Laying the Groundwork

Observing, Estimating, Measuring, Recording, Graphing, Analyzing,

Interpreting

…and Units!

We Are Scientists, We Use Scientific Notation!

Scientific Notation, Specifically

10n means 10 x 10 x 10 … [n times]10-n means 1/(10 x 10 x 10 ….) [n times]

10a •10b = 10 a + b

10a ÷10b = 10 a - b

We are Scientists, We use the Metric System!

Length Mass Time Temperature

First, a little historical information on the system

Then, a review of the prefixes

Finally, specifics for:

History of the Metric System Created at the end of the 18th Century to provide a Created at the end of the 18th Century to provide a consistent system of units amidst a wide variety of different consistent system of units amidst a wide variety of different standards. standards.

Previously, each area had its own units inherited from Previously, each area had its own units inherited from earlier times.earlier times.

Not reproducable, not standardNot reproducable, not standarde.g., a "cubit" was the length from the elbow to the tip e.g., a "cubit" was the length from the elbow to the tip of the middle finger.of the middle finger.e.g., a rundlet was worth 16 gallons in a certain town e.g., a rundlet was worth 16 gallons in a certain town and 18 gallons in another townand 18 gallons in another town

History, Part 2

The metric system became compulsory in France on The metric system became compulsory in France on Dec.10, 1799 (Napoleon was First Consul) and, being Dec.10, 1799 (Napoleon was First Consul) and, being practical, spread slowly across Europe. practical, spread slowly across Europe.

Not without resistance : a few years later, even France Not without resistance : a few years later, even France came back to the old system for several years. came back to the old system for several years. Japan made it official in 1868 and Russia in 1917. Japan made it official in 1868 and Russia in 1917.

England was the last European country to adopt it : the England was the last European country to adopt it : the adaptation period began in 1965 and was to end officially adaptation period began in 1965 and was to end officially in 1980.in 1980.

History, Part 3 In 1960, the In 1960, the SI (International System) SI (International System) was created was created

It fine tuned the system, introducing some new units It fine tuned the system, introducing some new units and shedding others. and shedding others.

It replaces the old systems, named MKSA, MTS, and It replaces the old systems, named MKSA, MTS, and CGS (although some intrepid physicists still use CGS CGS (although some intrepid physicists still use CGS from time to time, which is considered OK since they do from time to time, which is considered OK since they do at least provide a consistent set of secondary units.) at least provide a consistent set of secondary units.)

History, Part 4

The seven The seven primaryprimary units are now : units are now :

** length :length : meter (m) meter (m) ** mass :mass : kilogram (kg) kilogram (kg) ** time :time : second (s) second (s) ** electric current :electric current : ampere (A) ampere (A) ** temperature : temperature : Kelvin or Celsius (K or °C) Kelvin or Celsius (K or °C) ** quantity of matter :quantity of matter : mole mole ** light intensity : light intensity : candela (cd) candela (cd)

PrefixesOne of the clever ideas behind the system was to use One of the clever ideas behind the system was to use onlyonly multiples of ten. Today mainly multiples of 1000 are multiples of ten. Today mainly multiples of 1000 are in use. These are the only words to memorize (if you're in use. These are the only words to memorize (if you're not lucky enough to have enjoyed them since Grade 3) : not lucky enough to have enjoyed them since Grade 3) :

** 10101818 : : exa- (E) exa- (E) ** 10101515 : : peta- (P) peta- (P) ** 10101212 : : tera- (T) tera- (T) ** 101099 : : giga- (G) giga- (G) ** 101066 : : mega- (M) mega- (M) ** 101033 : : kilo- (k) kilo- (k) ** 1010-3-3 : : milli- (m) milli- (m) ** 1010-6-6 : : micro- (µ) micro- (µ) ** 1010-9-9 : : nano- (n) nano- (n) ** 1010-12-12 : : pico- (p) pico- (p) ** 1010-15-15 : : femto- (f) femto- (f) ** 1010-18-18 : : atto- (a)atto- (a)

Old, but not ForgottenSome prefixes by ten, around the main unit, are Some prefixes by ten, around the main unit, are still in use :still in use :

** 100 : hecto- (h) like in hectolitre (used by 100 : hecto- (h) like in hectolitre (used by the breweries - God save the beer !) the breweries - God save the beer !)

** 10 : deca- (da) like in decameter 10 : deca- (da) like in decameter (sometimes written dekameter)(sometimes written dekameter) ** 0.1 : deci- (d) like in decibel 0.1 : deci- (d) like in decibel

** 0.01 : centi- (c) like in centipoise (same 0.01 : centi- (c) like in centipoise (same root as "cent", you may say centidollar !)root as "cent", you may say centidollar !)

Length

Unit of length: meterUnit of length: meter

The meter is the length of the path traveled by The meter is the length of the path traveled by light in vacuum during a time interval of light in vacuum during a time interval of 1/299,792,458 of a second.1/299,792,458 of a second.

Meter Originally defined as one ten-millionth of the distance Originally defined as one ten-millionth of the distance between a Pole and the Equator as measured from 1792 between a Pole and the Equator as measured from 1792 along a meridian from Dunkirk to Barcelona across Paris along a meridian from Dunkirk to Barcelona across Paris

This measurement took several years through wars and This measurement took several years through wars and civil unrest civil unrest

Astronomers were arrested by revolutionaries because Astronomers were arrested by revolutionaries because they had lots of paper and white was the “King's color” !they had lots of paper and white was the “King's color” !

If the Earth were a perfect sphere, its circumference If the Earth were a perfect sphere, its circumference would be 40,000 km, and the distance from a Pole to the would be 40,000 km, and the distance from a Pole to the Equator would be 10 000 km.Equator would be 10 000 km.

A Fly in the Ointment It was already known that the Earth was flattened on the It was already known that the Earth was flattened on the Poles. Poles.

Nevertheless, a meridian was chosen (in a typical Nevertheless, a meridian was chosen (in a typical French Revolution way) because it was valid "for all people French Revolution way) because it was valid "for all people around the Earth, whereas the Equator only covers a small around the Earth, whereas the Equator only covers a small fraction of humanity".fraction of humanity".

The meter was set for a long time by its physical model in The meter was set for a long time by its physical model in platinum-iridium, in Paris. Hard to reproduce, and eventually platinum-iridium, in Paris. Hard to reproduce, and eventually scientists needed more precisionscientists needed more precision

Physicists introduced it as a multiple of a wavelength Physicists introduced it as a multiple of a wavelength (1, 650, 763.73) times the wavelength of the radiation (1, 650, 763.73) times the wavelength of the radiation associated with a certain atomic jump in Krypton 86.associated with a certain atomic jump in Krypton 86.

Historical Detail

Meter was first defined as the length of a pendulum Meter was first defined as the length of a pendulum which oscillated with a period of two seconds. This which oscillated with a period of two seconds. This was dropped because of the difficulty in measuring was dropped because of the difficulty in measuring the exact length of the string from the oscillation the exact length of the string from the oscillation axis to the center of the ball - and also the gravity axis to the center of the ball - and also the gravity "g" is not constant all over the Earth."g" is not constant all over the Earth.

QuickTime™ and aGIF decompressorare needed to see this picture.

Special Units

One millionth of a meter, or micrometer, is One millionth of a meter, or micrometer, is often called often called micronmicron

The The angstromangstrom, not SI but still used in , not SI but still used in physics, is equal to 10physics, is equal to 10-10-10 meter meter

Old Anglo Saxon Units

inchinch : 25.4 mm : 25.4 mm

footfoot = 12 inches = 0.3048 m = 12 inches = 0.3048 m yardyard = 3 feet = 0.9144 m = 3 feet = 0.9144 m

milemile = 1760 yards = 1609.344 m (derived from = 1760 yards = 1609.344 m (derived from the Roman Mile : "mille passus" equal to 1000 the Roman Mile : "mille passus" equal to 1000 paces or double steps, estimated at 1475 to 1522 paces or double steps, estimated at 1475 to 1522 m. This makes the step = 0.75 m (remember the m. This makes the step = 0.75 m (remember the Romans were not as tall as we are).Romans were not as tall as we are).

nautical milenautical mile = 6076.115 feet = 1852 m = 6076.115 feet = 1852 m

Used today ONLY in USA

USA and the Metric System Thomas JeffersonThomas Jefferson considered a conversion considered a conversion to the metric system. In 1889, to the metric system. In 1889, the US Congress adopted the US Congress adopted the meter as a standard and, the meter as a standard and, thereafter, the inch, foot, thereafter, the inch, foot, yard, etc. were defined in yard, etc. were defined in relation to the meter. relation to the meter.

The The Metric Conversion Act of 1975 Metric Conversion Act of 1975 committed committed the US to the increasing use of, and voluntary the US to the increasing use of, and voluntary conversion to, the metric system of measurement.conversion to, the metric system of measurement.

MassUnit of mass: kilogram  Unit of mass: kilogram  

The kilogram is the unit of mass; it is equal to the The kilogram is the unit of mass; it is equal to the mass of the international prototype of the mass of the international prototype of the kilogram.kilogram.

Kilogram

As the name implies, the original unit was the gram As the name implies, the original unit was the gram (weight of 1 cubic centimeter or 1 milliliter of water at 4 °C) (weight of 1 cubic centimeter or 1 milliliter of water at 4 °C) but it soon became the kg (or 1000 grams or one cubic but it soon became the kg (or 1000 grams or one cubic decimeter of water), and defined by its model in platinum-decimeter of water), and defined by its model in platinum-iridium kept in Paris. iridium kept in Paris.

One may also mention the One may also mention the caratcarat used in jewelry used in jewelry (5 carats = 1 gram). But carat is not an SI unit!(5 carats = 1 gram). But carat is not an SI unit!

Historical Detail Before the computations of the Dunkirk-Before the computations of the Dunkirk-Barcelona meridian were completed, a first Barcelona meridian were completed, a first measure was introduced : the measure was introduced : the gravegrave (same root (same root as gravity) equal to the weight of one cubic as gravity) equal to the weight of one cubic decimeter of water. decimeter of water.

Later, the (now well defined) milligrave - Later, the (now well defined) milligrave - already dubbed the already dubbed the gravetgravet - was renamed the - was renamed the gramgram..

Old Anglo-Saxon Units pound :pound : 0.45359237 kg in the Avoirdupois system (but 0.45359237 kg in the Avoirdupois system (but 0.3732417 kg in the Troy and Apothecaries systems.) The 0.3732417 kg in the Troy and Apothecaries systems.) The smallest unit common to the different systems is the grain ( = smallest unit common to the different systems is the grain ( = 64.7989 milligrams) with 7000 grains making one 64.7989 milligrams) with 7000 grains making one (Avoirdupois) lb. and 5760 grains for one pound in the other (Avoirdupois) lb. and 5760 grains for one pound in the other systems. The abbreviation "lb" comes from the equivalent systems. The abbreviation "lb" comes from the equivalent Roman weight "libra”.Roman weight "libra”.

ounce :ounce : In Avoirdupois : 437.5 grains ( = 28.3495 g -- 16 In Avoirdupois : 437.5 grains ( = 28.3495 g -- 16 oz = 1 lb.). In the other systems : 480 grains ( = 31.10348 g -- oz = 1 lb.). In the other systems : 480 grains ( = 31.10348 g -- 12 oz = 1 lb.) 12 Roman "unciae" made 1 "libra" - 12 oz = 1 lb.) 12 Roman "unciae" made 1 "libra" - unciauncia simply means simply means one twelfthone twelfth in Latin.) in Latin.)

Time

Unit of time: secondUnit of time: second

The second is the duration of 9,192,631,770 The second is the duration of 9,192,631,770 periods of the radiation corresponding to the periods of the radiation corresponding to the transition between the two hyperfine levels of transition between the two hyperfine levels of the ground state of the cesium 133 atom.the ground state of the cesium 133 atom.

Nature Gives Us Natural Time Scales

Originally, the Originally, the secondsecond was 1/86400 of the was 1/86400 of the mean solar day. mean solar day.

But, the mean solar day changes slowly, so it But, the mean solar day changes slowly, so it was redefined on a steadier atomic levelwas redefined on a steadier atomic level

Original Cesium clocks good to about 1 Original Cesium clocks good to about 1 second every 3,000 yearssecond every 3,000 years

Atomic Clock at NIST

The uncertainty of NIST-F1 is less than 2 x 10The uncertainty of NIST-F1 is less than 2 x 10-15-15, which , which means it would neither gain nor lose a second in 20 million means it would neither gain nor lose a second in 20 million years! years!

Seemed Like a Good Idea, but...

There was a trial to "metricate" the time and the There was a trial to "metricate" the time and the calendar during the French revolution. Months were calendar during the French revolution. Months were to be made of three weeks, each ten days long. to be made of three weeks, each ten days long. Each day had 10 hours. The system lasted only a Each day had 10 hours. The system lasted only a few years. The clockmakers opposed violently the few years. The clockmakers opposed violently the millihours ( = 8.64 sec), while the clergy resented millihours ( = 8.64 sec), while the clergy resented the cancellation of the Sabbath. This last opposition the cancellation of the Sabbath. This last opposition is probably at the root of the long time dislike is probably at the root of the long time dislike towards the metric system in the US.towards the metric system in the US.

Temperature

Unit of thermodynamic temperature: Unit of thermodynamic temperature: KelvinKelvin

The Kelvin, unit of thermodynamic The Kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of temperature, is the fraction 1/273.16 of the thermodynamic temperature of the the thermodynamic temperature of the triple point of water.triple point of water.

History of Temperature Scales

The first to seal mercury in a The first to seal mercury in a glass rod was Daniel glass rod was Daniel FahrenheitFahrenheit in Germany (1709). in Germany (1709). He had to build a scale from He had to build a scale from scrap : zero was allocated to scrap : zero was allocated to the temperature of a salty the temperature of a salty mixture, assuming that nothing mixture, assuming that nothing could ever be colder and 96 could ever be colder and 96 was was his estimatehis estimate of the human of the human body. With such a scale, water body. With such a scale, water would freeze at 32 and boil at would freeze at 32 and boil at 212.212.

1686 - 1736

History of Temperature Scales

In 1730, in France, Rene In 1730, in France, Rene Antoine Ferchault de Antoine Ferchault de ReaumurReaumur built the first alcohol thermometer. built the first alcohol thermometer. He allocated 0 to freezing water He allocated 0 to freezing water and 80 to boiling water.and 80 to boiling water.

In 1742, in Sweden, the In 1742, in Sweden, the astronomer Anders astronomer Anders CelsiusCelsius used used a scale allocating 100 to freezing a scale allocating 100 to freezing water and 0 (!) to boiling water. His water and 0 (!) to boiling water. His scale was later inverted (0 to scale was later inverted (0 to freezing water and 100 for boiling) freezing water and 100 for boiling) and long known as "and long known as "centigradecentigrade". ".

CelsiusCelsius1701 - 17441701 - 1744

Half a Dozen One, 6 to the OtherComparing the scales, Comparing the scales, 9° Fahrenheit = 4° Reaumur = 5° Celsius9° Fahrenheit = 4° Reaumur = 5° Celsius

** C = (F - 32) * 5/9 C = (F - 32) * 5/9 ** F = 32 + C * 9/5 F = 32 + C * 9/5

The two scales meet at - 40 The two scales meet at - 40

** - 40°F is the same as - - 40°F is the same as - 40°C40°C

Absolute Temperature Starting from the absolute zero Starting from the absolute zero (at -273.15 C or -459.67 F), it was (at -273.15 C or -459.67 F), it was tempting to follow the old idea of tempting to follow the old idea of Fahrenheit and have only a positive Fahrenheit and have only a positive scale. This was done by Sir William scale. This was done by Sir William Thomson, Lord Thomson, Lord KelvinKelvin, from the , from the Celsius scale. Celsius scale.

Water is freezing at 273.15 K, Water is freezing at 273.15 K, and boiling at 373.15 Kand boiling at 373.15 K

The The SISI uses the uses the KelvinKelvin scale, scale, defined by the triple point of water defined by the triple point of water (at 273.16 K or 0.01°C) and absolute (at 273.16 K or 0.01°C) and absolute zero.zero.

1824 - 19071824 - 1907

Counting and MeasuringPhysics is the science of measurement.

“When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the beginning of knowledge, but you have scarcelyAdvanced to the state of Science.”

Lord Kelvin (1824 - 1907)

Accuracy and Precision

Limit of precision of a measuring divide is one-half the smallest division of measurement the device is able to display

The accuracy of a measurement is the extent to which systematic errors make a measured value differ from its true value

Accurate Precise Accurate & Precise

Errors

Systematic Errors: errors due either to incorrect design or calibration of the measuring device, or to incorrect reading or interpretation of the device

Statistical Errors: differences in individual measurements of a quantity which are greater than the precision of the measuring device, these differences arise from fluctuations in the quantity being measured.

What It Means

Significant Digits

The digits in a measured or calculated quantity are those digits which are known with certainty

Rules:1. When adding or subtracting measured quantities, the precision of the answer can only be as great as the least precise term in the sum or difference. All digits up to this limit of precision are significant.2. When multiplying or dividing measured quantities, the number of significant digits can be only as great as the least number of significant digits in any factor in the calculation.

Insights into Sig Figs

Zeroes can be confusing. They often appear only to locate the decimal point…which means they are not significant. Using scientific notation will resolve this issue.

Calculators cannot increase the number of sig figs in nor the precision of your measurements. You must round off the result to the correct number of digits.

Vectors and ScalarsA scalar is a quantity that has a magnitude only

A vector is a quantity that has both a direction and a magnitude

There are specific rules for adding and subtracting vectors. We’ll learn more about this later.

Graphs

Graphs display in a ready visualized form the relationship between pairs of independent quantities.

Scientists tend to use the words “graphs” and

“plots” interchangeably.

Scatter Plots Data consists of pairs of numbers, e.g., Data consists of pairs of numbers, e.g., intensity and time, height and distance, salary and intensity and time, height and distance, salary and ageage Plot allows you to perform mathematical fits, Plot allows you to perform mathematical fits, looking for trendslooking for trends

Histogram

A histogram is defined as a bar graph that shows A histogram is defined as a bar graph that shows frequency data. The first step in making a frequency data. The first step in making a histogram is to collect data and sort it into histogram is to collect data and sort it into categories. To continue, you must label the data categories. To continue, you must label the data as the independent set or the dependent set. as the independent set or the dependent set. The characteristic you grouped the data by The characteristic you grouped the data by would be the independent variable and the would be the independent variable and the frequency of that set would be the dependent frequency of that set would be the dependent variable.variable.

Histogram HistogramsHistograms are "sorting bins." You have are "sorting bins." You have oneone variable, variable, and you sort data by this variable by placing them into and you sort data by this variable by placing them into "bins." Then you count how many pieces of data are in each "bins." Then you count how many pieces of data are in each bin. The height of the rectangle you draw on top of each bin bin. The height of the rectangle you draw on top of each bin is proportional to the number of pieces in that bin.is proportional to the number of pieces in that bin.

We Are Scientists, We Use the Scientific Method

• • It is important to be as It is important to be as objective as possible. objective as possible.

• • There is no right place to There is no right place to enter the cycle. enter the cycle.

• • Experiments must be Experiments must be reproducible. reproducible.

• • There is no end to the cycle.There is no end to the cycle. • • The cycle is not rigid.The cycle is not rigid.