Metrics and Measurement

Our first test will be in 5.

Fundamental units

A quantity that cannot be measured in a simpler form

Quantity Unit

Distance MeterMassKilogramTimeSeconds

SI (Systeme Internationale) System of units

Units are standardized and regulated by two organizations:

International Bureau of Weights and Measures (France)

National Institute of Science and Technology (Maryland)

All measurement tools are calibrated using the standards stored at these locations

Standard Unit Definitions

• Meter1790 – 1/10,000,000 the distance from the north pole to the equator, measured along a line passing through Lyons, France

1875 – The distance between two lines engraved on a platinum-iridium bar stored in Paris

1984 – the distance traveled by light in a vacuum during a time interval of 1/299,792,458 s

Standard Unit Definitions

• Secondold – 1/86,400 of the mean solar day

new – 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 cesium atom

(the vibration of the cesium atom in an atomic clock)

Standard Unit Definitions

• Kilogram1790 – mass of exactly one cubic decimeter of water1899 – mass of the international prototype of the kilogramThis apple sized piece of platinum-iridium protected behind glass in Paris is the definition of a kilogram.

Because of contaminants and cleaning, the mass does change ever so slightly.

This is the future standard of the kilogram.

The kilogram will soon be defined as a specific number of silicon atoms since atoms have a set mass that does not change due to cleaning, etc.

The Avogadro Project has created a grapefruit sized silicon ball which is the most perfectly spherical object ever created by man. Cost: $700,000They are in the process of COUNTING HOW MANY ATOMS IT IS COMPOSED OF!Avogadro’s number may even eventually change due to this experiment.

Derived unit – a unit that is composed of other units

Example: Newton, watt, volt

A Newton is a kg m/s2

Prefix (symbol) Conversion Factor Example

Mega- (M) 106 1 MW = 106 W

kilo- (k) 103 1 kg = 103g = 1000 g

centi- (c) 10-2 1 cm = 10-2 m = 0.01 m

milli- (m) 10-3 1 mL = 10-3 L = 0.001 L

micro- () 10-6 1 m s = 10-6 s = 0.000001 s

Metric Prefixes

A desk was measured to be 62.52 cm tall. How many millimeters tall is this desk?

The world's largest strawberry was measured to be 231 g. How many kilograms is this?

Factor Label Converting

When we convert units that are not metric system based (ex: feet, inches, miles, etc) we have to use conversion factors. 1 mile (mi) = 1609 m

1 inch (in.) = 2.54 cm2.2 pound (lb) = 1 kg

1 lb = 454 g1 mL = 1 cm3

1 gallon (gal) = 3.785 L1 gal = 8 pints

When factor label converting, we make fractions (ratios) out of the conversion factors so that the original unit cancels out and the new unit remains:

Example:

According to the Guinness Book of World Records (2008), a man from London balanced a 352 lb car (a Mini) on his head for 33 seconds. What is the mass of this car in kilograms?

160 kg

Usain Bolt ran the 100-m race at the Beijing Olympics in a world record time of 9.69 seconds. His average speed was 10.3 m/s.How fast was he running in miles per hour?

23 mi/hr

The speed of sound is 330 m/s. How fast is this in miles/hour?

An acre, which is 43,560 ft2, is an area unit often used to describe the size of a farm. What is the size of a 600 acre farm in square miles?

Factor Labeling1)When a woman turns 100 years old, how any seconds has she lived?2)If one Deutschmark (the West German unit of currency) is worth 40 cents and gasoline costs 1.30 Deustchmarks per liter, what is its cost in dollars per gallon?3)The gasoline consumption of a small car is 17 km/l. How many miles per gallon is this?4)The speed limit on a highway in Lower Slobbovia was given as 150,000 furlongs per fortnight. How many miles per hour is this? (One furlong is 1/8 mile and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)5)A speed limit sign on a Canadian road reads “80 km/h.” What is this limit in miles per hour?7)An acre, which is 43,560 ft2, is an area unit often used to describe the size of a farm. What is the size of a 600 acre farm in square miles?8)A football field is 120 yd long by 53 yd wide. What is the size of a football field in acres?

The Googol

Physicists, mathematicians and others often deal with very large numbers. The number 10100 has been given the name googol by mathematicians. Let’s compare some large numbers in physics to the googol.

Approximately now many atoms make up the earth? For simplicity, take the average atomic mass of the atoms to be 14 g/mole.

Mass of Earth = 6 x 1024 kg 2.58 x 1050 atoms

Approximately how many neutrons are in a neutron star? Neutron stars are made up of neutrons and have approximately twice the mass of the sun.

Mass of sun = 1.99 x 1030 kg

Mass of neutron = 1.675 x 10-27 kg

2.38 x 1057 neutrons

In one theory of the origin of the universe, the universe at a very early time had a density (mass divided by volume) of 1015 g/cm3, while it radius was approximately the present distance of the earth ot the sun. Assuming 1/3 of the particles were protons, 1/3 were neutrons and the remaining 1/3 were electrons, how many particles made up the universe?

Distance of earth to sun = 1.49 x1011 m

Mass of proton = 1.673 x 10-27 kg

Mass of electron = 9.11 x 10-31 kg

4.12 x 1078 particles

Googol fun facts:

A googolplex is a 1 followed by a googol of zeroes.

The word googol was invented in 1938 by the nine year old nephew of mathematician Edward Kasner.

The name of the website Google is a misspelling of the word.

Q: Who shops at the Googolplex Mall?

A: Phineas and Ferb