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Units! PTYS206-2 31-Jan-08

Units! PTYS206-2 31-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

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Page 1: Units! PTYS206-2 31-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

Units!

PTYS206-231-Jan-08

Page 2: Units! PTYS206-2 31-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

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.

Page 3: Units! PTYS206-2 31-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

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

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)

Page 4: Units! PTYS206-2 31-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

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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 Earth’s magnetic field in the region of space surrounding the Earth.

Page 5: Units! PTYS206-2 31-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

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

Check it out

Page 6: Units! PTYS206-2 31-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

Horoscope Resultsactual sign\answer Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricorn Aquarius Pisces TotalAries 0 1 1 0 0 1 1 0 3 1 0 0 8Taurus 0 1 2 0 0 1 2 0 1 0 1 0 8Gemini 3 1 1 0 0 1 0 1 2 0 0 2 11Cancer 1 1 1 0 1 1 0 0 5 1 0 0 11Leo 1 1 1 0 2 2 2 1 1 0 1 0 12Virgo 0 1 0 1 0 1 0 1 0 0 1 2 7Libra 1 2 3 1 0 2 0 0 2 2 1 1 15Scorpio 1 1 1 0 1 1 0 0 2 2 1 2 12Sagittarius 1 1 1 0 0 0 0 0 4 0 1 1 9Capricorn 1 1 1 0 0 0 0 1 0 0 0 0 4Aquarius 0 0 1 1 0 2 1 0 3 0 0 3 11Pisces 0 2 2 1 1 0 1 0 1 0 1 1 10Total 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

Page 7: Units! PTYS206-2 31-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

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?

Page 8: Units! PTYS206-2 31-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

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.

Page 9: Units! PTYS206-2 31-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

Solutions to Drake Equation

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40

log(N)

Number of Responses

Page 10: Units! PTYS206-2 31-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

UnitsAll 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 can’t 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.”

Page 11: Units! PTYS206-2 31-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

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

Page 12: Units! PTYS206-2 31-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

Units for Time

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

Ever wonder why different 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?

Page 13: Units! PTYS206-2 31-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

Time and BabylonThe 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 don’t know.

Some historians trace 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).

Page 14: Units! PTYS206-2 31-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

Derived UnitsSome 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 doesn’t have a separate unit, rather the unit for velocity is related in a specific way to the units for distance and time.

Page 15: Units! PTYS206-2 31-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

Signifying unitsUnits 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 second can be written as

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

Page 16: Units! PTYS206-2 31-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

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. When 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/min^2

Page 17: Units! PTYS206-2 31-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

ExampleYou 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/hour = ZZZZZZ hours

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

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

Page 18: Units! PTYS206-2 31-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

The Metric SystemIn 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) uniformity for all nations and 2) a base ten system.

Page 19: Units! PTYS206-2 31-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

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.

Page 20: Units! PTYS206-2 31-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

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Good book to read.

Page 21: Units! PTYS206-2 31-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

Important Physical Quantities and 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

Page 22: Units! PTYS206-2 31-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

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Not so much fun, but useful to have. We will post it on the web site.

Page 23: Units! PTYS206-2 31-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

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

Page 24: Units! PTYS206-2 31-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

Temperature UnitsTemperature 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 temperature in Kelvins (after Lord Kelvin, a British physicist).

Page 25: Units! PTYS206-2 31-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

Temperature ContinuedIn 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 at 0 ºC and boils at 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

Page 26: Units! PTYS206-2 31-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

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

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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.

Page 27: Units! PTYS206-2 31-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

Solid AnglesSolid 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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Page 28: Units! PTYS206-2 31-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

Weird Units

• Stones

• Furlongs

• Fathoms

• Knots

• light-years

• parsecs

Page 29: Units! PTYS206-2 31-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

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)

Page 30: Units! PTYS206-2 31-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

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?

Page 31: Units! PTYS206-2 31-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

Example

• You’re 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?

Page 32: Units! PTYS206-2 31-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

Density and Volume

The SI units for density and volume are defined so that the density of water is 1 gram/cm^3 and 1 liter of water has a mass of 1 kg.

How much volume is occupied by 1 liter of water?