MEASUREMENT

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Unit Conversions

MEASUREMENT

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/ 4

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


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.


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 =


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

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: Herbicide 150 feet 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: 1.0x10-4 cm 1 in 1 ft 60 s 60 min

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: 4 Volume of a sphere r3

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

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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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Roentgen

Roentgen

Pronounced rent’gen with a hard “g” Limitations

only applies to photons only applies in air only applies to energies less than 3

MeV

Named after Wilhelm C. Roentgen (thus the abbr... is capital “R”)

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rad

rad

1 rad = 1 Roentgen

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rem

rem

The unit of dose equivalent for any type of ionizing radiation absorbed by body tissue in terms of estimated biological effect - Unit of dose equivalent

Dose in health record is in units of rem

1 rem = 1 Roentgen

Roentgen Equivalent Man

Quality Factor (Q)

The specific value that accounts for the ability of different types of ionizing radiation to cause varying degrees of biological damage X-rays, gamma rays, & beta particles 1 Neutrons & High energy protons

10 Alpha Particles 20

Curie (Ci)

Radiation hazard does not solely depend on the activity. It also depends on the type of decay (alpha, beta, photon, etc.)

Named in honor of Pierre Curie

SI Radiation Protection Units

Becquerel (Bq) for Curie 1 Ci = 3.7 x 1010 Bq

Gray (Gy) for rad 1 Gy = 100 rad

Sievert (Sv) for rem 1 Sv = 100 rem

Unit Analysis

BASE UNIT CONVERSION TABLE

Unit Unit Conversion

1 Bq 2.7 x 10-11 Ci

1 Ci 3.7 x 1010 Bq 1 Bq 1 dis/sec

1 dis/sec2.7 x 10-11 Ci

1 Ci 3.7 x 1010 dis/sec

Unit Analysis (Con’t.)

BASE UNIT CONVERSION TABLE

Unit Unit Conversion

1 rem 0.01 Sv

1 Sv 100 rem

1 rad 0.01 Gy

1 Gy 100 rad

1 R 2.58 x 10-4 C/kg

1 meter 3.28 ft (39.37in)

Summary

Radiation Protection unit definitions (including SI units)

Unit Prefixes Unit conversions

Old Terms Roentgen-Based on the quantity of electrical

charges produced in air by X or Gamma photons 1R=2 billion pr

RAD-Radiation Absorbed Dose is the work energy resulting from the absorption of one ROENTGEN or 6.24 E5 Mev

More Old Terms REM- Roentgen Equivalent Mammal is equal to the

absorbed does in RADS multiplied by a quality factor

Quality Factors Beta = 1

Gamma & X ray photons = 1 Alpha = 10

Neutrons = 20

New Terms sort of

International Units have replaced the RAD and REM

GRAY (Gy) = 100 RAD

SIEVERT (Sv) = 100 REM

Same Quality Factors apply to the Sv

Units of Radioactivity Curie (Ci) = 2.22 E12 dpm or 3.7E10

dps Becquerel (Bq) = 1 dps Maximum Dose/year = 5 REM or 50

mSv Maximum Dose/year for Declared

Pregnant Woman & Minors= 0.5 REM or 5 mSv

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