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# Conversion (Unit 1).pdf

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McMaster University

Physics

PHYSICS 1L03

Reza Nejat

Fall

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Introduction
Introduction
•W iti?
Physical Modeling –Physicsisthestudyofthefundamental
laws of nature.
Concepts: Why study Physics
Physical Model –Physicsistheactivityoftryingtofind
Significant Figures the rules by which nature plays.
Scientific Notation
Measurement
Order of magnitude
Estimation
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
•Stihc:s •utihc:s
•hiueogotili •Whomantoryis
and good problem solving skills is harder to learn than other sciences?
•Imealipsmay •Pyitmsfat
equations to be memorized.
seems much simpler than learning –Learnthebasiclaws,fundamental
biology or chemistry.
–Howisthispossible? relationships, and the skill in applying
them
PPhhyyssMMaasstteerr UUnniivveerrssiittyy,, RR..NNPhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•Tgals:s
–decitpyilise
• Keep in mind that physics is not really •gatherknowledgeaboutit
about finding an appropriate equation
and plugging in numbers, but is •discoverthephysicallawsthatruleit
instead about understanding concepts. • How to accomplish the goal?
–through observation, developing a
good model with predictive ability, and
measurement
Phys. 1L03, Fall 2013, McMaster University, R.NejPPhhyyssMMaasstteerr UUnniivveerrssiittyy,, RR..NNeejjaatt
Introduction Introduction
•Osritn •OseaiPhyil del
–Observation:
–Baeooubeaisemae
•isessentialforfiguringoutalaworarule models
things follow.
–Amodel is a mental image of objects
–thecornerstoneofdiscoveringnaturallaws. or phenomena that we experience
•shouldbequantitative,having numerical directly.
value.
PPhhyyssMMaasstteerr UUnniivveerrssiittyy,, RR..NPhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•Moelyis Models in Physics
–Rltdrlaomlx •m dltm:
–Focusesonthemostimportantproperties
–Bymodeling,acomplexobjectorproblem of the system
is simplified:
–Ignorescomplexity
•Byexcludingallbuttheimportantpart –Hasminimumnumberofassumptions
–Usesobservablephenomena
–Like: Particle model of motion
»Simplifyingthemotionofacomplex –Shouldhave predictive power
object as a motion of a single point •Shmoilhcloel .
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
It is important to stress that So:
•Godhclose: •Phildlsmattf
rules that is sufficient to describe the
–simple
–makefewassumptions situation.
–focusonlyonafewrelevantparameters
–Theserulesshouldbegeneral:
while ignoring the rest
–havepredictivepower,canbetested. •“worksforone,shouldworkforall”
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•SiFirs
Make a physical model for:
–Foranymeasurement,onlycertaindigits
•nljt are “significant”.
•nljiped –Alldigitsuptothefirst(uncertain)doubtful
•nlrhtt
digit are called “significant figures”.
•Akir
•Acrfer –Thenumberofdigitsquotedinaresult
•Amahdaerll indicates how “accurate”thenumbi.s
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
eaEm
–Theresultsofmeasuringasheetofpaperby •Re:wmayiiir:
several people are:
–Non–zerodigitsarealwayssignificant
•27.93cm,27.92cm,27.96cm,27.95cm
▯ 345.23 (5 sig figs) , 56 (2 sig figs)
–Everyoneagreesonthe3firstdigitsandtheforth –Anyzerosbetweentwosignificant
one is doubtful.
digits are significant
–Thismeasurementhas4significantfigures,the
last of which is uncertain (least significant figure)▯ 505 (3 sig figs) , 1008 (4 sig figs) ,
54.0209 (6 sig figs)
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•Rl:m nSftirs •Em latirs
–Finalzerostotherightofthedecimal 26.38 (4 sig figs), 27 (2 sig figs)
are significant 0.00500 (3 sig figs),
▯ 5.6290 (5 sig figs) , 34.0 (3 sig figs) 0.03040 (4 sig figs)
–Theotherzeros, placeholders, are not
significant 3.0880 (5 sig figs),
▯ 0.00873 (3 sig figs) , 0.00380 (3 sig figs) 0.00418 (3 sig figs),
, 340 (2 sig figs)
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
•Cihftrs •iiirse
–When adding or subtracting numbers: –When multiplying or dividing numbers:
• the answer can have no more places after the
•theanswercanhavenomoresignificant
decimal than the least the numbers. figures than the least reliable (accurate)
•theresulthasthesame precision as the least measurement.
precise number.
•Eaml •aml
2.54 cm +1.2 cm = ? = 3.7 cm (Not 3.74) 56.78 cm ▯ 2.45 cm = ?
7.432 cm + 2 cm = ? = 9 cm (Not 9.432) = 139 cm 2 (Not 139.111) cm 2
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•Em l: Find the sum of 104.0 and •Eaml: Your Physics book is 23.22 cm
0.21342. wide and 28.3 cm long. Its are is:
104.0 + 0.21342 = 104.21342 28.3 x 23.22 = 657.126
3 4 ?
1 5 ?
104.0 + 0.21342 = 104.2 28.3 x 23.24 = 657
1 3
Phys. 1L03, Fall 2013, McMaster University, R.NePhys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
Examples: •Eaml: A tortoise races a rabbit by
•i: 56.791 + 4.5 = ? walking with a constant speed of 2.51
cm/s for 12.23 s. How much distance
–56.791 +4.5=61.291=61.2 does the tortoise cover?
•i: 3.4 x 0.982 x9000. = ?
4
–3.4x0.982x9000.=3.0x10 d = (speed) ▯ (time)
Phys. 1L03, Fall 2013, McMaster University, R.NePhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•cttin
•cttin
–Ashorthandwayofwritingverylargeand/or –Thenumberofdigitsyouuseinyour
very small numbers, as a product of a scientific notation communicates how reliable
you think your measurement is.
number between 1 and 10 and a power of 10
a▯10 b
•ml
–Theradiusofthesunis700000km
•Wrtieas:7.0▯ 10 km
–Theradiusofahydrogenatom:
•0.0000000000529m=5.29 ▯ 1011m
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
•Meurm:yQlnits •Meurmnt
–Apyilainib:
–N meil srmesiae
relative to some standard, or unit
•specifying how it is measured directly.
–e.g. distance and time –Tomaenumcmlauemnt
OR •Establishastandard(unit)
•statinghowitiscalculatedbyfrom •Comparethequantitytobe
other measurements. measured with the proper standard.
–e.g. average speed = (distance/time)
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•SItnri)suti
•U i
–Fudametlsuti
•Theunitsinwhichfundamentalphysical
quantities are measured
–Somefundamentalphysicalquantities
•Length,mass,timeandcharge
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction
Introduction
•efIr •Otrtmoti
–Cgs
•Length centimetre(cm)
•Mass gram(gr)
•Time second(s)
–Bih
•Length foot(ft)
•Mass slug(slug)
•Time second(s)
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•aI:in
•Dorusin
–Composedofcombinationsofbase
unit
•Energy: joule(J)
1 joule = 1 kg m2/s
derived unit base units
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction Introduction
•Utiein •Uivsin
–Convertingunitfromonetypeofunit –Example:
to another using a conversion factor . –1km=1000m
•Convertingmetertokilometre
•CovoFctr –Conversion factor (the ratio):
–isequivalencestatementexpressedin
» 1 = 1 km / 1000m
the form of ratio. •Convertingkilometretometre
–Psst it’sequalto one. Always! –Conversion factor (the ratio):
» 1 = 1000 m / 1 km
Phys. 1L03, Fall 2013, McMaster University, R.Nejat Phys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•xmp,ivin •Eaml: A warehouse is 20.0 yards long,
–Howmanymeteris65inches? 10.0 yards wide, and 15.0 ft high. What is its
volume in cubic meter?
–1in=0.0254m
–Conversion factor (the ratio of m/in): Where 1 yd = 3 ft, and 1 m = 3.281 ft
» 1 = 0.0254 m /1 in
• Simply multiply the quantity by the
V = L ▯ W ▯ H
conversion factor: 1 = (3 ft /1 yd)
0.0254 m
65 in ▯ 65 in ▯ (1 in ) ▯ 1.65 m 1 = (1 m /3.281 ft)
▯▯▯ ▯1
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat
Introduction
Introduction
•Eaml: continue •Eamel: Blood in the human aorta can
attain speeds of 35.0 cm/s. How fast is this
L = in ft/s?
W = Where:
H = 1 m = 3.281 ft,
V = L ▯ W ▯ H 1 m = 100 cm
V =
Phys. 1L03, Fall 2013, McMaster University, R.NejaPhys. 1L03, Fall 2013, McMaster University, R.Nejat Introduction Introduction
•Eampl: •Diesis
1 m = 3.281 ft, and 1 m = 100 cm –Dimensionsare basic types of quantity
regardless of the unit in which those

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