SI : SI : The International System The International System

of Measurementof Measurement

MEASUREMENT and

Measurement and Mathematics is how we explore nature.

All types of engineering harness math and measuresinto practical or utilitarian endeavors.

We even use measurement as a way to attempt todefine beauty.(Marquardt)

With all of these meaningful measures, it is obviously very important that they are correct. There are two areasof concern:

Accuracy- degree of closeness

Precision – repeatability or reproducibility

Inaccurate Imprecise

Inaccurate Precise

Accurate Imprecise

Accurate Precise

Cheese IS GOLD!!!Every Large pizza is intended to have 2 measured cups of cheese.

For a variety of reasons, they usually end up with more. Papa John’s corporate office has determined this amountto be around ¼ cup. This may not seem like a big deal… BUT IT IS.

Consider that Papa John’s makes over 5 million pizzas in a calendar year. After calculation, this is over 1,250,000cups of cheese…translating to over 2 million dollars lost.

Water IS LIFE…Let’s say you have a dripping faucet that leaks 5 gallonsLet’s say you have a dripping faucet that leaks 5 gallonsPer hour.(This is actually a pretty small looking drip)Per hour.(This is actually a pretty small looking drip)

Now, let’s say that every house in the AlbuquerqueNow, let’s say that every house in the Albuquerquecity limits has the same drip. As of current census info, city limits has the same drip. As of current census info, there are 183 236 households. That comes to .9 millionthere are 183 236 households. That comes to .9 milliongallons of water or ~ 1 million…PER HOUR.gallons of water or ~ 1 million…PER HOUR.

20 million gallons per day

7 billion gallons per year!!!

Imagine if these types of inconsistencies found their wayinto some of our most importantcalculations.

Seven Base Measures of SISeven Base Measures of SIThese measures are all based on physical objects or These measures are all based on physical objects or physical descriptions of reliable universal properties.physical descriptions of reliable universal properties.

meter(m) meter(m)

kilogram(kg)kilogram(kg)

second(s)second(s)

ampere(A)ampere(A)

kelvin(K)kelvin(K)

mole(mol)mole(mol)

candela(cd)candela(cd)

m - distance

Through its history, the meter has beenbased on the following constants:-Quadrant of the Earth-a metal bar-speed of light(299 792 458)

kg - mass

The kilogram is based on a platinum-iridium bar that is kept in Paris France. In its conception, the kilogramwas intended to be the mass of one liter of water.

s - time

Originally, seconds were based onthe solar day, but then we learnedthat it was not constant.

Now, the second is based on the radioactivedecay of the Cesium- 133 isotope. (atomic clock)

A – electric current

Amperes or amps are based on a ideal definition that involves infinitely long conductors and a perfect vacuum.Even though “the” definition cannot be reproduced in nature, the precision of the ideal permits scientists to make electromagnetic calculations.

K - temperature

Researchers have been attempting to reach absolute zero for many years. This figure is considered to be the lowest temperature possible. It is the temperaturewhere all atomic motion stops.

The Kelvin temperature scale is based on absolute zero.

The lowest naturally occurring temperature ever recordedwas measured in outer space(COBE). This temperature is thought to be the lowest possible temperature attainabledue to cosmic background radiation that is a remnant of the Big Bang…but I digress.

Antarctica

Triton

184 K

38 K

2.73 K

Avogadro’s number602.214 179 x 1021

mol – actual number of atomsin an object

The mol is based on the number of elementary particles thatExist in 12 grams of Carbon-12.

cd – intensity of light

This base measure has been related to:-the light of a burning candle-the filament of an incandescent light bulb-black bodies(perfect radiator of energy) and freezing platinum at 1 atmosphere.

It is now defined as the intensity of light at a frequency ofIt is now defined as the intensity of light at a frequency of540 THz with a power of 18.3988 milliwatts over a complete540 THz with a power of 18.3988 milliwatts over a completesphere centered at the light source.sphere centered at the light source.

Derived Measures in SIThese measures are combinations of the seven base measures. Of the 22, here are a few that receive more

common use in the High School classroom.

Hertz(Hz) = /s = s-1

Newton(N) = kg·(m/s2) = kg·m·s-2

Pascal(Pa) = N/m2 = kg·m-1·s-2

Joule(J) = N·m = kg·m2·s-2

Watt(W) = W = kg·m2·s-3

Hz – measure events that happen in a definite cycle

Many modern appliances operate at frequencies measured in hertz. (computers, televisions, phones, radio, remote controls, etc…)

N – measure of forceF = ma

A force of one newton will accelerate a mass of one kilogram at the rate of one meter per second per second

J - work

It is the work done by a force of one newton acting to move an object through a distance of one meter.

James Prescott Joule actuallyPronounced his name “jowl”.

W – powerThe rate at which work is done.

This unit links mechanical workand electrical work.

one joule of workper second of time

Pa - pressure

A pascal is actually quite small (only 0.000 145 pounds per square inch) and requires a prefix the majority of the time it is used.

one newton per square meter or one "kilogram per meter per second per second."

kilo 103

hecto 102

deka 10-base 1deci 10-1

centi 10-2

milli- 10-3

Most common metric prefixes.

Yotta-Yotta- 10102424

Zetta-Zetta- 10102121

Exa- Exa- 10101818

Peta-Peta- 10101515

Tera-Tera- 10101212

Giga- Giga- 101099

Mega- Mega- 101066

The Big

4 kilobytes RAM

TRS - 80Commodore 64

64 kilobytes RAM

Macintosh

128 kilobytes RAM

486 PC

64 Megabytes RAM(max)

This top of the line gamingpc has 12 Gigabytes of RAM

Here are the othersexpressed in GigabytesTRS-80 - .000004 Gbytes

C64 - .000064 Gbytes

First Mac - .000128 Gbytes

486PC - .064 Gbytes

An average digital picture takes around 500 kilobytes

An average music file takes ~3-5 Megabytes

Ipods (4-160 Gigabytes) Flash/thumbdrives up to 32 Gigabytes

Desktop hard drive up To 20 Terabytes

External hard drivesup to ~3 Terabytes

~100 Tb

24 Pb processed daily

1 Eb = 50 000 years of DVD 500+ Eb = sum of Earth’s digital data (2010)

The little…The little…

micro-micro- 1010-6-6

nano-nano- 1010-9-9

pico-pico- 1010-12-12

femto-femto- 1010-15-15

atto-atto- 1010-18-18

zepto-zepto- 1010-21-21

yocto- yocto- 1010-24-24

1mm

There are 1,000 µm in 1 mm.

That means there are 1,000,000 nm in 1 mm

µ = micro

Many cocci bacteria measure around 1 µm (1000X)1,000 of them could line up across the dime’s edge

One bacterium is 1,000 nm across.

How many microns? How many nanometers?

The wavelengths of the visible light spectrumRange from 400(violet) to 750(red) nm.

A major issue with the light microscope involves magnification beyond the wavelengthof light that is being observed. Thus, the limit of the light microscope is 1000Xmagnification.

X-ray wavelengths measure < 10 nm

1 nm = 1,000 pm p=pico

The radius of a helium atomis estimated to be around30 pm.

radius

1.6 x 107 helium atomsCould line up on the Edge of a dime.

That’s ~16,000,000 atoms across.

This is just the beginning of measurement…