Units of Measure, Historical Progression• Historical Units, “pre-science” measurement

– Human, plants, and animals as standards

– No tape measure … so use what’s readily available

• Introduction of Metric System

– Eliminate inconsistencies, odd multiples, inconvenient units

– Towards a global system, international acceptance

• Deployment of “Universal” natural constants

– Speed of Light available to anybody, anywhere … including E.T.

• Accuracy, Precision, Significant figures

– Definitions and Applications

Units of Measure• Mass

– Historical definitions & difficulties

– Mass versus Weight, Planetary influence

• Length

– Historical definitions & difficulties

– Modern Definition

• Time

– Historical Definitions & difficulties

– Modern definitions

• Combination Measurements

– Area and volume from lengths (2500 sqft home, 1 acre-foot)

– Density (grams/cm^3) from mass and volume

– Speed (miles/hour) from distance and time

Definition of Mass, “grains”

• First “standard”

• Easy access

• Consistent weight ?

• What variety to use?

• Inconveniently small

• Persists to this day

– Pharmacy

– Ammunition

• 7000 gr. ≡ 1 pound

Mass• “Grain” originated from a Barley grain (now defined as 64.8

milligrams), and still used in pharmacy ( 5 grains of Aspirin) and firearms (M-16 rifle bullet weighs 55 grains)

• “Carat” is a unit of mass still used for gems (equals 200 milligrams). The word is based on Greek keration (fruit of the carob). Carob seeds were once used as weights on scales due to a reputation for having uniform weight.

• “Avoirdupois pound” invented by London merchants in 1303 equals 7000 grains. 16 ounce/pound, 1 ounce = 28.3495 grams

• “Troy Pound” and “Troy Ounces” (12 per pound) still used in precious metals trade. One Troy Ounce = 31.1035 grams

• “Stone” is a unit of mass formerly used in parts of the United Kingdom. It is equal to 14 pounds avoirdupois, and 8 stone make a hundredweight in the Imperial system

• “Apothecary” or Pharmacy system of units, mostly phased out. Still used for shotgun shells. One dram= 3.888 grams

Barley, original standard for “Grain”

BARLEY Number of Grams grams grainsGrains of Weight per Grain per pound

Laura 100 4.040 0.0404 11,238

Julie 100 3.362 0.0336 13,504Elise 100 3.483 0.0348 13,035Nancy 100 3.957 0.0396 11,473Kan 100 3.880 0.0388 11,701Jacob 100 3.764 0.0376 12,062Annie 100 3.473 0.0347 13,072Oye 100 3.829 0.0383 11,857Connie 100 3.759 0.0376 12,078Average 100.00 3.73 0.0373 12,224Maximum 100.00 4.04 0.0404 13,504Miimum 100.00 3.36 0.0336 11,238Range (Max-Min) 0.00 0.68 0.0068 2,266Range % of Average 18%

Hard Wheat GrainsOld standard of measure for “London Pound”

HARD WHEAT Number of Grams grams grains

(for Bread Flour) Grains of Weight per Grain per poundKane 100.0 3.0490 0.0305 14,890Laura 100.0 2.9530 0.0295 15,374Yvonne 100.0 3.2250 0.0323 14,078Oye 100.0 3.1530 0.0315 14,399Annie 100.0 3.4940 0.0349 12,994Alvaro 100.0 3.3200 0.0332 13,675Julie 100.0 3.0300 0.0303 14,983Elise 100.0 3.2880 0.0329 13,808Uyen 100.0 3.162 0.0316 14,358Tommy 100.0 3.182 0.0318 14,268Average 100.00 3.19 0.0319 14,283Maximum 100.00 3.49 0.0349 15,374Miimum 100.00 2.95 0.0295 12,994Range (Max-Min) 0.00 0.54 0.0054 2,380Range % of Average 17%

Spelt (Ancient Wheat) grains

SPELT Number of Grams grams grainsGrains of Weight per Grain per pound

kane 100.0 4.376 0.0438 10,375

laura 100.0 4.080 0.0408 11,127alvaro 100.0 3.991 0.0399 11,376oye 100.0 3.992 0.0399 11,373amnnie 100.0 3.827 0.0383 11,863elise 100.0 4.355 0.0436 10,425Julie 100.0 4.043 0.0404 11,229Elias 100.0 4.035 0.0404 11,252Tommy 100.0 3.491 0.0349 13,005Average 100.00 4.02 0.0402 11,336Maximum 100.00 4.38 0.0438 13,005Miimum 100.00 3.49 0.0349 10,375Range (Max-Min) 0.00 0.89 0.0089 2,630Range % of Average 22%

Grain used in pharmacy, but being phased out

• Standard dose for aspirin is 5 grains, 325mg

Winchester 30-30

• Introduced 1895 for model 1894 Winchester and still one of the most popular cartridges after 115 years

– Why “30-30” designation?

– 30 caliber (0.300 inch)

– 30 grains of gunpowder, 170 grain lead bullet

• Similar description 45-70 Springfield & 30-40 US Krag

• The “grain” has survived as a unit of measure

Which pound was it ?…• Avoirdupois Pound, from England

– 16 ounces per pound, still in use … mostly USA

– 1 pound ≡ 7,000 grains of Barley (originally)• Troy Pound, from Troyes in France

– 12 Troy ounces per Troy pound

– 1 Troy Pound ≡ 5,760 grains of Barley

– At least the grains were the same kind!• Tower Pound

– Tower Pound = 7200 grains of Wheat … not Barley

– 7200 grains of wheat ≈ 5400 grains of Barley

What’s in a pound?• Merchant’s Pound

– 9600 wheat grains

– 16 Tower ounces

– 15 Troy ounces

• London Pound

– 7200 Troy (wheat) grains

– Pennyweight = 22.5 Troy grains

• Wool Pound

– Wool Pound = 6,992 grains (probably Barley)

• Roman Libra (Latin pound), = 327 grams

– 12 uncia (ounces) per libra … Libra gives abbreviation “lb”

Competing “Pound” definitions

Apothecary (Pharmacy) Mass“Grain” a constant value in old systems

Pharmacy pound unlike other “pound” definitions

Apothecary (Pharmacy) VolumeGallon is “Imperial” size from UK

Other definitions related to Pounds

• Shotgun Gauges, based on weight of lead

– 12 gauge = 12 lead balls per pound

– 20 gauge = 20 lead balls per pound

• Money defined by weights of silver

– 1 pound of silver = 1 pound sterling

• Today 1 troy ounce of Ag worth ≈ $10

• 12 troy ounce = 1 troy pound ≈ $120 per pound for silver in today’s bullion market. British Pound Sterling worth about $2, so Silver has appreciated 60x

Mass was a mess!• >12 variations on the pound• Other units of measure add to confusion

– Drams, pennyweights, Stones, tons …

• International trade a problem

– A “pound” is not always the same

• Standardization difficult

– Same names for different metrics (ounce)

• A better method was needed ….

– And helped give rise to the “metric system”

Definitions of Temperature

• Fahrenheit scale

– Arbitrary values

• Centigrade scale

– Based on water

• Kelvin scale

– Zero not arbitrary

– Same increments as centigrade = Celsius

Defining Temperature• Temperature scales are arbitrary

– Fahrenheit Scale from year 1724

• 0oF based on a mixture of ice, water, salt– Alternatives include history of coldest climate at 0 degrees

• 100oF based on temperature inside horse’s mouth– Alternatives include use of armpit=96oF,“too hot to work”=100oF

• Water freeze at 32oF, boils at 212oF

• Handy size degree, scales divisible by 4, avoids fractions

– Celsius (Centigrade) scale based on water

• Established in 1744, the work of Anders Celsius

• 0oC defined as freezing point of water

• 100oC defined as boiling point of water

Arbitrary scales = problematic• Fahrenheit, Celsius require negative values

– Inconvenient complexity from minus temperatures

• Temperature relationships arbitrary, ratios don’t make sense

– 100oF (or 100oC) not “twice as hot” as 50o

– 10oF is not “infinitely hotter” than 0oF

• Needed: a new scale: linear, proportional … with a “true zero”

– Solution to define “absolute zero” as absence of all motion

– Kelvin scale resolves the zero problem

– Absolute zero translates to water freezing at 273oK, boils at 373oK

– Twice the Kelvin temperature IS “twice as hot”

– Just add 273 to degrees centigrade to get degrees Kelvin

– For Fahrenheit Abs zero = -460oF, “Rankine” scale (rarely used)

Kelvin Scale (oC + 273)utilizes “true zero”, temperatures proportional

Exact temperature relationships

Temperature Summary• Fahrenheit named for German physicist Gabriel Fahrenheit (

1686–1736), proposed in 1724. Several versions of it’s creation include using the mouth of a horse to establish 100 degrees. In this scale, freezing point of water is 32 degrees, and the boiling point is 212 degrees. It’s use continues partly due to smaller increments than Centigrade, which helps avoid fractions.

• Centigrade or Celsius scale is based on properties of water, 0 is defined as freezing point and 100 used for the onset of boiling.

• Kelvin scale provides an “absolute” value with zero defined as absence of temperature. Absolute zero is -273 degrees referred to water freezing at 0 degrees centigrade, but it’s more logical to define 0 centigrade as 273 Kelvin, avoiding negative numbers and providing linearity (avoids mistake of thinking 100 degrees centigrade is “twice as hot” as 50 degrees).

• Temperature definitions largely resolved, have achieved close to absolute zero with boiling point of liquid helium

Temperature Conversions• Zero NOT same temp. in both scales

– 0oF ≠ 0oC, Δ =32oF

– Celsius degree is larger = 5oC/9oF

– 5/9 is “exact” ratio, no sig-figs involved

• Fahrenheit = (Celsius * 9oF/5oC) + 32oF

– Convert size of degrees first, then add zero offset

– (100oC * 9oF/5oC) + 32oF = 180 + 32 = 212oF

• Celsius = (Fahrenheit - 32)oF * 5oC/9oF

– Get rid of offset first, then use ratio of scales

– (212–32)oF * 5oC/9oF = 180*5/9 = 100oC

– 98.6oF body temp = (98.6-32)*5/9 = 37.0oC

Kelvin Temperature Conversions

• Celsius to Kelvin

– “True Zero” = - 273oC

• Therefore, Celsius + 273 ≡ Kelvin

– Common Examples

• Melting Ice = 0oC + 273 = 273oK

• “Room Temperature” = 25oC + 273 = 298oK

• Boiling Water = 100oC + 273 = 373oK

Fig. 3-8, p. 77

Definitions of Time

• Arbitrary units

– Earth cycles reference

– 12 or 24 hour basis, but 24 is less confusing and avoids AM/PM notation

• Depends on location

– “Zulu” time = “GMT” Greenwich Mean Time based on one longitude.

– “UTC” = universal coord. Time, broadcast by NIST, used by “atomic” clocks.

Time … is also arbitrary• “Year” is defined as earth’s circumnavigation time around the sun, NOT

an integer multiple of any other measurement. All planets are different.

• “Day” defined by earth’s Rotation on its own axis. There are 365.25 days per year, leading to “leap years” every 4th year to keep seasons as they are.

• “Hour” was defined by the ancient Egyptians as either 1/12 of daytime or 1/12 of nighttime, hence both day and night hours varied with the seasons (must have been confusing), but the sum was always 24 hours per day.

• “Minutes” per hour multiple of 60 comes from the Babylonians who used factors of 60 in their counting system

• “Seconds” originally referred to Babylonian subdivision of a minute called the “second minute”, later simplified to the “second”… also a factor of 60

• “Leap Seconds” accommodate the Earth's rotation slowing down due to tidal action.. The length of a solar day increased from an exactly defined 86,400 seconds per day (60 sec/min*60min/hr*24hr/day=86,400sec/day) in 1820 to 86,400.002 seconds per day in 1999, The difference amounts to nearly one second per year (365 days * 0.002 sec/day = 0.73 sec) which is handled by inserting a leap second into reference clocks about once a year.

Time• Time is a fundamental measurement

– The definition should not be changing

• Time denominated by arbitrary definitions

– Based on planet where we live, and changing!

– NOT the same for other planets

• Time also is unidirectional

– Unlike other physical measurements

• Need to stabilize/freeze the definition

– GPS requires nanosecond accuracy

Length• “Foot” originally referred to somebody’s appendage, probably a King

• “Inch” defined as 1/12 of “Foot” … why 12?

• “Rod” was used in surveying, 16.5 feet long (11 cubits), with a piece of Jasper mineral at each end to prevent wear of the bar.

• “Chain” also used for surveying, 66 feet long with 100 links, so land measurements employed both units (e.g. width of property = 2 chains + 4 links)

• “Yard” defined as 3 Feet (why 3?)

• “Fathom” is distance between fingertips of outstretched arms (now re-defined as exactly 6 feet) … and still in nautical use.

• “Furlong” agricultural measurement, based on distance a horse could pull a plough before needing a rest. Still used by racetracks, 660 feet or 220 yards

• “Mile” English parlaiment of Elizabeth I defined the mile as eight furlongs or 1,760 yards; 5,280 feet; or 63,360 inches.

• “League” originally defined by length of an hour's walk, now considered equal to about three miles.

• Train tracks use standard separation of wagon wheels, originally from Roman 2-horse Chariots established by breadth of 2 horse’s behinds (4 ft 8-1/2 inch)

Giza Pyramid SpecificationsCompleted 2551 BC, tallest structure for 3800 years

280 Cubits High

440 cubits wide

Current unit conversions:

Height = 146.5 meters

Width = 230.4 meters

Mass = 5.9E6 tons

Stone Blocks = 2.3E6

Volume = 2.5E6 meter^3

(Egyptian cubit ≈ 20.6 in)

Noah’s Ark Specifications

Genesis 6:15

God said to Noah, "The end of all flesh has come before me, for the earth is filled with violence through them. Behold, I

will destroy them with the earth.

14 Make a ship of gopher wood. You shall make rooms in the ship, and shall seal it inside and outside with pitch.

15 This is how you shall make it. The length of the ship will be three hundred cubits, its breadth fifty cubits, and its

height thirty cubits.

Might just be the first recorded “engineering specification”, two sentences used to define a large scale construction project

This simple spec. would never be accepted in today’s world !

What’s a Cubit?Cubit is the name for any one of many units of measure used

by various ancient peoples.

The natural cubit is based on the distance between thumb and another finger to the elbow on an average person (a more common definition measures from elbow to end of

longest finger).

In ancient Egypt, the Cubit was approximately 20 inches, based on pyramid specifications.

It was employed consistently (for example, to measure cords and textiles) through the Middle-Ages up to the Early

Modern Times. The natural cubit measures 24 digits or 6 palms. This is about 45 cm or 18 inches (1.50 ft.)

Early engineering projects depended only on human anatomy (no Home Depot for tape measures). Major projects relied on basically simple dimensions based on the people

who built them. No permits, no inspections, no safety rules?

OSHA CowboyWhat would Noah’s ark look like if built today?

Ancient Dimensions … the "Cubit"Defined as distance between elbow (upright on table) to farthest fingertip

Noah's Ark length, Biblical reference 300 Cubits

Convert Convert Person measured Cubit Inches accuracy to Feet to MetersBill 20.0 0.063 500 152Mariemay 16.9 0.063 422 128Vickie 19.0 0.063 475 145Micah 20.5 0.063 513 156Laura 18.8 0.063 469 143Megin 18.3 0.063 456 139Devarier 20.5 0.063 513 156Ken 17.0 0.063 425 129Dan 18.5 0.063 463 141Kenneth 18.0 0.063 450 137Elise 16.0 0.063 400 122Annie 16.5 0.063 413 126Oye 23.0 0.063 575 175 Biggest ArkHong Diem 17.0 0.063 425 129Julie 18.5 0.063 463 141Sam 16.0 0.063 400 122Jacob 18.0 0.063 450 137Vu 18.0 0.063 450 137Uyen 15.5 0.063 388 118 Smallest ArkElyas 19.0 0.063 475 145Tommy 19.0 0.063 475 145eshette 21.0 0.063 525 160Average 18.40 0.06 460.09 Var. to AvgMaximum 23.00 0.06 575.00 25.0%Miimum 15.50 0.06 387.50 -15.8%Range 7.50 0.00 187.50 40.8%

Noah’s Ark ? (or barge)

How big was the Ark?(by today’s measurements)

Dr. Max D. Younce says by his calculations from Genesis 6:15 that

Noah’s ark was 450 feet long, 75 feet wide, and 45 feet deep. He goes on to

say that it’s equivalent to "522 standard stock cars or 8 freight

trains of 65 cars each."

Length Dimension also in trouble

• Competing arbitrary definitions

– Foot subject to change ?, whose foot?• Unnecessarily complex relationships

– Acre = 160 square rods, 43,560 square feet

– 1 square rod = 272.25 sq feet• Unnatural multiples

– 5280 feet per mile

– 12 inches per foot, 3 feet per yard• Need something better … more universal

– “meter” invented to solve the problem

Commodities, Currency• Historical definitions abound, many still in use

– Dozen = 12, Baker’s Dozen = 13

– Bushel of corn = 9.3 gallons

– Bale of hay = 45 pounds (small square variety)

– Cord of wood = 128 cubic feet (4’ x 4’ x 8’) simple to use

– Barrel of Oil = 42 gallons of crude

– Acre feet = 43,560 cubic feet (agricultural water, intuitive)

• Currency

– Quid = pound sterling, 20 shillings/pound, 12 pence/shilling,

– UK went metric in 1971, got rid of confusing system

• Some quantities are just names, no numbers

– School of fish, Gagle of geese, Pride of Lions

“Pieces of 8” coinage

Peso is the name of the currency in many Latin American countries because of Spanish influence 500 years ago. The peso was a silver coin minted in Spain. The Americas had vast deposits of silver which was used to mint millions of pesos over several centuries.

The old silver peso was worth 8 reales ("royals"), just as the U.S. Dollar is worth 100 cents. Pesos were often physically cut into eight "bits", or sometimes four quarters, to make smaller change. People began to call the silver peso coins "pieces of eight." A peso cut into quarters came to be called "two bits" a term still used in the United States to mean a quarter of a dollar, or twenty five cents.

Early measurements a mess!• Length based on King’s foot

– What happens when we change Kings? (save the foot!)

– The King’s foot might change with age …

• Mass depends on bits of something natural

– Inconsistent by location, time, plant variety, humidity …

• Nonsensical multiples abound over time

– 4 quarts/gallon, 32 ounces/quart, barrels, cords …

– 12 inch/foot, 3 feet/yard, 5280 ft/mile, leagues, fathom …

– 7000 grains/pound, 14 pounds/stone

– 20 schillings per currency “pound”, reams of paper, …

• France attacked the problem

– Defined new measurements (no plants or people)

– Based values using powers of 10, became the “metric” system

SI system of units• Employ a Decimal System, of powers of 10

– Defined kilometer, meter, centimeter, millimeter, nanometer

• Replacing feet, fathoms, knots, cubits, furlongs, etc.

• Volume defined as 1 liter = 10 x 10 x 10 cm = 1000cm^3

– Kilogram, gram, metric ton (1000 Kg)

• Replacing pounds, stones, grains, ounces, drams

• Related to water (1 liter = 1000 cm^3 = 1 kilogram)

– Second, millisecond, microsecond

• Preserved historical units, impractical to change all clocks

• Tied old units to more precise standards

Basic CGS metric schemePreceded SI / ISO system of units (cm vs meter)

1 cm^3 = 1 milliliter = 1 gram H2O

Where did the meter come from?

• Objective was to dispense with artifacts

• Use something “universal” to measure

• Why not the earth itself?

– Everybody has access

– Easy to understand

– Conceptually simple

– Reproducible result

Basis of Metric SystemNorth pole to equator ≡ 10^7 meters

Original Meter Definition• Early measurement systems were problematic, so a new

definition of length was desired NOT to be tied to human or animal-centric artifacts.

• In 1791, the French Academy of Sciences adopted a meridional definition to establish a universally accepted definition of the metre. The Bureau des Longitudes commissioned an expedition, from 1792 to 1799, to measure length of the meridian between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, was to serve as the basis for the length of the quarter meridian, connecting the North Pole with the Equator.

• in 1793, France adopted provisional results from the expedition, but it was later determined that the first definition was short by 1/5 millimetre from miscalculation of flattening of Earth. The length of this quarter-circumference divided by 10,000,000 became the standard meter. This measurement was transferred to scribed lines on a metal bar kept in Paris.

Historical International Prototype Metre bar, made of an alloy of

platinum and iridium, which was the standard from 1889 to 1960

Problems with Artifact based Standards

• Only ONE “master” or “gold” standard (meter bar in Paris).• Copies made of master become “secondary” or “silver”

standards (sent to USA, England, Germany, etc.)• “Silver” standards (our National Secondary standards)

used to create “Reference standards” for science and industry, and “Working Standards” are made from those.

• Errors are cumulative as copies are made from copies, and defects propagate through the system. Consider a 10th generation Xerox copy … quality degradation obvious.

• Users must have access to the standards for calibration, risk of damage to the standard and measurement error.

• Complex schemes evolve, groups of objects whose average value is “the standard”, etc. Disk Drive example, NBS used 20 pieces of media to define a “gold average”.

A thought experiment …

• Assume we establish radio & TV communication with intelligent life from another galaxy. After sharing pictures of our families and technical data, the questions begin.

• When asked “how tall are you”, the response of 6 feet 2 inches is met with an obvious question: “What is a foot?” Same issue with measurement in meters.

• Advice for our friends in the other world to come to Paris for a copy of meter bar is not too practical.

• A more universal solution is required ….

Light to the rescue!

• In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using wavelength of light as a standard of distance.

• By 1925, interferometry was in regular use by standards organizations, although the International metal bar Metre remained the primary standard until 1960.

• In 1960 the metre was redefined as equal to 1,650,763.73 wavelengths of the orange-red emission line of the krypton-86 atom in a vacuum. The original international prototype of the metre metal bar is still kept in Paris under the conditions specified in 1889.

“Universal” ISO dimensions

• The Meter was redefined again in 1983 as the path length traveled by light during a time of 1/(299,792,458) second. This fixes speed of light at exactly 299,792,458 meters per second. Definitions based on light are more precise and reproducible because properties of light are believed to be universally constant. … E.T. would agree.

• Length and time are related by the speed of light, a universal constant, so time can be similarly defined.

• The “Second” is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition eliminates any relationship to time variations of planetary motion.

Seven Basic SI Measurements

• Mass = Kilogram

• Length = Meter

• Time = Second

• Temperature = degrees Kelvin

• Quantity of matter = mole

• Energy Rate = Ampere

• Light Energy = Candela

Why are we still using inches?• Reluctance to Change

– Relearning, converting old values to new

• Economic Impact (a BIG deal)

– Cost to make the switch is significant

• Tools & tooling, lost inventory, packaging resizing, construction, etc.

– Marketing trend to reduce cost by giving less (cereal, candy bars)

• Metric units often larger (500 gram vs 1 pound, 1 liter is 1.06 quart)

– UK currency metrification in 1971

• Needed to change ALL cash registers, vending machines

• A gradual shift towards metric IS in progress

– Global economy drives standards

• Ford owns Volvo and Mazda, 2 standards more costly to maintain

• All wine now in 750 ml bottles (same as 1/5 gallon), sodas are 2 liters

• NASA crashed a mars landing due to metric/English mix-up

Chem 32A, Fall 2010

• Stop here for measurements

• Density is for week 4

Table 3-3, p. 75

Derived Units• Area is a 2-dimensional multiplication of lengths. An

acre was defined by length of one furlong (220 yards) and breadth of one chain (22 yards), or 4,840 square yards per acre. Square feet still common in US

• Volume a 3-Dimensional concept, based on (length)3 Early definitions were arbitrary (quart, gallon), “metric” system is based on 1 Liter = 1000 cm3

• Density is mass per unit volume. The initial metric system “CGS” (Centimeter, Gram, Second) used water defined as 1.0 gram per cubic centimeter. CGS evolved to MKS (Meter, Kilogram, Second), now called SI (System Internationale) or ISO (International Standards Organization) units system.

Density

• Water all around us, a useful reference

– Easy to obtain, purify, & measure

• Density is temperature sensitive

– Usually expand with rising temperature

– Water has a maximum density at 4oC

• Water at < 0oC forms ice, which floats

• Density defined as 1.0000 gm/cm^3 at 4oC

Ice and Water

Density• Mass/Volume defined by water

– Grams/cm^3 =1 (also defined as 1 milliliter)

– Kilograms/liter = 1 (1000x gm and ml)

– 1000 kilogram/meter^3 (1000 liter/meter^3)

• Density is important on a “water planet”

– Objects >1 gm/ml sink in water, <1 gm/ml float

– Ships float due to mass < water displacement

– Ice floats due to expansion <4oC

• If not, ice would sink … life on planet changes

Density TriangleMass=D*V, Density=M/V, Volume=M/D

Utility of Density• Does it Float in Water? … Density < 1.0

– water covers >70% earth surface

• 1.3 billion cubic kilometers of ice & water

– Density an important feature for ships

• Also works for balloons in air

• Does it Sink in water? … Density > 1.0

– Conventional material property

– Helps identify elements and compounds

• Is your gift of “gold” for real? (better be 19.3 gm/ml)

Density of Water

Density of material groups(water is 1000 kg/m^3)

Table 3-4, p. 82

Helium and/or Hot AirDensity difference provides the lift

Proposed new “cruise ship” dirigible

Dimensions  (feet): 165' H x 244' W x 647'  L

14  million cubic feet of helium hoist only two-thirds of the craft's  weight. The  aerodynamic body is driven by huge rear-ward  propellers, with enough lift to keep the aircraft

and its  400-ton payload aloft while cruising.

UNofficial dimensions• Ratio of igloo's circumference / diameter = Eskimo Pi

• Time between slipping on a peel and smacking the pavement = 1 bananosecond

• Time to sail 220 yards at 1 nautical mph = Knotfurlong

• 365.25 days drinking low calorie beer = 1 Lite year

• Half a large intestine = 1 semicolon

• 1,000,000 aches = 1 megahurtz

• Basic unit of laryngitis = 1 hoarsepower

• Shortest distance between two jokes = a straight line

• 1 million microphones = 1 megaphone

More UNofficial dimensions

• 2000 mockingbirds = two kilomockingbirds• 52 cards = 1 deckacard• 1000 grams of wet socks = 1 literhosen• 1 millionth of a fish = 1 microfiche• 1 trillion pins = 1 terrapin• 10 rations = 1 decaration• 100 rations = 1 C-Ration• 2 monograms = 1 diagram• 8 nickels = 2 paradigms

Last Slide

• Now to the experiment !