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Units Conversions

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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
- 1000 paces, 5280 feet

- furlong
- 220 yards

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
- 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

Symbol

Length

Mass

time

force

electric current

absolute temperature

luminous intensity

[L]

[M]

[T]

[F]

[A]

[q]

[/]

DimensionsFundamental Dimension

time

electric current

absolute temperature

luminous intensity

amount of substance

second (s)

ampere (A)

kelvin (K)

candela (cd)

mole (mol)

Base UnitsBase 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?

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

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 PrefixesSupplementary SI Dimensions

Supplementary Dimension

Base Unit

plane angle

solid angle

radian (rad)

steradian (sr)

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

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

- 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..

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?

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

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Reality Check...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