physics 1710—section 4 instructor—matteson session #2 chapter 1 measurement

Physics 1710Physics 1710—Section 4—Section 4Instructor—Matteson Instructor—Matteson

Session #2Session #2

CChapter 1 Measurementhapter 1 Measurement

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Joe College Seat# 53

1/14/02 Session #1Foolscap “Quiz”

Physics 1710Physics 1710—C—Chapter 1 Measurementhapter 1 Measurement

Fact:Fact:

The earth has a circumference of The earth has a circumference of approximately 40 million meters (4. X 10approximately 40 million meters (4. X 1077 m). How fast must one move on average to m). How fast must one move on average to travel around the world in 80 days?travel around the world in 80 days?


11′′ Lecture Lecture• First First 3 Fundamental Units:3 Fundamental Units:

–TimeTime, measured in , measured in secondsseconds = 1/86 400 of = 1/86 400 of m.s. daym.s. day–LengthLength, measured in, measured in meters meters = c = c (1/ (1/299 792 299 792 458 sec) 458 sec) –MassMass, measured in , measured in kilogramskilograms = specimen = specimen

• Prefixes scale units to convenient size.Prefixes scale units to convenient size.• Density is mass per unit volume. [Density is mass per unit volume. [kg/mkg/m3 3 ]]• Avogadro’s number is the number of Avogadro’s number is the number of atomsatoms in a mole of an element, N in a mole of an element, NAvogadroAvogadro = = 6.022x106.022x102323

• Significant figures tell the tale.Significant figures tell the tale.• Scientific notation saves ink.Scientific notation saves ink.


Q&A:Q&A:Q:Q: Is this class mainly for engineers? I ask this Is this class mainly for engineers? I ask this because I am pre-med. Does this course apply to because I am pre-med. Does this course apply to my field?my field?

A(s):A(s): No, it is for scientists as well. No, it is for scientists as well. Yes, it does apply to your field. Yes, it does apply to your field. You will learn facts about how things move, You will learn facts about how things move,

e.g. consider muscles, joints, blood, air. e.g. consider muscles, joints, blood, air. You will grow an understanding of dynamics, You will grow an understanding of dynamics,

e.g. energy, momentum and trauma.e.g. energy, momentum and trauma. You will develop analytical and qualitative You will develop analytical and qualitative skills,skills,

e.g. think about diagnosis and drug dosing.e.g. think about diagnosis and drug dosing. This course is for all scientists This course is for all scientists andand engineers. engineers.


Laboratory IntroductionLaboratory Introduction

Physics 1730Physics 1730

Dr. John PrinceDr. John Prince


Matteson’s Dicta Numbers 1 & 2:Matteson’s Dicta Numbers 1 & 2:

1. Physics is that branch of science 1. Physics is that branch of science concerned with the concerned with the interaction of matter-interaction of matter-energyenergy in space-time. in space-time.

2. The physical universe consists of 2. The physical universe consists of only only matter and energy and the vacuum.matter and energy and the vacuum.

• Late breaking news: what about “Late breaking news: what about “dark dark mattermatter” and “” and “dark energydark energy?” They are 95% ?” They are 95% of universe and we don’t yet know what of universe and we don’t yet know what they are.they are.


MeasurementMeasurement is the quantitative is the quantitative comparison of a physical parameter to a comparison of a physical parameter to a standard unit.standard unit.


“Existential Physics” Activity:

Measure the width of the top of your desk in “hands.”

Why did we observe a variety of Why did we observe a variety of values values

in our measurement?in our measurement?


MeasurementMeasurement is the quantitative is the quantitative comparison of a physical parameter to comparison of a physical parameter to a a standard unitstandard unit..

‽ ‽ A “hand” is A “hand” is notnot a standard unit. a standard unit.

Our measurement is subject to error. Our measurement is subject to error.

Our measurement is coarse. Our measurement is coarse.

MeasurementMeasurement is the quantitative is the quantitative comparison of a physical parameter to a comparison of a physical parameter to a standard unit. Therefore we need standards.standard unit. Therefore we need standards.

Accuracy Accuracy is the difference of a is the difference of a measurement from the (unknown) true measurement from the (unknown) true value. All measurement contain value. All measurement contain experimental error.experimental error.

Precision Precision is the “fineness” of the division is the “fineness” of the division of the scale used to compare to the standard of the scale used to compare to the standard unit. Precision limits our knowledge.unit. Precision limits our knowledge.


80/2080/20PrecisionPrecision is the fineness of a is the fineness of a measurement.measurement.

80/2080/20AccuracyAccuracy is the correspondence of a is the correspondence of a measurement to an (unknown) true measurement to an (unknown) true value.value.

Less Less preciseprecise

Less Less accurateaccurate

StandardStandard

MeasuremeMeasurementnt


What numbers one writes down reveals What numbers one writes down reveals one’s knowledge (and ignorance) of the one’s knowledge (and ignorance) of the actual true (but unknown) value.actual true (but unknown) value.

Example:Example:2. 2.0 2.01 2.0085 2.00852 2. 2.0 2.01 2.0085 2.00852 represent the values of a measurement at represent the values of a measurement at various levels of precision. various levels of precision.


Significant figures:Significant figures:

•When multiplying (or dividing) numbers, When multiplying (or dividing) numbers, round result to same number of significant round result to same number of significant figures as the factor with figures as the factor with leastleast number of number of significant figures.significant figures.

•When adding (or subtracting), first round to When adding (or subtracting), first round to same decimal place as contribution with the same decimal place as contribution with the least least precision, then compute.precision, then compute.


Rules for Computing Rules for Computing with Significant Figures:with Significant Figures:


Rules for RoundingRules for Rounding

• If remainder is less than 5, truncate, i.e. round down.

Example: 3.1415927… ~ 3.14

• If remainder is larger than 5, round up.

Example: 3.1415927… ~3.1416

• If remainder is exactly 5, round up or down to leave last digit even.

Example: 31½ = 31.5000… ~32.

Scientific Notation

Number = Mantissa x 10 Exponent = _._____ E__

Big Numbers: 1.234567 x 10 3 = 1234.567

Small Numbers: 1.234567 x 10 –2 = 0.01234567


Activity:Activity:

Enter: “Enter: “1.234567” ; “EXP” or “EE”; 1.234567” ; “EXP” or “EE”; “03” “03”

Display should read: Display should read: “1.234567 “1.234567 03”03” or or

“1.234567E03”“1.234567E03”

Enter: “Enter: “1.234567”; “EXP”; “03” ;1.234567”; “EXP”; “03” ;“+/-” or ““+/-” or “⇄” or “(-)”⇄” or “(-)”

Display should read: “Display should read: ““1.234567“1.234567-03-03” or ” or

“1.234567E-03”“1.234567E-03”


Know Your Calculator

1770 1780 1790 1800 1810


Fundamental UnitsFundamental Units

• Système International de Metrique (SI)— “Metric System”

• First introduced in France in 1799—(on Napoleon’s coup)

La La $$

American Rev

US Constitution

French Rev

Napoleon


Time Standard: Time Standard: secondsecond [s] [s]

• (1/60)(1/60)(1/24) =1/86,400 (1/60)(1/60)(1/24) =1/86,400 mean solar daymean solar day

• 9,192,631,770 (exactly) times the 9,192,631,770 (exactly) times the period period

of vibration of a Cesium-133 of vibration of a Cesium-133 atomic clock.atomic clock.

• Time DemonstrationTime Demonstration

Length standard: Length standard: metermeter [m] [m]

• Meter defined in 1799, by Napoleon’s Meter defined in 1799, by Napoleon’s Republic.Republic.

• 1/101/107 7 quadrant of Earth; C quadrant of Earth; C= 4.00x 10= 4.00x 107 7 mm

• Distance light travels in 1/299,792,458 Distance light travels in 1/299,792,458 secsec

• Meter DemonstrationMeter Demonstration


Derived Units of area and Derived Units of area and volumevolume• Area: Area: 10 m 10 m xx 10 m = 100 m 10 m = 100 m 22 = 1 are = 1 are

100 ares = 1 hectare = 1x10100 ares = 1 hectare = 1x1044 m m22 1 US acre = 0.4046 ha1 US acre = 0.4046 ha

• Volume: Volume: m m xx m m xx m = m m = m 33 = 1000 liter = = 1000 liter = 1000 l1000 l

e.g. 1000 cm e.g. 1000 cm 33 = 1 liter = 1 liter1 US gallon = 3.7854118 liters ~ 3.8 l1 US gallon = 3.7854118 liters ~ 3.8 l


Mass Standard : kilogram [kg]Mass Standard : kilogram [kg]• kilo = 1000, 1 kg = 1000 gramkilo = 1000, 1 kg = 1000 gram

• 1 kg is the mass of approximately 1 kg is the mass of approximately 1/1000 m1/1000 m33 (=1 liter) of water (=1 liter) of water

• Mass is a fundamental property of all Mass is a fundamental property of all matter.matter.

• Each atom has a mass of ~1.66 x 10Each atom has a mass of ~1.66 x 10-27-27 kg kg times its “atomic mass number”times its “atomic mass number”


Mass Standard : kilogram [kg]Mass Standard : kilogram [kg]

•1 kg weighs on earth about 2.2 1 kg weighs on earth about 2.2 pounds.pounds.


Amedo AvogadroAmedo Avogadro

(1776-1856)(1776-1856)• Italian PhysicistItalian Physicist

• Proposed Avogadro’s Proposed Avogadro’s Law Law (1811)(1811)


22.8 liters = 1 mole of gas = 6.022 x1023 molecules or atoms 12 g C = 1 mole

NNAA = 6.0221367(28) x 10 = 6.0221367(28) x 10 2323 atoms/mole atoms/mole

Atomic mass unit = u Atomic mass unit = u

u = 1.660 540 2(10) x 10 u = 1.660 540 2(10) x 10 –27–27kgkg(~ 1 (~ 1 22//33 yoctogram) yoctogram)

NNAA ‧ ‧ u = 1.00 x 10 u = 1.00 x 10 –3–3 kg = 1.00 gram kg = 1.00 gram

NNAA is the number of atoms in one is the number of atoms in one “gram molecular weight” of an “gram molecular weight” of an element.element.

Avogadro’s NumberAvogadro’s Number


Practice:Practice:

How much does a 5 US Gal can of water How much does a 5 US Gal can of water weigh?weigh?Density of water = 1.0 kg/l

M = ρ V = (1.0 kg/l )(5 gal x 3.8 l/gal) = 19. kg

W = 2.2 lbs/kg x 19. kg = 42. lbs


SummarySummary•Fundamental Fundamental DimensionsDimensions and and UnitsUnits

TimeTime, measured in , measured in secondsseconds;;

LengthLength, measured in, measured in metersmeters;;

MassMass, measured in , measured in kilogramskilograms..

• PrefixesPrefixes scale units to convenient size. scale units to convenient size.k =1000, M = 1 000 000k =1000, M = 1 000 000c = 1/100, m = 1/1000, c = 1/100, m = 1/1000, μ =1/1 000 000μ =1/1 000 000

• DensityDensity is mass per unit volume. is mass per unit volume.ρ = m/V ρ = m/V [[kg/mkg/m3 3 ]]

• Avogadro’s numberAvogadro’s number is the number of atoms is the number of atoms in a mole of an element. in a mole of an element. 6.022 x106.022 x102323 atom/mole atom/mole


11′ Essay′ Essay• What was that about?What was that about?• An “Aha!”An “Aha!”• A QuestionA Question

Turn in Foolscap.Turn in Foolscap.

Come to Come to

Recitation in Room 102Recitation in Room 102

1:00 p.m. Today!1:00 p.m. Today!


physics 1710—section 4 instructor—matteson session #2 chapter 1 measurement

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