Clay-BoingBoing Lab

3,197 views

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
3,197
On SlideShare
0
From Embeds
0
Number of Embeds
7
Actions
Shares
0
Downloads
18
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Clay-BoingBoing Lab

  1. 1. Tabattanon 1 KamolnatTabattanon Simple Harmonic Oscillations Lab Introduction: Simple harmonicoscillationsrefertothe motionof an oscillatingsystem, i.e.aspringor a light blade,which followsHooke’slaw F = -kx [Equation1] where Fis the linearrestoringforce inthe system, kisthe springconstant,andx is the displacement fromthe equilibriumline,alsoknownasamplitude. The graphof a simple harmonicoscillatinggraphis sinusoidal. In thisexperiment,ahacksawblade wasclampedontoawoodenblock. Massesof clay were stuck ontothe unclampedendof the hacksaw blade. The free endwaspulledbackandallowedto oscillate freelyforaperiodof time. Picture 1) Lab set-up The purpose of thislab will be tofindthe relationshipof the periodof asimple harmonic oscillationtothe massof oscillatingsystem. If we assume simple harmonicoscillationinthe movementof the hacksaw blade, we canapply the formula ω = √ (k/m) [Equation 2]
  2. 2. Tabattanon 2 and fromthisequation,aformulaforthe periodinrelationtothe mass can be derivedas T2 = (4π2 /k)*m [Equation3] where,forbothequations2and 3, T isthe periodexpressedinsecondspercycle,kisthe spring constantof the blade in Newtonpermeter,andmis massin kilograms. Itcan be predictedthatthe periodsquaredwill be proportional tothe mass,andthe proportionalityconstantwill be (4π2 /k). Design: ResearchQuestion: Whatisthe relationshipbetweenthe periodandthe massof a simple harmonic oscillation? Controlledfactors: The length of the hacksaw blade allowedtooscillate waskeptconstant. At the beginningof the experimentwhenthe bladewasclamped,the lengthwasmeasuredwithametricruler. Tokeepthe lengthconstantthe blade waskeptinplace for the whole experiment. The particularblade itself was paintedsothat half of the blade waspaintedred. The red half wasusedas the free end,therefore makingiteasyto keepthe lengththe same throughout. The heightat whichthe experimentwasperformedwaskeptconstantbykeepingthe labset-up on a single table andnotmovingitto any otherheightlevel. The set-upwasnottiltedatanypointin the experiment. Althoughthe amplitudeatwhichthe blade waspulledbackwaskeptroughlythe same,the periodof the oscillationisunaffectedbythe amplitude. Toprove this,a separate testwasdone witha relativelyheavymassoveralongerperiodof time. The periodwascalculatedforthe beginningof the oscillationandlateronafterdampingtookeffect. The periodwasthe same despitechange in amplitude.
  3. 3. Tabattanon 3 Graph 1) Shows20 secondsof a heavymassat the endof the blade withdamping. The frequencywas measuredatthe beginningandtowardsthe endof the oscillation. Variables: Independent:The massof the clayaddedto the endof the blade wasincreasedforeachtrial. The mass was measuredviaelectronicbalance. Dependent:The resultingoscillationwasgraphedwithamotiondetector. Tencycleswere countedto calculate the periodwithreasonablyminimal uncertainties. Procedure: A hacksawblade wasmassedwithanelectronicbalance. Itwasthenclampedontoa wooden blockso that half of itsfull lengthisprojectedfromthe edge of the brick,asseeninPicture 1, and this lengthwasmeasuredwithametricruler. A motiondetectorwassetbehindthe system. In the controlledtrial,the hacksaw blade waspulledbackandreleased. The oscillationof the blade wasgraphed. Thisprocesswas repeatedthree times. A piece of claywas massedviathe electronicbalance andstuckontothe endof the blade. The ball of clay wascarefullypositionedsothatthe endof the blade reachedapproximatelythe middle of the ball of clay. The blade wasagainpulledbackandreleased. The trial wasrepeatedthree timeswith the same mass. A total of five differentmassesof claywere used;three trialsweredone foreachmass, carefullypositioningthe middle of the claytoreach roughlythe endof the blade.
  4. 4. Tabattanon 4 Data Collectionand Processing: Mass of Blade:14.59 ± 0.01 g Lengthof Blade:16.0 cm ± 0.1 cm Distance to Centerof Clayon Blade: 16.0 cm ± 0.1 cm Mass ( ± .00001 kg) tIn (± .02 sec) tF (± .02 sec) t10 Periods (± .02 sec) t1 Periods (± .02 sec) Average (±.02 sec) 0.01459 0.72 1.38 0.66 0.07 0.07 0.56 1.22 0.66 0.07 0.82 1.50 0.68 0.07 0.02256 0.55 2.10 1.55 0.16 0.15 0.50 2.00 1.50 0.15 0.42 1.90 1.48 0.15 0.03284 0.45 2.60 2.15 0.22 0.21 0.55 2.65 2.10 0.21 0.29 2.43 2.14 0.21 0.04360 0.28 2.96 2.68 0.27 0.27 0.74 3.42 2.68 0.27 0.90 3.58 2.68 0.27 0.06416 0.96 4.20 3.24 0.32 0.32 0.78 4.02 3.24 0.32 0.68 3.94 3.26 0.33 0.07730 1.14 5.20 4.06 0.41 0.41 0.82 4.88 4.06 0.41 1.08 5.12 4.04 0.40 Table 1) Raw data obtainedfromthe oscillationgraphs. Uncertaintyforaveragesis 0.01.
  5. 5. Tabattanon5 Sample Graph: Graph 2) 3rd mass-trial 3. Frequencyobtainedbymeasuringthe time for10 cycles. Sample Calculation: (Time at Cycle 10- Time at Cycle 1) / 10 cycles (3.58-0.90) ± 0.02 seconds/10 cycles= .27 ± 0.02 cycles/sec
  6. 6. Tabattanon 6 Graph 3) The relationshipbetweenperiodandmassof the blade Sample Calculations:T2 Uncertainty:Mass 3, Trial 4 High:0.352 = 0.1225 => 0.12 Actual:0.332 = 0.1089 => 0.11 Low: 0.312 = 0.0961 => 0.10 Uncertainty= 0.01
  7. 7. Tabattanon 7 Mass ( ± .00001 kg) Period^2(± .01 sec) 0.01459 0.01 0.02256 0.02 0.03284 0.04 0.0436 0.07 0.06416 0.10 0.0773 0.17 Table 2) Mass vs the periodsquared. Graph 4) The relationshipappearsfairlylinear.
  8. 8. Tabattanon 8 Graph 5) High-Lowfit. The uncertaintyforthe y-interceptcomesouttobe 0.01 and the uncertaintyfor the slope is 0.3. Conclusion: The predictedrelationshipbetweenthe massof the blade and the periodof a cycle was proportional,wherethe proportionalityconstantwas(4π2 /k). Inthe final graph,however,the relationshipwasindeedlinear,butitwasnot proportional. The reasonforisthat the mass of the blade was neverzero. Inthe derived[Equation3] the periodcouldhave onlybeenzeroif the massof the blade waszero. The blade cannotachieve zeromass,andtherefore,the graphmustexhibitay- intercept. The acquiredequationforthe relationshipis T2 = (2.4 ± 0.3)*m – (0.03 ± 0.01) [Equation4] The slope inthe final graphcan be usedto findthe k,springconstant,of the hacksaw blade used. The original massof the blade withoutanyclayaddedshouldbe usedalongwith[Equation3]
  9. 9. Tabattanon 9 Sample Calclation:k T2 = (4π2 /k)*m .072 = (4π2 /k)*0.01459 k = 117.549 Uncertaintyfork High:(.07 – 0.02)2 = (4π2 /k)*(0.01459 - .00001) k = 230.238 Actual:.072 = (4π2 /k)*0.01459 k = 117.549 Low: (.07 + 0.02)2 = (4π2 /k)*(0.01459 + .00001) k = 71.159 The uncertaintyis80. The large uncertaintymakesthe kvalue very unreliable. The y-interceptonthe graphrepresents the periodwhenthe massof the blade iszero. The mass of the blade can, inreality,approachzero,butit can neverbe trulyzero. The x-interceptrepresentsthe effective massof the blade (the half thatisallowedtooscillate). Whenthe periodiszero,the blade isessentiallynotoscillating. The equationderived inthisexperimentaswell asthe proportionalityof the periodsquaredand the mass can be appliedtoobjectsinthe earth’satmosphere andfollowsHooke’sLaw. Evaluation: Weaknessesof thislabinclude the shakingof the woodenblockthatthe blade wasclampedon, the uncertaintyof the centerof mass of the clay,and the instrumental errorof the motiondetector. The shakingof the woodenblockwouldhave includedthe blockintothe systembeingstudied. The movementwould nothave beensimple harmonicoscillation. Tofix thisproblem, the woodenblack can be properlyclampeddown,oradifferentmeansof clampingthe blade downcanbe used. For example,asturdyextensiontoatable wouldbe heavyenoughnottomove withthe blade. The centerof masseffectshowquicklythe blade oscillates. The furtherbackthe clayispushed alongthe blade, the clearerthe difference becomes. The clayusedwasshapedintoa ball. Perhapsa
  10. 10. Tabattanon 10 more accurate shape to have usedmayhave beena square,where the centerof masscouldbe measuredmore accurately. The centerof massin thisexperimentwasapproximatedtobe the endof the blade. It wasimpossibletosee where the centerof massactuallywas. A see throughmass like a clearball witha sloton the side or a clear gel matterwouldmake iteasiertosee the center. The motiondetector’ssample rate maxedoutat50 samplespersecond. Evenso,the uncertaintyforthe labtrialswas lessthanthat of the instrumentitself. A betterqualitymotiondetector can minimize the uncertaintyevenmore.

×