Dimensional Analysis, Unit Conversions, and Course Overview Notes

Strategy for English and Metric Dimensional Analysis

  • General conversion pathways:
    • English to Metric conversion workflow:
    • Start with given English units.
    • Convert within the English system to reach inches (or pounds/quarts depending on the physical quantity).
    • Use the exact metric bridge conversion factor: 1 inch=2.54 cm1\,\text{inch} = 2.54\,\text{cm}.
    • Convert within the metric system from centimeters (or grams/liters) to the target metric unit.
    • Metric to English conversion workflow:
    • Start with given metric units.
    • Convert within the metric system to base units (centimeters, grams, or liters).
    • Use the bridge conversion factor to convert to English base units (e.g., centimeters to inches).
    • Convert within the English system from inches (or pounds/quarts) to the target English unit.
  • Examination conversion rules:
    • All English-to-English conversions (e.g., inches to feet, feet to miles, feet to yards, ounces to pounds) are provided on examinations.
    • Metric-to-English conversions are provided on examinations, though the provided conversion factor may require multi-step dimensional analysis rather than direct conversion.
    • Metric system prefix conversions (e.g., centi-, milli-, kilo-) must be memorized by students.

Speed Limit Unit Conversion Analysis

  • Problem Statement: A car is traveling at 28.0 m/s28.0\,\text{m/s}. Determine if the vehicle is violating a speed limit of 65 mph65\,\text{mph}.

  • Standard Conversion Factors Provided:

    • 1 inch=2.54 cm1\,\text{inch} = 2.54\,\text{cm}
    • 12 inches=1 foot12\,\text{inches} = 1\,\text{foot}
    • 5280 feet=1 mile5280\,\text{feet} = 1\,\text{mile}
    • 1 cm=0.01 m1\,\text{cm} = 0.01\,\text{m} (or 1 m=100 cm1\,\text{m} = 100\,\text{cm})
    • 60 seconds=1 minute60\,\text{seconds} = 1\,\text{minute}, 60 minutes=1 hour60\,\text{minutes} = 1\,\text{hour} →3600 seconds=1 hour\rightarrow 3600\,\text{seconds} = 1\,\text{hour}

  • Step-by-Step Dimensional Analysis:

    • Step 1 (Meters to Centimeters): Multiply by 1 cm0.01 m\frac{1\,\text{cm}}{0.01\,\text{m}}.
    • Step 2 (Centimeters to Inches): Multiply by 1 inch2.54 cm\frac{1\,\text{inch}}{2.54\,\text{cm}}.
    • Step 3 (Inches to Feet): Multiply by $ Kudash\frac{1\,\text{foot}}{12\,\text{inches}}.\n - Step 4 (Feet to Miles): Multiply by \frac{1\,\text{mile}}{5280\,\text{feet}}.\n - Step 5 (Seconds to Hours): Multiply by \frac{3600\,\text{s}}{1\,\text{hour}}.\n\n- Full Dimensional Setup:\n  \frac{28.0\,\text{m}}{1\,\text{s}} \times \frac{1\,\text{cm}}{0.01\,\text{m}} \times \frac{1\,\text{inch}}{2.54\,\text{cm}} \times \frac{1\,\text{foot}}{12\,\text{inches}} \times \frac{1\,\text{mile}}{5280\,\text{feet}} \times \frac{3600\,\text{s}}{1\,\text{hour}}\n\n- Calculation & Significant Figures:\n - Raw numerical result: 62.636…\,\text{mph}.\n - Significant figure rules for conversions:\n - The initial value 28.0\,\text{m/s} has 3 significant figures.\n - 1\,\text{inch} = 2.54\,\text{cm} is an exact definition by international agreement, possessing an infinite number of significant figures.\n - English unit definitions (12\,\text{in/ft},,5280\,\text{ft/mi})andmetricdefinitions() and metric definitions (1\,\text{cm} = 0.01\,\text{m}) are exact and have infinite significant figures.\n - The limiting measurement is 28.0\,\text{m/s}, which contains 3 significant figures.\n - Final rounded velocity: 62.6\,\text{mph}.\n\n- Conclusion: The vehicle is traveling at 62.6\,\text{mph},whichdoesnotexceedthepostedspeedlimitof, which does not exceed the posted speed limit of65\,\text{mph}.\n\n# Metric to English Conversion Rules and Significant Figures\n\n- Exact vs. Measured Conversion Factors:\n - Standard Metric-to-English conversions are empirical measurements rather than defined quantities and contain finite significant figures.\n - Non-exact conversion examples:\n - 1\,\text{lb} = 454\,\text{g}:Thevalue: The value1\,\text{lb}isexact(infinitesigfigs),whileis exact (infinite sig figs), while454\,\text{g} contains 3 significant figures.\n - 1\,\text{qt} = 1.057\,\text{L}:Thevalue: The value1\,\text{qt}isexact(infinitesigfigs),whileis exact (infinite sig figs), while1.057\,\text{L} contains 4 significant figures.\n - Exception to the rule: 1\,\text{inch} = 2.54\,\text{cm} was redefined internationally as an exact definition and has infinite significant figures.\n\n# Fuel Economy Conversion Problem\n\n- Problem Statement: Convert a fuel efficiency rating of 29\,\text{mpg}(milespergallon)intokilometersperliter((miles per gallon) into kilometers per liter (\text{km/L}).\n\n- Conversion Factors Used:\n - 1\,\text{mile} = 5280\,\text{feet}\n - 1\,\text{foot} = 12\,\text{inches}\n - 1\,\text{inch} = 2.54\,\text{cm}\n - 1\,\text{cm} = 0.01\,\text{m}\n - 1000\,\text{m} = 1\,\text{km}\n - 1\,\text{gallon} = 4\,\text{quarts}\n - 1.057\,\text{quarts} = 1\,\text{liter}\n\n- Dimensional Analysis Execution:\n - Distance Conversion:\n    \frac{29\,\text{miles}}{1\,\text{gallon}} \times \frac{5280\,\text{feet}}{1\,\text{mile}} \times \frac{12\,\text{inches}}{1\,\text{foot}} \times \frac{2.54\,\text{cm}}{1\,\text{inch}} \times \frac{0.01\,\text{m}}{1\,\text{cm}} \times \frac{1\,\text{km}}{1000\,\text{m}}\n - Volume Conversion:\n    \times \frac{1\,\text{gallon}}{4\,\text{quarts}} \times \frac{1.057\,\text{quarts}}{1\,\text{liter}}\n\n- Calculation & Significant Figures:\n - Unrounded calculated output: 12.33\,\text{km/L}.\n - Significant figure analysis:\n - 29\,\text{mpg} contains 2 significant figures.\n - 1.057\,\text{quarts} = 1\,\text{liter} contains 4 significant figures.\n - Pure definitions have infinite significant figures.\n - Smallest count of significant figures among terms is 2.\n - Final rounded result: 12\,\text{km/L}.\n\n# Derived Unit Conversions: Volume and Area\n\n- Fundamental Volume Equivalence:\n - 1\,\text{mL} = 1\,\text{cm}^3 (1 milliliter is defined as exactly 1 cubic centimeter).\n - Essential for laboratory conversions where liquid volumes are measured in milliliters using graduated cylinders, but physics formulas require standard SI cubic meters (\text{m}^3).\n\n- Cubing Conversion Rules:\n - When converting derived volumetric units, both the unit label and the numerical conversion factor must be cubed.\n - Derivation of metric linear-to-cubic conversion factor:\n - Linear relation: 1\,\text{cm} = 0.01\,\text{m} = 10^{-2}\,\text{m}\n - Cubic relation: (1\,\text{cm})^3 = (0.01\,\text{m})^3 = (10^{-2}\,\text{m})^3 = 1 \times 10^{-6}\,\text{m}^3\n\n- Sample Volume Calculation:\n - Problem: Convert a volume of 25.0\,\text{mL}tocubicmeters(to cubic meters (\text{m}^3).\n - Conversion setup:\n    25.0\,\text{mL} = 25.0\,\text{cm}^3\n    25.0\,\text{cm}^3 \times \frac{1 \times 10^{-6}\,\text{m}^3}{1\,\text{cm}^3} = 25.0 \times 10^{-6}\,\text{m}^3\n - Final scientific notation: 2.5 \times 10^{-5}\,\text{m}^3\n\n- Squaring Conversion Rules for Area:\n - For area units (e.g., \text{cm}^2toto\text{m}^2), square both the numerical conversion factor and the units:\n    (1\,\text{cm})^2 = (0.01\,\text{m})^2 = 1 \times 10^{-4}\,\text{m}^2$$

Instructor Background and Personal History

  • Geographic Chronology:

    • Born: Great Lakes Naval Base outside Chicago, Illinois.
    • Early Childhood: Memphis, Tennessee (acquired initial Southern accent).
    • Early Elementary School: Jacksonville, Florida.
    • Late Elementary / Middle School: New Jersey (suppressed Southern accent after being teased).
    • 4th Grade through 8th Grade: West Des Moines, Iowa.
    • High School: Pekin, Illinois (outside Peoria, central Illinois).
    • Undergraduate Studies: Attended college in Kirksville, Missouri for 4 years.
    • Graduate Studies: University of Arkansas in Fayetteville for 7 years (re-acquired Southern accent).
    • Postdoctoral Fellowship: University of Michigan in Ann Arbor, Michigan (2-year postdoctoral fellowship in nuclear medicine; specialized background in nuclear applications).
    • Long-term Employment: Joined Briar Cliff University faculty in Sioux City, Iowa in 1999.

  • Family & Relocation Details:

    • Sophomore year college transition: Parents relocated to Seattle, Washington after Christmas. Sister remained in Illinois with a family friend to finish her senior year of high school before attending the same Missouri college. Spent 2.5 months living in Seattle that summer.
    • Son 1: Computer engineer residing in Austin, Texas.
    • Son 2: Department of Defense contractor with the 185th Air Guard in Sioux City, living in Colorado Springs performing computer networking work for the Department of Defense.

Student Introductions and Course Goals

  • Student Profiles:
    • Jana: 19 years old, from Barcelona, Spain. Studying in the U.S. and playing soccer; taking physics to transfer into Biomedical Engineering.
    • Axel: Aiming for a Ph.D. in Chemistry / Pharmaceutical Chemistry to develop improved medications.
    • Cameron: From Sioux City; taking physics to pursue studies in Kinesiology.
    • Ruth Pineda: 20 years old, from Denison; taking physics as a prerequisite for dental school.
    • Jocelyn: From Sioux City, graduate of East High School; currently undecided on major and taking general exploratory courses.
    • Jeffrey: From Kansas City, Missouri (raised primarily in Sioux City); taking physics to satisfy engineering prerequisites for transfer next year.
    • John: From Sioux City; completing general education requirements to transfer to Iowa State University for Geology.
    • Evan: Lived in Sioux City; completing general education credits to transfer to University of Northern Iowa (UNI) for Cybersecurity.
    • Nam: International student from Vietnam.
    • Daniel: International student from Veneto / Venice, Italy; taking course to fill general education credits and explore fields.

Institutional Announcements

  • Iowa State University Transfer Visit:
    • A representative associated with Iowa State University contacted the department regarding 12 Western Iowa Tech (WIT) students transferring into engineering at Iowa State University.
    • The representative requested to speak with physics students (targeting calculus-based engineering physics students, but opening the presentation to all physics students).
    • Scheduled visit: Upcoming Tuesday (in one or two weeks).