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Units Conversions

Units Conversions. Chapter 14. It is absolutely essential to report units with the number answers. Unit History. inch width of your thumb foot originally the length of your foot, now greater yard three feet, from nose to middle finger. Unit History. fathom 6 feet, arm span mile

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Units Conversions

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  1. Units Conversions Chapter 14 It is absolutely essential to report units with the number answers.

  2. Unit History • inch • width of your thumb • foot • originally the length of your foot, now greater • yard • three feet, from nose to middle finger

  3. Unit History • fathom • 6 feet, arm span • mile • 1000 paces, 5280 feet • furlong • 220 yards

  4. 14.7 Temperature Scales Example: T = 77 K

  5. Mass • the quantity of matter in an object • the measurement of the inertia • measured in kilograms (kg)

  6. Weight • the force upon an object due to gravity • Weight = Mass  Acceleration of gravity Fg = mg • measured in Newtons (N) in the metric system or pounds (lb) in the British system

  7. Engineering Mass and Weight • Pound-Mass • lbm • One pound-mass weighs 1 pound. • 1 slug = 32.2 lbm • Pound-Force • lbf • It is the same as a pound (lb). • 1 lbf = 1 lb

  8. 1 lbf = 32.2 lbm ft/s2

  9. In-class Assignment

  10. Chapter 15

  11. Dimension Symbol Length Mass time force electric current absolute temperature luminous intensity [L] [M] [T] [F] [A] [q] [/] Dimensions

  12. Base Unit Fundamental Dimension time electric current absolute temperature luminous intensity amount of substance second (s) ampere (A) kelvin (K) candela (cd) mole (mol) Base Units

  13. Fundamental Dimension Base Unit length [L] mass [M] time [T] electric current [A] absolute temperature [q] luminous intensity [l] amount of substance [n] meter (m) kilogram (kg) second (s) ampere (A) kelvin (K) candela (cd) mole (mol) The International System of Units (SI)

  14. What are these things? • See fundamentalSI.ppt for information about these 'things'

  15. Decimal Multiplier Prefix Symbol nano micro milli centi deci deka hecto kilo mega giga 10-9 10-6 10-3 10-2 10-1 10+1 10+2 10+3 10+6 10+9 n m m c d da h k M G SI Prefixes

  16. Supplementary SI Dimensions Supplementary Dimension Base Unit plane angle solid angle radian (rad) steradian (sr)

  17. Force = (mass) (acceleration)

  18. Fundamental Dimension Base Unit length [L] force [F] time [T] foot (ft) pound (lb) second (sec) U.S. Customary System of Units (USCS) Derived Dimension Unit Definition lbf sec2/ft mass [FT2/L] slug

  19. Force = (mass) (acceleration) F = ma W = mg

  20. Fundamental Dimension Base Unit length mass force time electric charge [Q] absolute temperature luminous intensity amount of substance foot (ft) pound (lbm) pound (lbf) second (sec) coulomb (C) degree Rankine (oR) candela (cd) mole (mol) American Engineering System of Units (AES)

  21. Converting Between Foot and Meter • To convert from foot to meter, multiply by 3.048* E-01 • To convert from meter to foot, multiply by (3.048* E-01)-1

  22. Thought Item • Concerning the previous slide, which of the following is true? a. There are exactly 0.3048 m/ft. b. There are exactly 0.3048 ft/m. c. Neither a not b. • Hint: Think about this physically..

  23. American Engineering System • Note, there is a problem when we use the same unit(“pound”, meaning lbf and lbm) to describe two different dimensions. • Newton's Second Law: F = ma  1 lbf = 1 lbm ft/s2 ??? NO!!! • Must have conservation of units.

  24. Conservation of Units • Principle of conservation of units: • units on the left side of an equation must be the same as those on the right side of an equation • dimensional homogeneity

  25. AES and Newton’s Law • Must maintain dimensional homogeneity: • Now we have lbf = lbf • See gcderived.ppt for the derivation of gc

  26. Pairs Exercise (5 min.) • Use a different pairing... • The force of wind acting on a body can be computed by the formula: F = 0.00256 Cd V2 A where: F = wind force in lbf , Cd= drag coefficient (no units), V = wind velocity in miles per hour and A = projected area in ft2 • Is this dimensionally homogeneous? • What are the dimensions of 0.00256?

  27. Are units really important? Is checking your work and your team’s work really important? Mars Lander (ABC news) Mars Lander (NASA) Reality Check...

  28. Homework

  29. Temperature Exercise • You take water from the faucet (80 oF) and bring it to a boil on the stove. • What is the temperature change in oC? • What is the initial temperature in oC?

  30. A Solution • For the temperature change, the best solution process is to use degree equivalents

  31. A Solution • For the temperature value we use temperature conversion: oC = (5/9)*(80 - 32) = 26.7 oC

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