I II III Unit Conversions MEASUREMENT. Are Units important? 3

I

II

III

Unit Conversions

MEASUREMENT

Are Units important?

3

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/ 4

International System of Units (SI)

Fundamental

Dimensions: Derived Dimensions:

Length = m Force = N (newton) = kg*m/s2

Mass = kg Energy = J (joule) = N*m

Time = s Power = W (watt) = J/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

Dimensions: Derived Dimensions:

Length = ft Mass = slug = lb f*s2/ft = 32.174 lb

m Force = lb f

Energy = ft*lb f Time = s

Power = ft*lb 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.

To the leftor right?


mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

mo

ve le

ft

mo

ve r

igh

t BASE UNIT --- 100


1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

=


NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532

3

3

cm

gcm

B. Dimensional Analysis

The “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g

Converting units

Factor label methodFactor 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!


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.

Common conversion factors English FactorFactor

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


Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

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?

mgg

mg

kg

gkg

mgg

gkg

000,000,11000

1

10001

10001

10001


How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L


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

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g


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

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L

1000 cm3


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

cm in


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

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft


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= 86 pieces

m pieces

1 piece

1.5 cm

As an Individual (on a piece of paper)...

Use the Factor Label Method to convert the following:

1) 34.6 m/s to mph

2) 15 ft3 to Liters

3) Can you use FLM when converting from Celsius to Kelvin? Why or why not?

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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?

10 m 20 m 30 m 2 s s

12 mile 28 mile 40 mile hour hour hour

8 H:\classes\eng1101\fall05\lectures\spring05\en1.13b.sketch.amy.sxi

Converting Area and Volume

Caution: Make sure the units cancel

Area: 150 ft2 to yd2

150 ft2 1 yd 1 yd 150 ft2 (10)2 yd2 OR 3 ft 3 ft (3)2 ft2

Volume: 12 ft3 to Liters

12 ft3 (12)3 in3 (2.54)3 cm3 (1)3 m3 1000 L (1)3 ft3 (1)3 in3 (100)3 cm3 1 m3

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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: 4 Volume of a sphere r3

3

diameter 2 r 23 3 V www.algonquin.org/pw.htm

4

Assumptions: • tower is spherical

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Solution:

1.00 x106 kg 1 m3 1000 L volume of water = = 1.00 x 106 L 999 kg 1 m3

4 Volume of a sphere r3 diameter 2 r 23 3 V

3 4

1.00 x 106 L 0.035315 ft3 volume of water = = 3.53 x 104 ft3 1 L

3.53 x 104 ft3 diameter 2 r 23 3 40.7 ft 4

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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? 20

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I II III Unit Conversions MEASUREMENT. Are Units important? 3