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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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Units conversions
Units Conversions

Chapter 14

It is absolutely essential to report units with the number answers.


Unit history
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 history1
Unit History

  • fathom

    • 6 feet, arm span

  • mile

    • 1000 paces, 5280 feet

  • furlong

    • 220 yards


14 7 temperature scales
14.7 Temperature Scales

Example:

T = 77 K


Units conversions
Mass

  • the quantity of matter in an object

  • the measurement of the inertia

  • measured in kilograms (kg)


Weight
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


Engineering mass and weight
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 lb f 32 2 lb m ft s 2
1 lbf = 32.2 lbm ft/s2




Dimensions

Dimension

Symbol

Length

Mass

time

force

electric current

absolute temperature

luminous intensity

[L]

[M]

[T]

[F]

[A]

[q]

[/]

Dimensions


Base units

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


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)

The International System of Units (SI)


What are these things
What are these things?

  • See fundamentalSI.ppt for information about these 'things'


Si prefixes

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


Supplementary si dimensions
Supplementary SI Dimensions

Supplementary Dimension

Base Unit

plane angle

solid angle

radian (rad)

steradian (sr)



U s customary system of units uscs

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



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)

American Engineering System of Units (AES)


Converting between foot and meter
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
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..


American engineering system
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
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
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
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)

Reality Check...



Temperature exercise
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
A Solution

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


A solution1
A Solution

  • For the temperature value we use temperature conversion:

    oC = (5/9)*(80 - 32) = 26.7 oC


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