 16 ounces = 1 pound can be used to derive these two unit fractions:
16 ounces 1 pound
and
1 pound 16 ounces
Write the two unit fractions given by the equation, 60 seconds = 1 minute:
Write the two unit fractions given by each of the equations you gave in problem 1.
NASA - AMATYC - NSF
- Use unit analysis to convert 7200 seconds to hours.
Unit analysis can also be used to convert a rate to a different rate. For example, suppose you want to convert 60 miles per hour to feet per second. You will need to convert the miles to feet and the hours to seconds. To do this you need to know the following facts: 1 mile = 5280 feet 1 hour = 60 minutes 1 minute = 60 seconds
Once again, start with the given 60 miles per hour, which is written
60 miles 1 hour
. Then multiply by
unit fractions generated from the fact list so that the unwanted units cancel and you finish with feet second
. Note that the order in which you multiply the fractions does not matter since
multiplication is commutative. You can work with the distance measure first, and then the time measure, or vice versa. Here’s how one solution looks:
60 miles 1 hour
×
5280 feet 1 mile
×
1 hour 60 minutes
×
1 minute 60 seconds
= 88 ft / sec
- Convert 110 feet per second to miles per hour.
We can also use unit analysis for area and volume conversions. Suppose you have a surface that
has an area of 1872 in^2 and you want to convert this to ft^2. You know there are 12 inches in one foot, but if you want to convert from square inches to square feet, you need to use more than a single 12. There are 12 (^) × 12 or 144 square inches in 1 square foot. Using unit analysis, the conversion looks like this:
1872 square inches 1
×
1 square foot 144 square inches
= 13 square feet
- Convert 100 square feet to square inches.
Now suppose you have a container that has a volume of 100 ft^3 , and you want to convert this to
in^3. You know that there are 12 inches in one foot but if you want to convert from cubic feet to cubic inches, you need to use more than a single 12. There are 12 × 12 × 12 or 1728 cubic inches in 1 cubic foot. Using unit analysis, the conversion looks like this:
100 cubic feet 1
×
1728 cubic inches 1 cubic foot
= 172,800 cubic inches
NASA - AMATYC - NSF
Convert 50 cubic feet to cubic centimeters. To do this you will need to use: 1 cubic foot = 1728 cubic inches 1 cubic inch = 2.54 × 2.54 × 2.54 or 16.387064 cubic centimeters
Convert 56,633 cubic centimeters to cubic feet.
Discussion: Is there a way you can tell ahead of time whether your answer is going to have a larger or smaller numerical value? For instance, if you are converting from feet to miles, will you get a larger or smaller value? If you convert from feet to inches? Write a short paragraph explaining to a classmate how you can tell whether the value of the answer will be larger or smaller than your starting value.
NASA - AMATYC - NSF
