Unit Conversions

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MEASUREMENT

• Unit Conversions

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Today's Objectives
1) Importance of unit conversions 2) Parts of a
measurement 3) Units in equations
4) Documenting unit conversions
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Are Units important?
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Are Units important?
"The 'root cause' of the loss of the spacecraft
was the failed translation of English units into
metric units in a segment of ground-based,
navigation-related mission software, as NASA has
previously announced," said Arthur Stephenson,
chairman of the Mars Climate Orbiter Mission
Failure Investigation Board. "The failure review
board has identified other significant factors
that allowed this error to be born, and then let
it linger and propagate to the point where it
resulted in a major error in our understanding of
the spacecraft's path as it approached Mars."
http//mars.jpl.nasa.gov/msp98/orbiter/
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International System of Units (SI)
Fundamental
Derived Dimensions
Dimensions
Force N (newton) kgm/s2
Length m
Energy J (joule) Nm
Mass kg
Power W (watt) J/s
Time s
SI prefixes listed in table need to have prefixes
with a memorized for exams!!!
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U. S. Customary System (USCS)
Fundamental
Derived Dimensions
Dimensions
Mass slug lb
fs2/ft
Length ft
32.174 lb
Force lb
m
f
Energy ftlb
Time s
f
Power ftlb
f/s
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A. SI Prefix Conversions

• 1. Find the difference between the exponents of
  the two prefixes.
• 2. Move the decimal that many places.

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A. SI Prefix Conversions
Prefix
Symbol
Factor
move left
move right
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A. SI Prefix Conversions
0.2

• 1) 20 cm ______________ m
• 2) 0.032 L ______________ mL
• 3) 45 ?m ______________ nm
• 4) 805 dm ______________ km

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45,000
0.0805
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A. SI Prefix Conversions
0.532
532 m _______ km
NUMBER
UNIT
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B. Dimensional Analysis

• The Factor-Label Method
• Units, or labels are canceled, or factored out

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Converting units

• Factor label method
• Regardless of conversion, keeping track of units
  makes things come out right
• Must use conversion factors
• - The relationship between two units
• Canceling out units is a way of checking that
  your calculation is set up right!

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B. Dimensional Analysis

• Steps
• 1. Identify starting ending units.
• 2. Line up conversion factors so units cancel.
• 3. Multiply all top numbers divide by each
  bottom number.
• 4. Check units answer.

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Common conversion factors

• English Factor
• 1 gallon 4 quarts 4 qt/gal or 1gal/4 qt
• 1 mile 5280 feet 5280 ft/mile or 1 mile/5280
  ft
• 1 ton 2000 pounds 2000 lb/ton or 1 ton/2000
  lb
• Common English to Metric
• 1 liter 1.057 quarts 1.057 qt/L or 1
  L/1.057 qt or
  0.946 L/qt
• 1 kilogram 2.2 pounds 2.2 lb/kg or 1
  kg/2.2 lb
• or 0.454 kg/lb
• 1 meter 1.094 yards 1.094 yd/m or
  1m/1.094 yd
• or 0.917m/yd
• 1 inch 2.54 cm 2.54 cm/inch or 1
  in/2.54 cm

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B. Dimensional Analysis

• Lining up conversion factors

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1 in 2.54 cm
2.54 cm 2.54 cm
1
1 in 2.54 cm
1 in 1 in
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Line Mole Method
Process to convert from one unit to another
Example Convert 3.00 m to inch
? 3.00 m
100 cm
1 in
1 m
2.54 cm
ANSWER 118 in
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Line Mole Method
Process to convert from one unit to
another
Example Convert 3.00 m/s to m/hr
? 3.00 m
60 s
60 min
s
min
hr
ANSWER 10,800 m/hr
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Example Metric conversion
How many milligrams are in a kilogram?
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B. Dimensional Analysis

• How many milliliters are in 1.00 quart of milk?

1.00 qt
1 L 1.057 qt
1000 mL 1 L
946 mL
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B. Dimensional Analysis

• You have 1.5 pounds of gold. Find its volume in
  cm3 if the density of gold is 19.3 g/cm3.

1 cm3 19.3 g
1.5 lb
1 kg 2.2 lb
1000 g 1 kg
35 cm3
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B. Dimensional Analysis

• How many liters of water would fill a container
  that measures 75.0 in3?

75.0 in3
(2.54 cm)3 (1 in)3
1 L 1000 cm3
1.23 L
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B. Dimensional Analysis

• 5) Your European hairdresser wants to cut your
  hair 8.0 cm shorter. How many inches will he be
  cutting off?

8.0 cm
1 in 2.54 cm
3.1 in
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B. Dimensional Analysis

• 6) Taft football needs 550 cm for a 1st down.
  How many yards is this?

550 cm
1 in 2.54 cm
1 ft 12 in
1 yd 3 ft
6.0 yd
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B. Dimensional Analysis

• 7) A piece of wire is 1.3 m long. How many 1.5
  cm pieces can be cut from this wire?

1.3 m
100 cm 1 m
1 piece 1.5 cm
86 pieces
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As an Individual
(on a piece of paper)...
Use the Factor Label Method to convert the
following
34.6 m/s to mph
1)
15 ft3 to Liters
2)
3) Can you use FLM when converting from Celsius
to Kelvin? Why or why not?
Conversion Factors Handout
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Units in Equations
Addition/Subtraction All terms must have the
same units
Multiplication/Division Units may cancel, like
variables
Homogeneity Units on both sides of the "" sign
must be the same
Transcendental Functions (sin x , ln x , ex )
the argument (x) does not have a dimension
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Valid Units?
30 m 2
10 m
20 m
s
s
12 mile
28 mile
40 mile
hour
hour
hour
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H\classes\eng1101\fall05\lectures\spring05\en1.13
b.sketch.amy.sxi
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Converting Area and Volume
Caution Make sure the units cancel
Area 150 ft2 to yd2
1 yd
1 yd
150 ft2
(10)2 yd2
150 ft2
OR
3 ft
3 ft
(3)2 ft2
Volume 12 ft3 to Liters
(12)3 in3
(2.54)3 cm3
12 ft3
(1)3 m3
1000 L
(1)3 ft3
(1)3 in3
(100)3 cm3
1 m3
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Chemical Herbicide Spill
Line Mole Method - Example
Problem
The permeability of sand is 1.0x10-4cm/s. If a
chemical herbicide is dumped on a sandy soil, how
long (in hours) will it take for the contaminant
to reach the well 150 feet away.
Diagram
150 feet
Herbicide
Well
Permeability of Sand 1.0x10-4 cm/s t Time
(hours) 1.0x10-4 cm/s __?__ ft/hr
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Chemical Herbicide Spill
Factor Label Method - Example
Theory
Permeability Distance/Time Assumptions
Sand has constant permeability in area Herbicide
moves per permeability of sand
Solution 10-4 cm s
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Chemical Herbicide Spill
Line Mole Method - Example
Theory
Permeability Distance/Time Assumptions
Sand has constant permeability in area Herbicide
moves per permeability of sand
Solution
1 in
1 ft
60 s
60 min
1.0x10-4 cm
s
2.54 cm
12 in 1 min
1 hr
0.011811 ft/hr
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Chemical Herbicide Spill
Line Mole Method - Example
Solution
Permeability 0.011811 ft/hr Time Distance /
Permeability
t 150 ft
OR t 150 ft
hr
0.011811 ft/hr
0.011811 ft
t 12700 hours 13000 hours
How many years is that?
t 12700 hr
1 day
1 yr
1.4 yr
24 hr
365 day
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As an individual, solve... Water Tower Problem
Problem Statement

• Your home town is growing so rapidly that another
  water tower is necessary to meet the needs of the
  community. Civil and environmental engineers
  predict that the water tower will need to hold
  1.00 x 10.06 kilograms of water. The engineers
  also estimate the density of the water to be 999
  kilograms per cubic meter.

• If this tower is 50.0 meters high and spherical,
  what volume (gal) of water will the tower hold
  and what will the diameter (ft) of the tower have
  to be?

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Diagram
mass of water 1.00 x 106 kg
density of water 999 kg/m3
tower height 50.0 m
? volume of water (L)

? diameter (ft)

Theory
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r3
Volume of a sphere
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23 3 V
diameter
2 r
www.algonquin.org/pw.htm
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Assumptions
tower is spherical
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Solution
1.00 x106 kg
1000 L
1 m3
volume of water
1.00 x 106 L
1 m3
999 kg
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23 3 V
r3
diameter
2 r
Volume of a sphere
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4
1.00 x 106 L
0.035315 ft3
volume of water
3.53 x 104 ft3
1 L
3.53 x 104 ft3
23 3
diameter
2 r
40.7 ft
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http//en.wikipedia.org/wiki/Golf
Golf Ball Design
Minimum allowed diameter of a golf ball is
42.67mm Maximum Mass 45.93g
The surface usually has a pattern of 300-400
dimples designed to improve the ball's
aerodynamics.
The method of construction and materials greatly
affect the ball's playing characteristics such as
distance, trajectory, spin and feel.
Have a two-, three-, or four-layer design
constructed from various synthetic materials
Harder materials, such as Surlyn, usually result
in the ball's traveling longer distances,
Softer covers, such as Balata, tend to generate
higher spin, more "feel" and greater stopping
potential.
Golf balls are separated into three groups
depending on their construction two-, three-, or
four-piece covers.
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http//en.wikipedia.org/wiki/Golf
Golf Ball Design
Minimum allowed diameter of a golf ball is
42.67mm
Assuming a golf ball has a spherical shape
What is the golf ball diameter in inches? What
is the volume of a golf ball in cubic centimeters
and cubic inches?
Maximum Mass 45.93g
What is the mass of a golf ball in pounds? What
is the density of a golf ball in g/cm3 and
lb/in3?
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Golf Shafts
Golf shafts are what connects the grip to the
golf head
The profile of the golf shaft is circular in
shape and is usually thicker at the grip end than
at the club head end.
Any strong and light material may be used to make
the golf shaft.
Almost all shafts today are made of either
graphite or tempered steel
The shaft is a tapered tube made of metal
(usually steel), or graphite fiber. The shaft is
roughly 1/2 inch in diameter (12 mm) near the
grip and between 35 to 45 inches (89-115 cm) in
length.
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Golf Shafts
Almost all shafts today are made of either
graphite or tempered steel
Graphite 2.09-2.23 g/cm3
Steel 7,861.093 kg/m³ (0.284 lb/in³)
How much would the shaft of a golf club weigh in
pounds if it were constructed from graphite or
steel?
Assume
Shaft Diameter 1/2 inch and solid Shaft
Length 40 inches
Why would you choose a graphite club over a steel
club or vice versa?
What is tempered steel?
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