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

1

Units Conversions

Chapter 14

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

2

Unit Historyinch width of your thumb

foot originally the length of your foot, now

greater

yard three feet, from nose to middle finger

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Unit Historyfathom 6 feet, arm span

mile 1000 paces, 5280 feet

furlong 220 yards

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14.7 Temperature Scales

32C5

9F oo 32F

9

5C oo

15.273K Co

Example:

T = 77 K

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Mass Mass the quantity of matter in an object

the measurement of the inertia

measured in kilograms (kg)

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WeightWeightthe 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

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Engineering Mass and Engineering Mass and WeightWeight

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

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1 lbf = 32.2 lbm ft/s2

WeightMass

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In-class Assignment

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Chapter 15

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Dimensions

Dimension Symbol

Length

Mass

time

force

electric current

absolute temperature

luminous intensity

[L]

[M]

[T]

[F]

[A]

[

/]

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Base Units

Fundamental Dimension Base Unit

time

electric current


luminous intensity

amount of substance

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

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The International System of Units (SI)


length [L]

mass [M]

time [T]

electric current [A]

absolute temperature []

luminous intensity [l]

amount of substance [n]

meter (m)

kilogram (kg)

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

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What are these things?

See fundamentalSI.ppt for information about these 'things'

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SI Prefixes

nano

micro

milli

centi

deci

deka

hecto

kilo

mega

giga

PrefixDecimal

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

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Supplementary SI Dimensions

Supplementary Dimension Base Unit

plane angle

solid angle

radian (rad)

steradian (sr)

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Force = (mass) (acceleration)

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U.S. Customary System of Units (USCS)


length [L]

force [F]

time [T]

foot (ft)

pound (lb)

second (sec)

Derived Dimension Unit Definition

mass [FT2/L] slug lbf sec2/ft

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Force = (mass) (acceleration)

2f ft/secslug1lb1

F = ma

W = mg

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American Engineering System of Units (AES)


length

mass

force

time

electric charge [Q]


luminous intensity

amount of substance

foot (ft)

pound (lbm)

pound (lbf)

second (sec)

coulomb (C)

degree Rankine (oR)

candela (cd)

mole (mol)

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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

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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..

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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.

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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

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AES and Newton’s Law

Must maintain dimensional homogeneity:

Now we have lbf = lbf

See gcderived.ppt for the derivation of gc

cg

maF

2f

mc

sec lb

ft lb32.174g

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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?

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Reality Check...

Are units really important?Is checking your work and your team’s work really important?

Mars Lander (ABC news)Mars Lander (NASA)

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Homework

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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?

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A Solution

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

C deg 3.73

F deg )80212(

C deg

F deg 8.1

C deg 1

x

x

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A Solution

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

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

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