Units

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Units!

• PTYS206-231-Jan-08

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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 1575 miles and a
  period of 115 minutes.
  
• Operated until May 23, 1958
• Re-entered atmosphere, crashed into Pacific on
  March 31, 1970.

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Spacecraft Dimensions (not including rocket)?
Length 203 centimeters (80 inches)?
Width 15.9 centimeters (6.25 inches) in
diameter? Weight 14 kilograms (30.8 pounds)
William Pickering (Director of JPL), James Van
Allen (Prof. at U. of Iowa, and Wernher von Braun
holding a model of Explorer 1.
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The most important scientific discovery from the
early explorers were the Van Allen radiation
belts. These are energetic ions trapped by the
Earths magnetic field in the region of space
surrounding the Earth.
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Check it out
http//www.jpl.nasa.gov/explorer/videos/
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Horoscope Results
Number of correct choices 10
Number if chosen randomly 118/12 9.83
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Most Common Answer

• i) There's much to learn before you can move
  forward with your goals. You find all you need to
  know by asking good questions and knowing when to
  remain silent.
• Maybe some correlation with first week of classes?

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Are Horoscopes Scientific?

• It is falsifiable? Apparently so.
• They do make predictions, but apparently not very
  accurately because predictions are subject to an
  enormous range of interpretation - not
  quantitative in any way.
• The rules in astrology are not open or subject to
  revision. They are not based on hypotheses about
  patterns in nature, but are simply handed down
  from supposed authorities. This means that the
  rules cannot be revised, astrology cannot
  progress. It is not science.
• The only authority in science are experiments and
  observations.

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(No Transcript)
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Units
All physical quantities are associated with
units. The simplest example is distance, which
can be measured in a variety of units including
inches, feet, miles, meters, kilometers, etc.
You cant say my house is 10 from your house.
The value needs a unit to make sense, so we say
my house is 10 feet from your house.
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Units of Distance
Inches, feet, yards, miles, fathoms, nautical
miles, furlongs, meters, kilometers, micrometers
(microns), lightyears, parsecs,
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Units for Time
Another simple example is time. We dont say
the class lasts 75, but the class last 75
minutes. Units of time are seconds, minutes,
hours, days, years, etc. Ever wonder why differ
ent cultures have different units for distance,
different languages, different currencies, but
everyone uses hours, minutes, and seconds? Days
and years are easy to understand, but why hours,
minutes, and seconds?
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Time and Babylon
The history of the second, minute, and hours can
be based to the ancient Summerians that ruled the
area around modern day Iraq though city states
such as Babylon, Ur, and Uruk. The Summerians
were accomplished mathematicians and used a base
60, rather than base 10, number system.
Why base 60? We dont know. Some historians trac
e the beginning of modern science to the joining
of Greek geometric and philosophical thought
with Summerian mathematics following the conquest
of Babylon by Alexander the Great. (Science since
Babylon, by Derek Price).
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Derived Units
Some physical quantities are related in a
specific way to other physical quantities. If
so, this defines the relationship between their
units. The simplest example is velocity, which
is distance divided by time. So, if a car is
traveling 60 mph (miles per hour) this means that
if it were going that speed constantly for one
hour it would travel 60 miles. Velocity doesnt
have a separate unit, rather the unit for
velocity is related in a specific way to the
units for distance and time.
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Signifying units
Units can be written in a variety of ways. For
example, we can write 60 miles per hour or 60
mph. Often we abbreviate the 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 se
cond can be written as 10 meters per second squa
red or 10 m/s2 or 10 m s-2.
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Acceleration
Acceleration is the change in velocity with time.
So, if a car is traveling 40 mph and accelerates
to 60 mph in one minute, the acceleration is to
the change in velocity divided by the time, or 20
mph/ 1 minute. This brings up another point. Whe
n using physical quantities in calculations you
have to make sure the units are the same. In the
example above we have miles per hour per minute.
It is usual easer to stick to one unit for each
quantity, I.e. either minutes or hours, but not
both. So, 20 mph/minute 20/60 miles/min2
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Example
You have to get from home to the UofA to see the
Lincoln Jazz Orchestra. You live 5000 yards away
and you can drive approximately 30 mph on Tucson
city streets. How long will it take you to get
there (not including parking)?
First you have to convert yards to miles because
miles are used in the units for velocity. There
are 1760 yards in 1 mile so 5000 yards is XXXXXXX
miles and it will take Xxxxx miles / 30 miles/ho
ur ZZZZZZ hours You can check the units by doin
g the calculation algebraically on the units,
i.e. miles/(miles/hour) 1/(1/hour) hour
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The Metric System
In a spirit of pan-european unity that predated
the euro by 200 years, a group of european
scientists defined the metric system in 1795.
The idea was to get away from a system where the
unit of distance differed from country to country
according to the size of the monarch feet. So,
what should be the standard length? There have
been several. There were two goals 1) uniformit
y for all nations and 2) a base ten system.
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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 at a specific temperature in a lab in
  Paris.
• In 1960 the meter was redefined again to be based
  on the wavelength of light emitted by Kyrpton-86
  
• In 1983 the meter was redefined as the the length
  of the path travelled by light in vacuum during a
  time interval of 1/299 792 458 of a second.

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Good book to read.
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Important Physical Quantities and SI Units

• Time s (seconds)
• Distance m (meters)
• Mass kg (kilograms)
• Velocity m/s
• Acceleration m/s2
• Force kg m/s2 (Newtons)
• Area m2
• Volume m3
• Density mass/volume kg/m3

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Not so much fun, but useful to have. We will
post it on the web site.
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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 101 decameter
• kilo 103 kilometer
• mega 106 megameter
• giga 109 gigameter
• terra 1012 terrameter

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Temperature Units
Temperature in the US is commonly measured in
degrees farenheit, often written as ºF.
In most countires temperature is measured in
celcius or centigrade. Scientists measure tempera
ture in Kelvins (after Lord Kelvin, a British
physicist).
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Temperature Continued
In the Farenheit system, water freezes at 32 ºF
at (a pressure of 1 atmosphere) and boils at 212
ºF. In the centigrade system, water freezes a
t 0 ºC and boils at 100 ºC. In SI units water f
reezes 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
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Angles
Angles are commonly measured in degrees but may
also be measured in radians.
The radian is defined as the ratio of the arc
length defined by the angle to the radius of the
circle. We say that angle a in the figures
subtends AB/R radians. There are 2? radians in a
circle and 360 degrees.
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Solid Angles
Solid angle refers to the fraction of a sphere
subtended by a cone. It is defined as the ratio
of the area on the sphere to the radius of the
sphere. The units of solid anlge are steradians.
There are 4? steradians in a sphere.
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Weird Units

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

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Conversions
1 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)

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Example

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

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Example

• Youre interested in buying a new chinese car and
  the sales information says it has a top speed of
  1 meter/sec. How fast is that in mph?

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Density and Volume
The SI units for density and volume are defined
so that the density of water is 1 gram/cm3 and 1
liter of water has a mass of 1 kg.
How much volume is occupied by 1 liter of water?