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Physical SciencePhysical Science

MeasurementMeasurement

Slides subject to changeSlides subject to change

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What to Measure? Fundamental Units such as

Length (meter, abbr. m) Mass (kilogram, abbr. kg) Time (second, abbr. s)

Derived Units such as Velocity: kilometers/hour, miles/hour Area: square meters (abbr. m2 ) Volume: cubic meters (abbr. m3)

3Vitruvian Man (Leonardo da Vinci)

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Metric SystemMetric System The international “decimalised” system of The international “decimalised” system of

measurement was first adopted by France in measurement was first adopted by France in 1791. Common system of measuring units 1791. Common system of measuring units used by most of the world.used by most of the world.

In the United States, metric units are widely In the United States, metric units are widely used in science, military, and industry.used in science, military, and industry.

Some names for metric system

“mks” = m − kg − s

or SI (“Le Système international d'unités”)

or simply, the “metric system”

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LengthLength Historically, in 1790, French must make a Historically, in 1790, French must make a

decision:decision: 1 meter = length of a pendulum with1 meter = length of a pendulum with

a “half-period” of one second. a “half-period” of one second. OROR

000,000,10

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1 meter = one ten-millionth of the 1 meter = one ten-millionth of the distance from the equator to the distance from the equator to the north pole.north pole.

DunkirkDunkirk

BarcelonaBarcelona

MeterMeter So ... distance was chosen. So ... distance was chosen. One meter defined in 1793 as the distance One meter defined in 1793 as the distance

between two scratches on a metal bar in between two scratches on a metal bar in Paris, Paris, pending completion of the surveypending completion of the survey. .

Became official in 1795, lasted to 1960.Became official in 1795, lasted to 1960.

Today one meter equals the distance Today one meter equals the distance travelled by light in vacuum during a time travelled by light in vacuum during a time interval of 1/299,792,458 of a second.interval of 1/299,792,458 of a second.

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Lengths in Metric SystemLengths in Metric System Common multiples, submultiples:Common multiples, submultiples:

kilokilometer (10meter (1033 meter) meter)

centicentimeter (0.01 or 10meter (0.01 or 10-2-2 meter) meter) millimillimeter (0.001 or 10meter (0.001 or 10−3−3 meter) meter) micromicrometer (10meter (10−6−6 meter) meter) nanonanometer (10meter (10−9−9 meter) meter)

larg

er >

Compare to English 1 inch = 2.54 cm (approx. width of your

thumb) 1 meter = 1.09 yard

Slightly more than three feet. 100 meter race is longer or shorter

than 100 yard race? 1 kilometer = 0.6 mile

10 km (10K) race is what distance in miles?

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International 1-kg StandardInternational 1-kg Standard 1 gram (mass of 1.0 cm1 gram (mass of 1.0 cm33 H H22O).O). 1,000 grams is a kilogram.1,000 grams is a kilogram.

Exact mass kept in France.Exact mass kept in France. Accurate copy sent to U.S. in 1899.Accurate copy sent to U.S. in 1899. Platinum-iridium cylinder. Platinum-iridium cylinder.

1 kg = 2.2 lbs.1 kg = 2.2 lbs.

More About Grams 1 gram = tiny cube of water. 1.0 cm X 1.0 cm X 1.0 cm. = 1.0 cm3

In medicine this volume is called a “cc”–— “cubic centimeter.”

In drinking water, it is called a milliliter (ml).

Common bottle of water is 500 ml or 500 cc. Mass is 500 g or 0.500 kg.

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Time Egyptians subdivided daytime into twelve Egyptians subdivided daytime into twelve

hours since at least 2000 BC.hours since at least 2000 BC. Greeks divided a full day into 24 equal Greeks divided a full day into 24 equal

hours around 150 BC.hours around 150 BC. Hour subdivided into 60 units to

what we call “minutes,” to 60ths of that − to what we call

“seconds” − by the Babylonians after 300 BC.

hour: Latin hora, hour, time, season..minute: Latin pars minuta prima, first small part.second: Latin pars secunda minuta, second small part.

One SecondOne Second Today ... Today ...

Officially one second is related to the Officially one second is related to the frequency of the radiation from cesium-frequency of the radiation from cesium-133–the time to perform 9,192,631,770 133–the time to perform 9,192,631,770 oscillations. oscillations. 

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Time in MetricTime in Metric Common multiples, submultiples:Common multiples, submultiples:

millimillisecond or “ms” (10second or “ms” (10-3-3 s) s) micromicrosecond or “second or “μμs” s” (10(10-6-6 s) s) Minute (60 s) ... Minute (60 s) ... hmmm, this isn’t hmmm, this isn’t

metric.metric. Hour (60 minutes) ... Hour (60 minutes) ... hmmm, this isn’t hmmm, this isn’t

metric either.metric either.

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Metric 10-Hour WatchMetric 10-Hour Watch What time is it?What time is it? Decimal time introduced Decimal time introduced

during the French during the French Revolution in the decree of Revolution in the decree of October 5, 1793.October 5, 1793.

Midnight is 10 o’clock.Midnight is 10 o’clock. Noon is 5 o’clock.Noon is 5 o’clock.

7:45:07 pm7:45:07 pm

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Major Submultiples, MultiplesMajor Submultiples, Multiples

SubmultiplesSubmultiples MultiplesMultiples

centi-centi- 1010-2-2 kilo-kilo- 101033

milli-milli- 1010-3-3 mega-mega- 101066

micro-micro- 1010-6-6 giga-giga- 101099

nano-nano- 1010-9-9 tera-tera- 10101212

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Convert UnitsConvert Units The power of “One”The power of “One”

Conversion factor: 2.54 cm = 1 inchConversion factor: 2.54 cm = 1 inch

And so does ...And so does ...

2.54 cm2.54 cm

== 111 in1 in

1 in1 in

== 112.54 cm2.54 cm

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Convert UnitsConvert Units Convert 5 inches to centimetersConvert 5 inches to centimeters 5 in. = 5 in. x 5 in. = 5 in. x 11

= 5 in. x = 12.7 cm= 5 in. x = 12.7 cm2.54 cm2.54 cm

1 in1 in

Use Use dimensional analysisdimensional analysis to get the units to get the units straight. “Inches” cancel, leaving straight. “Inches” cancel, leaving centimeters (cm).centimeters (cm).

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Convert SpeedConvert Speed Conversion factors:Conversion factors:

1 m = 3.28 ft1 m = 3.28 ft 1 mile = 5280 ft1 mile = 5280 ft

What is 60 mi/hr in km/hr?What is 60 mi/hr in km/hr?

x x xx x x

= 97 km/hr= 97 km/hr

5280 ft5280 ft

1 mi1 mi

1 m1 m

3.28 ft3.28 ft

1 km1 km

101033 m m

60 mi60 mi

hrhr

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Another ExampleAnother Example

Given 1 mile = 5,280 feetGiven 1 mile = 5,280 feet What is 60 mi/hr in ft/s ?What is 60 mi/hr in ft/s ?

x x xx x x

= 88 ft/s= 88 ft/s

5280 ft5280 ft

1 mi1 mi

1 hr1 hr

60 min60 min

1 min1 min

60 s60 s

60 mi60 mi

hrhr

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RoundingRounding Round 387 to “two places”Round 387 to “two places”

Locate the digit in that place (the “Locate the digit in that place (the “88”).”). Consider the digit to its right (the “Consider the digit to its right (the “77”).”). If the digit to the right (the “If the digit to the right (the “77”) is 5 or ”) is 5 or

higher, round up; if the digit to the higher, round up; if the digit to the right is less than 5 round down. right is less than 5 round down.

Answer is Answer is 390390..

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Rounding ExerciseRounding Exercise Round 3872.2459 to the nearest:Round 3872.2459 to the nearest:

a. thousandtha. thousandth b. hundredthb. hundredth c. tenthc. tenth d. oned. one e. tene. ten f. hundredf. hundred g. thousandg. thousand

View View ππ (pi(pi) on your calculator. Round to four ) on your calculator. Round to four significant figures.significant figures.

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More about Sig FigsMore about Sig Figs 0.00052 has two sig figs, 1.00052 has six, 0.00052 has two sig figs, 1.00052 has six,

1.230 has four.1.230 has four. When we say one foot has 12 inches, the When we say one foot has 12 inches, the

12 is 12 is exactexact, don’t consider it when figuring , don’t consider it when figuring the number of significant figures.the number of significant figures.

Assume values in text problems are exact, Assume values in text problems are exact, thus the text’s “100 miles” has thus the text’s “100 miles” has threethree sig sig figs.)figs.)

Scientific notation is relatively easy for Scientific notation is relatively easy for significant figures: 5.66x10significant figures: 5.66x1088 has 3 sig figs. has 3 sig figs.

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Even More on Sig FigsEven More on Sig Figs In multiplication or division, your answer will In multiplication or division, your answer will

have lowest sig. figs. of the terms you are have lowest sig. figs. of the terms you are calculating. calculating.

4.2 x 3.4159 - least significant figure term has 4.2 x 3.4159 - least significant figure term has 2 sig figs (14). 2 sig figs (14).

Answer is 14. (not 14.34678).Answer is 14. (not 14.34678).

If you do the entire problem on your calculator, If you do the entire problem on your calculator, adjust the answer for significant figures at the adjust the answer for significant figures at the endend..

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An Equation: DensityAn Equation: Density Density is the mass per unit volume of an Density is the mass per unit volume of an

object.object. In Words: Density = Mass / VolumeIn Words: Density = Mass / Volume

SymbolsSymbols mass = mass = mm density = density = ρρ volume = volume = VV Equation Equation ρρ = = mm//VV

Example: Example: Water density is 1.00 gram/cm Water density is 1.00 gram/cm33..

Greek letter “Greek letter “rhorho””

4. Solveρρ = 9,650 g / 500 cm = 9,650 g / 500 cm33

= 19.3 g/cm= 19.3 g/cm33

4. Solveρρ = 9,650 g / 500 cm = 9,650 g / 500 cm33

= 19.3 g/cm= 19.3 g/cm33

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DensityDensity A certain bar of gold has a mass of A certain bar of gold has a mass of 9,650 g 9,650 g

and volume of and volume of 500500 cm cm33. . What is its density What is its density (in g/cm(in g/cm33)? )?

2. Givens

m = 9,650 g (√ right units)

V = 500 cm3 (√ right units)

2. Givens

m = 9,650 g (√ right units)

V = 500 cm3 (√ right units)

3. Potential Formula

ρρ = = mm//VV

3. Potential Formula

ρρ = = mm//VV

1. Understand the problem.1. Understand the problem.