It is absolutely essential to report units with the number answers. Chapter 14 Units Conversions This is truly a joint class between the instructors. This may seem like a lot of slides for half of a class, but over half of them are quick lists that do not require much discussion. The supplements fundamentalSI.ppt and gcderived.ppt are linked on the web, so students can access them that way. Also, in an attempt to keep the students on task and avoid them doing the class exercises in advance, many of the numerical/unit values in the last two pairs exercises have been replaces with ‘?’ in the student version. It is absolutely essential to report units with the number answers.

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

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

14.7 Temperature Scales Example: T = 77 K

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

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

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

1 lbf = 32.2 lbm ft/s2

In-class Assignment

Chapter 15

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

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

The International System of Units (SI) 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)

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

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

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

Force = (mass) (acceleration)

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

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

American Engineering System of Units (AES) 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)

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

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.. Answer: A

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.

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

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

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?

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

Homework

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?

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

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