203-measurements - CCNY Lab Manual
Physics 203 - Lab 1 - Measurements
Introduction
Anyphysicalsciencerequiresmeasurement.Thislabwillinvolvemakingseveralmeasurementsofthefundamentalunitsoflength,mass,and
time.Thereisnotraditional'hypothesis-test-analysis'methodology,butjustaseriesofexercisestohelpyougetusedtomakingscientific
measurements.
Also,inphysics,weoftenusefunctionalrelationshiptounderstandhowonequantityvariesasafunctionofanother.Forexample,ifyouapply
aconstantforcetoanobject,theaccelerationoftheobjectwillbedirectlyproportionaltothisforce: a ∝ F.Thisisanexampleofalinear
relationship.Thislabwillexploreseveralotherrelationshipsinthecontextofphysicalmeasurements.Belowareseveraldifferentfunctional
relationshipsbetweenxandywhicharelikelytocomeupinphysics.
y
y
y
x
linear
y
x
squared
x
square root
1
logarithmic
x
Asyoudothislab(aswellasalltheothersthissemester),youbeaskedtoentercertaindatapointsintothecomputer.Thisismeanttoserveasa
partialrecordofthelabactivities.Youshouldalsokeepmorethoroughanddetailednotesinanotebooktorefertowhenwritingyourlab
report.Inprofessionalscienceandotherlabsettings,thereisoftenamixofdigitalandanalogdata-it'sgoodpracticetogetusedtodealing
withboth.
Sometimes,you'llcreatedatafilesduringthelab,eitherinExcelorperhapsanotherformat.Youcaneitheremailthosetoyourselvesorusea
thumbdrivetomakesureyouhaveaccesstothedatalateron.
Equipment check
Pleasemakesureyourstationhasallofthefollowingitems.Ifnot,checkagain,thentalktoyourlabinstructor.
Measurement 1a
Asawarmuptogetusedtomeasuringthings,usethepapertapemeasuretomeasurethecircumferenceofyourhead,incentimeters.Enterthis
valueintheboxbelow.(Performbothmeasurementsonthesameperson.)
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203-measurements - CCNY Lab Manual
Head Circumference [cm] = ________________
Next,usethestopwatchonthebenchtomeasuretheheartrateofthepersonwhoseheadwasmeasured.Youcanexpressthemeasurmentin
beatsperminute.
Heartrate [bpm] = ________________
Measurement 1b
Now,takethemeasurementsofoneperson'swristandneckcircumferencesusingthepapertapemeasure.
Wrist Circumference [cm] = ________________
Neck Circumference [cm] = ________________
Great.We'llcomebacktothesemeasurementsattheendofthelab.
Circles
Thefirsttypeoffunctionalrelationshipwe'llinvestigateisalinearrelationship.Sucharelationshipisusuallygivenbyafunctionthatlooks
likey = f(x) = mx.Heremisaconstantvalue,andxisourindependentvariable,and yisthedependentvariable.
Averywellknownlinearrelationshipisthatbetweenthecircumference, cofacircleandthediameter,d,ofthatcircle.Therelation,ina
mathematicalformulaisc = πd,wherethesymbolπrepresentsthelinearcoefficientterm.Thefollowingexperimentswillattempttomeasure
πusingseveraldifferentmethods.Eachmethodwillinvolveseveralmeasurementsofdiametersandcircumferences.
Exercise
Measurement 2
Usethetapemeasuretomeasurethecircumferenceandthediameterofthecircularobjectsonthetable.Recordyourdatainatablelikethe
following.
Object#
Diameter
Circumference
1
2
3
Then,manuallyinputthesevaluesinExcel.Plottheresultswithascatterplotandusethe'trendline'featuretoestablishaslopeforthisline.The
slopeshouldbeyourfirstestimateforπ.Enteritintheboxbelow.HereisalinktoanExceltemplate(http://localhost/~james/physicslabs/docs/203lab1template.xlsx)togetyoustarted.**Note,forfuturelabsyouwillbeexpectedtoknowhowtosetupyourownexcelgraphs
andanalysis.Takesometimebetweennowandthentoplayaroundwithit.**
Estimate of Pi (#1) = ________________
Measurement 3
Usethesetoothpickstoestimate π.
Hint
Estimate of Pi (#2) = ________________
Measurement 4
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203-measurements - CCNY Lab Manual
UsegooglemapstoestimatethevalueofPi.Findacircularfeatureandmeasureitscircumferenceanddiameterusingthemapsinterface.
(Here'show(http://localhost/~james/physics-labs/measure-distance.pdf)ifyou'renotfamiliar)Inyourlabnotebook,indicatewhichfeatures
you'verecordedandthemeasurementsofcircumferenceanddiameterinatablesimilartothepreviousone.Findthevalueofπbasedonthis
measurement.**Iftheinternetistooslowinthelabtodothisexperiment,itmaybedonelaterbythestudentsindividually.**
Goto Google Maps (http://maps.google.com) Hint #1
Hint #2
Hint #3
Estimate of Pi (#3) = ________________
Report
Question
Discussthelimitationsofthesemethodsforcalculating π.Whichmethodwasthebest?Theworst?Arethereimprovementstobemade?
Uncertainty in Measurements
Fromtheabovemeasurements,you'veprobablydiscoveredthatyourvalueof πdiffersfromtheacceptedvalueof3.14159...Itmightbealittle
higher,oralittlelowerdependingonhowgoodyourmeasurementwas.Thisdegreeof'goodness'willbedeterminedbymanyfactors:the
qualityoftheinstruments,theirinherentresolution,yourskillasanexperimentalist,etc.Wecanquantifythis'goodness'byconsideringthe
errorassociatedwiththemeasurement.Inscience,errordoesnotmeanamistake,ormess-up,orincorrectanswer,asitdoesincommon
speech.Inthesciencemeasurements,errorspecificallyreferstohowconfidentweareinourmeasurement.Thebiggertheerror,theless
confidentwecanbeaboutourmeasurements.Ourmeasurementcanstillbecorrect,wejustarelesscertainaboutit.
We'llconsidertheerrorassociatedwithasimplelengthmeasurementfirst.Belowisapictureofapencilbeingmeasuredbyaruler.
0
1
2
3
4
5
[cm]
6
7
8
9
10
9
9.5
10
Wecanseethatthepencilisgreaterthan9centimeterslong,butlessthan9.5.Becauseofthespacingofthemarksontheruler,wecanonlybe
socertainaboutthismeasurement.Wecanofcourseseethatthepenciliskindacloseto9.25centimeters.Thus,asageneralrule,we'llsaythat
theuncertaintyinthismeasurementisequaltoonehalfofthesmallestspacingontheruler,which,onthisruleris0.5centimeters.
δL =
0.5
= .25 cm
2
Thus,themeasurementwe'llreportforthispencilis:9.25 ± 0.25cm.
Measurement 4: Measure the fish.
Onthebenchisapaperfish.Usetherulertomeasurethelengthofthefish,andreportyourresult,withtheuncertaintyinyourmeasurementin
thespacebelow.(Reportthismeasurementincentimeters.)
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203-measurements - CCNY Lab Manual
Length [cm] = ________________
±
Length Uncertainty = ________________
Experiment: Density of Wood
Onthebenchisablockofwood.Thetypeoftreeitcamefromisunknown.Yourtaskistoattempttoidentifythepiecebymeasuringthe
densityofthewood.
Usingtheverniercaliperwhenpossible,andthemeterstick,measurethethreedimensionsofthewood.Recordthesevaluesanddeterminethe
density.Findthemassoftheblockusingthedigitalscale.Thedensity,ρ,istheratioofthemasstothevolumeoftheblock.
ρ=
m
V
Reportyourmeasureddensityofthispieceofwood(ing/cm 3 ).
Density = ________________
Report
Question
Determinetheuncertaintyofyourdensitymeasurement.Thiswillinvolvesomealgebraiccalculation.Youcanfindsomepointershere:
Infoabouterroranalysis(http://localhost/~james/physics-labs/errors.php).Next,findanonlinedatabasethatyoucanusetolookupthe
densityofvariouswoods.Trytomatchyourpieceofwoodwithaknowntree.Discusswhetheryoucanbecertainofyouridentification.
Experiment: Time of oscillations
Althoughyouhaven'tstudiedthemyetinclass,let'stakealookatabasicpendulum.We'regoingtomeasureitsperiodofoscillation-thatis
thetimeittakestoswingbackandforthonce.
1. Startbymakingalongpendulumabout1.5meterinlength.Recordtheexactlengthofthestringfromthefixedpointofrotationtothe
centerofthemassonthefreeend.
2. Letthemassswingbackandforththroughasmallangle.(Meaning,don'tswingthependulumtoomuch.)
3. Recordthetimeittakesforonefullswing(i.e.backandforth).
4. Repeatthismeasurementfor5differentlengths,between10cmand1.5meter.
5. Createaplotinexcelthatshowsthetimeforoneoscillationasafunctionofthelengthofthestring
Report
Question
Basedonlyonyourexperimentaldata,canyousayhowthetimeforoneswingrelatestothelengthofthependulum?Isthereaclear
functionaldependence?Whatcouldyoudotomaketheexperimentbetter?
Measurement Analysis
Let'sreturntothefirstmeasurementswedid.Clickthe'refreshdata'buttonbelow.Atableshouldappearthatshowstheotherlabbench's
results.CopythistableintoexcelusingtheCopybuttonbelow.Thenplotthedatapointsinascatterplot,withheadsizeontheverticalaxis,
andheartbeattimeonthehorizontalaxis.Dothesamewiththemeasurementsofwristandneckcircumferences.
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Report
Question
Usingthetableofdatathatthewholelabacquired,canyousayifthereisanycorrelationbetweenthecircumferenceofsomeone'sheadand
thetimebetweenheartbeats?Wouldyouexpecttheretobeone?
Whataboutthemeasurementsofthewristandneckcircumferences?Doanypatternsemergebasedonthatdata?
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