Units!

PTYS206-231-Jan-08

Explorer 1: 50 years ago today

• Sputnik launch by Soviet Union on Oct 4,1957

• Sputnik 2 launched on Nov 3, 1957• Explorer 1 launched on Feb 1, 1958• Orbit with perigee (lowest altitude) of 224

miles and apogee (highest altitude) of 1575miles and a period of 115 minutes.

• Operated until May 23, 1958• Re-entered atmosphere, crashed into Pacific

on March 31, 1970.

William Pickering (Director of JPL), James Van Allen (Prof.at U. of Iowa, and Wernher von Braun holding a model ofExplorer 1.

Spacecraft Dimensions(not including rocket)Length: 203 centimeters(80 inches)Width: 15.9 centimeters(6.25 inches) in diameterWeight: 14 kilograms(30.8 pounds)

The mostimportant scientificdiscovery from theearly explorerswere the Van Allenradiation belts.These areenergetic ionstrapped by theEarth’s magneticfield in the regionof spacesurrounding theEarth.

http://www.jpl.nasa.gov/explorer/videos/

Check it out

Horoscope Resultsactual sign\answer Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricorn Aquarius Pisces Total

Aries 0 1 1 0 0 1 1 0 3 1 0 0 8

Taurus 0 1 2 0 0 1 2 0 1 0 1 0 8

Gemini 3 1 1 0 0 1 0 1 2 0 0 2 11

Cancer 1 1 1 0 1 1 0 0 5 1 0 0 11

Leo 1 1 1 0 2 2 2 1 1 0 1 0 12

Virgo 0 1 0 1 0 1 0 1 0 0 1 2 7

Libra 1 2 3 1 0 2 0 0 2 2 1 1 15

Scorpio 1 1 1 0 1 1 0 0 2 2 1 2 12

Sagittarius 1 1 1 0 0 0 0 0 4 0 1 1 9

Capricorn 1 1 1 0 0 0 0 1 0 0 0 0 4

Aquarius 0 0 1 1 0 2 1 0 3 0 0 3 11

Pisces 0 2 2 1 1 0 1 0 1 0 1 1 10

Total 9 13 15 4 5 12 7 4 24 6 7 12 118

Number of correct choices = 10

Number if chosen randomly = 118/12 = 9.83

Most Common Answer

i) There's much to learn before you canmove forward with your goals. Youfind all you need to know by askinggood questions and knowing when toremain silent.

Maybe some correlation with first week ofclasses?

Are Horoscopes Scientific?• It is falsifiable? Apparently so.• They do make predictions, but apparently not very

accurately because predictions are subject to anenormous range of interpretation - not quantitative inany way.

• The rules in astrology are not open or subject torevision. They are not based on hypotheses aboutpatterns in nature, but are simply handed down fromsupposed authorities. This means that the rulescannot be revised, astrology cannot progress. It isnot science.

• The only authority in science are experiments andobservations.

UnitsAll physical quantities are associated with units.

The simplest example is distance, which can be measured ina variety of units including inches, feet, miles, meters,kilometers, etc. You can’t say “my house is 10 from yourhouse.” The value needs a unit to make sense, so we say“my house is 10 feet from your house.”

Units of DistanceInches, feet, yards, miles, fathoms, nautical miles,furlongs, meters, kilometers, micrometers (microns),lightyears, parsecs, …

Units for Time

Another simple example is time. We don’t say “the classlasts 75,” but “the class last 75 minutes.” Units of time areseconds, minutes, hours, days, years, etc.

Ever wonder why different cultures have different units fordistance, different languages, different currencies, buteveryone uses hours, minutes, and seconds? Days andyears are easy to understand, but why hours, minutes, andseconds?

Time and BabylonThe history of the second, minute, and hours can be basedto the ancient Summerians that ruled the area aroundmodern day Iraq though city states such as Babylon, Ur, andUruk. The Summerians were accomplished mathematiciansand used a base 60, rather than base 10, number system.

Why base 60? We don’t know.

Some historians trace the beginning of modern science tothe joining of Greek geometric and philosophical thoughtwith Summerian mathematics following the conquest ofBabylon by Alexander the Great. (Science since Babylon, byDerek Price).

Derived UnitsSome physical quantities are related in a specific way toother physical quantities. If so, this defines therelationship between their units. The simplest example isvelocity, which is distance divided by time. So, if a car istraveling 60 mph (miles per hour) this means that if it weregoing that speed constantly for one hour it would travel 60miles. Velocity doesn’t have a separate unit, rather theunit for velocity is related in a specific way to the units fordistance and time.

Signifying unitsUnits can be written in a variety of ways. For example, wecan write 60 miles per hour or 60 mph. Often we abbreviatethe symbols for common units.

10 meters per second is often written as 10 m/s or 10 m s-1.

10 meter per second per second can be written as

10 meters per second squared or 10 m/s^2 or 10 m s-2.

AccelerationAcceleration is the change in velocity with time. So, if acar is traveling 40 mph and accelerates to 60 mph in oneminute, the acceleration is to the change in velocity dividedby the time, or 20 mph/ 1 minute.

This brings up another point. When using physicalquantities in calculations you have to make sure the unitsare the same. In the example above we have miles perhour per minute. It is usual easer to stick to one unit foreach quantity, I.e. either minutes or hours, but not both.

So, 20 mph/minute = 20/60 miles/min^2

ExampleYou have to get from home to the UofA to see the LincolnJazz Orchestra. You live 5000 yards away and you candrive approximately 30 mph on Tucson city streets. Howlong will it take you to get there (not including parking)?

First you have to convert yards to miles because miles areused in the units for velocity. There are 1760 yards in 1mile so 5000 yards is XXXXXXX miles and it will take

Xxxxx miles / 30 miles/hour = ZZZZZZ hours

You can check the units by doing the calculationalgebraically on the units, i.e.

miles/(miles/hour) = 1/(1/hour) = hour

The Metric SystemIn a spirit of pan-european unity that predated the euro by 200years, a group of european scientists defined the metricsystem in 1795. The idea was to get away from a systemwhere the unit of distance differed from country to countryaccording to the size of the monarch feet. So, what should bethe standard length? There have been several.

There were two goals: 1) uniformity for all nations and 2) abase ten system.

History of the Meter• The original definition (1791) was 10-7 of the distance

from the pole to the equator.• In 1889 the definition was changed and 1 meter was

defined as the length of a platinum-iridium rod kept ata specific temperature in a lab in Paris.

• In 1960 the meter was redefined again to be basedon the wavelength of light emitted by Kyrpton-86

• In 1983 the meter was redefined as the the length ofthe path travelled by light in vacuum during a timeinterval of 1/299 792 458 of a second.

Good book to read.

Important Physical Quantitiesand SI Units

Time: s (seconds)Distance: m (meters)Mass: kg (kilograms)Velocity: m/sAcceleration: m/s^2Force: kg m/s^2 (Newtons)Area: m^2Volume: m^3Density = mass/volume: kg/m^3

Not so muchfun, but usefulto have. Wewill post it onthe web site.

Common Prefixes• pico 10-12 : picometer , picogram, picosecond• nano 10-9 : nanometer• micro 10-6 : micrometer• milli 10-3 : millimeter• centi 10-2 : centimeter• deci 10-1 : decimeter• deca 10+1 : decameter• kilo 10+3 : kilometer• mega 10+6 : megameter• giga 10+9 : gigameter• terra 10+12 : terrameter

Temperature UnitsTemperature in the US is commonly measured in degreesfarenheit, often written as ºF.

In most countires temperature is measured in celcius orcentigrade.

Scientists measure temperature in Kelvins (after LordKelvin, a British physicist).

Temperature ContinuedIn the Farenheit system, water freezes at 32 ºF at (apressure of 1 atmosphere) and boils at 212 ºF.

In the centigrade system, water freezes at 0 ºC and boilsat 100 ºC.

In SI units water freezes at 273 K and boils at 373 K.

Conversions:

ºC = (ºF-32)x100/180 = (ºF-32)x5/9

ºF = (9/5) x ºC + 32.

K = ºC + 273

AnglesAngles are commonly measured in degrees but may also bemeasured in radians.

The radian is defined as theratio of the arc length definedby the angle to the radius ofthe circle. We say that anglea in the figures subtendsAB/R radians. There are 2πradians in a circle and 360degrees.

Solid AnglesSolid angle refers to the fraction of a sphere subtended bya cone. It is defined as the ratio of the area on the sphereto the radius of the sphere. The units of solid anlge aresteradians. There are 4π steradians in a sphere.

Weird Units

• Stones• Furlongs• Fathoms• Knots• light-years• parsecs

Conversions1 inch = 2.54 cm

1 mile = 5280 feet

1 quart = 0.946 meters

1 kg = 2.2 pounds (only on the surface of the Earth)

Example

• An on line dating service in Franceclaims that your perfect mate is 90 cmtall. How tall is that in feet and inches?

Example

• You’re interested in buying a newchinese car and the sales informationsays it has a top speed of 1 meter/sec.How fast is that in mph?

Density and VolumeThe SI units for density and volume aredefined so that the density of water is 1gram/cm^3 and 1 liter of water has a massof 1 kg.

How much volume is occupied by 1 liter ofwater?