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Sheet1~~~~~~~~~~~~~~~~~~~~~~~~~~Understanding the color code for P.docx
- 1. Sheet1~~~~~~~~~~~~~~~~~~~~~~~~~~Understanding the color code for PHYSICSPI Name:~Raw Data Formula that needs to be enteredOpen Response areaDA Name:~Researcher Name:~Initial Values~start position(m)spring tensionkinitial height (m)mass of hook (kg)mass on hook (kg)unstreched length(m)??????When entering equations in F through M columns make sure you use: ~0.381.019126.3130.4050.0360.30.32a. absolute references ($X$1) when using Initial Value cells.~b. relative references (X1) when using Data Table cells.~c. Refer to your Prelab for hints to improve the accuracy of your calculations.~Data Table~Time (s)Position (m)Velocity (m/s)Acceleration (m/s^2)heightΔE of the Cart frictionΔE of the Pully frictionKE (j)GPE (j)SPE (j)TE (j)Uncertainty of TE~0.050.483884-0.3006988889-1.05324037040.301116- 0.00263014290.000379530.03555759490.885281040.353356822 51.27194484450.0329796392~0.10.471233-0.3563794444- 0.92693370370.313767- 0.00442806210.000638970.04994523080.922474980.300907841 1.2695389597~0.150.449934-0.406891-0.65629518520.335066- 0.0043596630.00062910.06510658240.985094040.22211914181 .2685892012~0.20.428964-0.4289138889- 0.25114685190.356036- 0.00469479780.000677460.07234507151.046745840.156209141 31.2712827151~0.250.406382-0.433960.23898160490.378618- 0.00458668980.000661860.0740573441.113136920.0981718285 1.2814412627~0.30.38432-0.40798055560.80885919750.40068- 0.00411101460.000593220.06545572861.17799920.0544292615 1.2943663954~0.350.364546- 0.35433888891.4307620370.420454- 0.00342639990.000494430.04937491591.236134760.026107049 71.3086847557~0.40.348065- 0.27226888892.16051388890.436935- 0.00275987250.000398250.02915175931.28458890.0103626412
- 9. All Energies GPE 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.0499999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.6500000000000004 4.7 4.75 4.8 4.8499999999999996 4.9000000000000004 4.95 0.88528104000000019 0.92247498000000006 0.98509404000000012 1.04674584 1.1131369200000001 1.1779992000000001 1.2361347600000001 1.2845888999999999 1.3236174000000001 1.3311585000000001 1.3071622200000002 1.27327872 1.22986668 1.1741272200000001 1.1162974200000002 1.0468487400000002 1.0023165599999999 0.9577344000000001 0.91340507999999998 0.88971456000000004 0.89338368000000012 0.90112764000000012 0.91656557999999999 0.95946606000000012 1.00257234 1.0550013600000001 1.1103351000000001 1.1621526 1.2112711800000002 1.2507583200000001 1.2790881599999999 1.29370878 1.2946260600000001 1.2862705800000001 1.2528457200000001 1.2158546400000001 1.1707638600000001
- 10. 1.12337694 1.0738026600000001 1.0248898800000001 0.97928754000000007 0.95513544000000017 0.93429672000000008 0.91906164000000012 0.92492106000000007 0.94856160000000012 0.97750296000000014 1.0050184200000001 1.0560215400000001 1.10095944 1.1440657200000002 1.1853345 1.22630046 1.25126694 1.26018396 1.26354732 1.2549860400000001 1.2358789800000001 1.2075520800000001 1.1725455 1.1337228000000001 1.0938270000000001 1.05433986 1.0097047800000001 0.9919736400000001 0.97108494000000001 0.96216791999999995 0.96140352000000007 0.97454826000000006 0.99380820000000014 1.0203534599999999 1.0547985 1.0901079 1.12643454 1.1595036600000002 1.1950159200000001 1.21774212 1.23241566 1.2304782000000001 1.2338415600000001 1.22110254 1.2016897200000001 1.1692850400000001 1.1398879800000001 1.1076861600000001 1.0757901000000001 1.0463901 1.02213804 1.00369248 0.99528702000000002 0.99248226000000006 0.99803592000000008 1.0119480000000001 1.0320723000000001 1.05642726 1.0845542400000001 1.11247542 1.1391735600000001 1.16836776 KE 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.0499999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998
- 11. 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.6500000000000004 4.7 4.75 4.8 4.8499999999999996 4.9000000000000004 4.95 3.5557594914622875E-2 4.9945230787035687E-2 6.5106582422703244E-2 7.234507154520145E-2 7.4057343989199997E-2 6.5455728582158423E-2 4.9374915946427567E-2 2.9151759294706515E-2 7.4315787872455416E-3 4.9786058275184963E-4 1.169554090258125E-2 2.6512403578837801E-2 4.2967649276144708E-2 5.6520114144541757E-2 6.4529378355796585E-2 5.568979736766809E-2 4.0348678061556127E-2 3.1364061030746924E-2 1.6521405068471946E-2 2.666437931686908E-3 1.8226864458290422E-4 3.6103209511297953E-3 1.4549164699961538E-2 2.9630646229673305E-2 4.0684158826780302E-2 4.9241700385106175E-2 4.9722491476217261E-2 4.4102186538231246E-2 3.340667676090215E-2 1.9861904790103475E-2 8.1263938230974036E-3 1.1643150890963984E-3 4.5787121891915678E-4 7.237170423890619E-3 1.9408588333500783E-2 2.9451727450745601E-2 3.7345248636231253E-2 4.1498556281730041E-2 4.1615882490140414E-2 3.5581248814734005E-2 2.1962508305374155E-2 1.0659779931935525E-2 4.4681610481164986E-3 1.5743985329400202E-4 2.7806843827851008E-3 1.0213069805331248E-2 1.6479159665837444E-2 2.6858194338086106E-2 3.5944398414924993E-2 3.5149627432875502E-2 3.2291740112184247E-2 2.7333829988447082E-2 1.7124992398799999E-2 5.9420648664038839E-3 8.575533732205693E-4 1.751802619915594E-4
- 12. 3.3116459739993996E-3 9.5891590178312485E-3 1.7099471075739454E-2 2.3413171690972144E-2 2.7297785140927958E-2 2.8256382199581247E-2 2.6889377411140551E-2 1.7024112228684059E-2 8.0365089188312502E-3 3.4121590718681175E-3 3.3869027956160124E-4 6.0735352070333303E-4 4.2463513715619346E-3 9.4504050280275025E-3 1.5796135369299996E-2 2.0580119469731251E-2 2.2412943574587226E-2 2.1681717827608013E-2 1.9477667064352763E-2 1.3553724023125E-2 6.059893657653118E-3 1.2030288663249999E-3 1.2293200849377829E-5 7.1097649480000001E-4 4.4900782809666603E-3 1.0653090630324998E-2 1.5614771079418775E-2 1.7201579170540136E-2 1.7775620017530507E-2 1.6091925686335665E-2 1.239301287975425E-2 7.7100247196954779E-3 3.2506211407880084E-3 6.0541467137047297E-4 4.9613527411223433E-5 1.6068952181011017E-3 4.845524259340343E-3 8.5401200793399773E-3 1.1757789947032445E-2 1.3545370080988996E-2 1.3556076568531075E-2 1.3157366037942823E-2 1.1008579335075905E-2 SPE 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.0499999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.6500000000000004 4.7
- 13. 4.75 4.8 4.8499999999999996 4.9000000000000004 4.95 0.3533568225218639 0.30090784103222851 0.22211914176971395 0.15620914133882402 9.8171828525106031E-2 5.4429261465599982E-2 2.6107049675153971E-2 1.0362641246212504E-2 2.8779067516499883E-3 1.9662471478124953E-3 5.4682330558484937E-3 1.3398260475935998E-2 2.8665851676545999E-2 5.6681040764848492E-2 9.5743590221968419E-2 0.15610880651491649 0.20254239370394406 0.25507529599439988 0.31330948467390601 0.3468838234693441 0.34157211036009594 0.33049585893563382 0.30895957640516858 0.25292186903185637 0.20225845465993655 0.14826186594458393 0.10034991737321249 6.3933802561649988E-2 3.6960792385408447E-2 2.0602331500295994E-2 1.1790382929024014E-2 8.1984909862485075E-3 7.9948340498564845E-3 9.9445385171684931E-3 1.9869670486386007E-2 3.481848169178399E-2 5.8674068849896462E-2 9.0414680830456493E-2 0.13093687081243646 0.17825076662622599 0.22892289319297651 0.25832439597434387 0.28511941813773606 0.30554565130643391 0.29760609252835651 0.26663449164239994 0.23103459005306387 0.19955314313756856 0.14729418096427646 0.10781218353914399 7.5716223808385968E-2 5.0288492867812527E-2 3.0175062696376521E-2 2.0422587620956518E-2 1.7399286480114007E-2 1.6321812914945978E-2 1.9132208034114001E-2 2.62091253 40828469E-2 3.8746100688455971E-2 5.7614032067812473E-2 8.29015325586E-2 0.11366824594124994 0.1488910206286965 0.19442100720164843 0.21419083068083394 0.23870917573705655 0.24958017096045607 0.25052333729001602 0.23455220642251648 0.2121009478108499
- 14. 0.18300796069177655 0.14845466509781255 0.11678322788921248 8.8160336658376526E-2 6.5597168607736456E-2 4.5074103533255958E-2 3.395486361342602E-2 2.7610858741336487E-2 2.8410947330850009E-2 2.7029322430193976E-2 3.2444143200976508E-2 4.1645751450785966E-2 5.9561273414664009E-2 7.8579328773928481E-2 0.10243113714842396 0.12916837545071244 0.15655626150071247 0.18112905560051398 0.20101734337641597 0.21042377283392849 0.21361039754221653 0.2073238506052559 0.19198806816000005 0.1708469149519124 0.14691021851071653 0.12151315529270391 9.86839127 25268469E-2 7.9074257713793963E-2 6.0114932615303977E-2 ΔE of the Pully friction 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.0499999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.6500000000000004 4.7 4.75 4.8 4.8499999999999996 4.9000000000000004 4.95 3.7952999999999902E-4 6.3897000000000042E-4 6.2909999999999962E-4 6.7745999999999974E-4 6.6186000000000077E-4 5.9322000000000042E-4 4.9442999999999905E-4 3.9825000000000114E-4 7.6949999999999512E-5 -2.4486000000000012E-4-
- 15. 3.4575000000000025E-4 -4.4298000000000004E-4- 5.6877000000000013E-4 -5.90099999999999E-4 - 7.0866000000000093E-4 -4.5441000000000069E-4- 4.5491999999999869E-4 -4.5234000000000111E-4- 2.4174000000000027E-4 3.7440000000000807E-5 7.9020000000000758E-5 1.575299999999985E-4 4.3776000000000145E-4 4.3985999999999862E-4 5.3499000000000125E-4 5.6462999999999934 E-4 5.2875000000000003E-4 5.0121000000000085E-4 4.029299999999991E-4 2.8907999999999934E-4 1.4919000000000016E-4 9.3600000000010352E-6 - 8.5260000000000346E-5 -3.4107000000000055E-4- 3.7745999999999944E-4 -4.6010999999999969E-4- 4.8354000000000062E-4 -5.0585999999999969E-4- 4.9911000000000042E-4 -4.6532999999999991E-4- 2.4644999999999913E-4 -2.1264000000000114E-4- 1.5545999999999895E-4 5.9789999999999013E-5 2.4123000000000062E-4 2.9532000000000061E-4 2.8076999999999849E-4 5.2044000000000092E-4 4.5854999999999979E-4 4.3986000000000025E-4 4.2110999999999895E-4 4.1802000000000007E-4 2.5475999999999998E-4 9.0990000000000238E-5 3.4320000000001013E-5 -8.7360000000000776E-5- 1.9496999999999931E-4 -2.8905000000000011E-4-3.5721E-4 -3.9615000000000071E-4-4.0709999999999916E-4- 4.0293000000000078E-4 -4.5545999999999922E-4-1.80930 00000000026E-4 -2.1315000000000084E-4- 9.0990000000000238E-5 -7.7999999999994747E-6 1.3413000000000007E-4 1.9653000000000088E-4 2.7086999999999863E-4 3.5148000000000015E-4 3.6030000000000063E-4 3.7067999999999932E-4 3.3744000000000108E-4 3.623700000000002E-4 2.3189999999999878E-4 1.497300000000007E-4 - 1.9770000000000619E-5 3.4320000000001013E-5 - 1.2999000000000094E-4 -1.9808999999999907E-4- 3.3066000000000096E-4 -2.9996999999999945E-4-
- 16. 3.285899999999997E-4 -3.2546999999999996E-4- 3.000000000000003E-4 -2.4747000000000023E-4- 1.8822000000000006E-4 -8.5770000000000014E-5- 2.8620000000000312E-5 5.6670000000000886E-5 1.4195999999999876E-4 2.0535000000000139E-4 2.4851999999999877E-4 2.8701000000000144E-4 2.8490999999999933E-4 2.7243000000000015E-4 2.9789999999999981E-4 1.9239000000000007E-4 1.143549E-2 ΔE of the Cart friction 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.049 9999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.650000000000 0004 4.7 4.75 4.8 4.8499999999999996 4.9000000000000004 -2.6301428999999932E-3- 4.4280621000000022E-3 -4.3596629999999971E-3- 4.6947977999999974E-3 -4.5866898000000052E-3- 4.1110146000000024E-3 -3.426399899999993E-3 - 2.7598725000000076E-3 -5.3326349999999656E-4 1.6968798000000004E-3 2.3960475000000016E-3 3.0698513999999999E-3 3.9415761000000009E-3 4.0893929999999924E-3 4.911013800000006E-3 3.1490613000000043E-3 3.1525955999999905E-3 3.1347162000000071E-3 1.6752582000000018E-3 - 2.5945920000000557E-4 -5.4760860000000518E-4- 1.0916828999999895E-3 -3.0336768000000097E-3-
- 17. 3.0482297999999903E-3 -3.7074807000000085E-3- 3.9128858999999952E-3 -3.6642375E-3 - 3.4733853000000051E-3 -2.7923048999999936E-3- 2.0033243999999953E-3 -1.033886700000001E-3 - 6.4864800000007165E-5 5.9085180000000232E-4 2.3636151000000034E-3 2.6157977999999959E-3 3.1885622999999978E-3 3.350932200000004E-3 3.5056097999999975E-3 3.4588323000000021E-3 3.2247368999999992E-3 1.7078984999999939E-3 1.4735952000000077E-3 1.0773377999999925E-3 - 4.1434469999999311E-4 -1.6717239000000042E-3- 2.0465676000000037E-3 -1.9457360999999894E-3- 3.6066492000000061E-3 -3.1777514999999979E-3- 3.0482298000000015E-3 -2.9182922999999926E-3- 2.8968786000000001E-3 -1.7654867999999998E-3- 6.305607000000016E-4 -2.37837600000007E-4 6.0540480000000529E-4 1.3511420999999951E-3 2.0031165000000007E-3 2.4754652999999997E-3 2.7453195000000045E-3 2.8212029999999939E-3 2.7923049000000049E-3 3.1563377999999941E-3 1.2538449000000017E-3 1.4771295000000058E-3 6.305607000000016E-4 5.4053999999996349E-5 - 9.295209000000005E-4 -1.36195290000000 6E-3 - 1.8771290999999902E-3 -2.4357564000000004E-3- 2.4968790000000039E-3 -2.5688123999999951E-3- 2.3384592000000072E-3 -2.5112241000000012E-3- 1.6070669999999913E-3 -1.0376289000000047E-3 1.3700610000000427E-4 -2.37837600000007E-4 9.0083070000000645E-4 1.3727636999999935E-3 2.2914738000000064E-3 2.0787920999999956E-3 2.2771286999999979E-3 2.2555070999999995E-3 2.0790000000000019E-3 1.7149671000000013E-3 1.3043646000000003E-3 5.9438610000000006E-4 1.9833660000000215E-4 -3.9272310000000609E-4- 9.8378279999999127E-4 -1.4230755000000093E-3- 1.7222435999999911E-3 -1.9889793000000097E-3-
- 18. 1.9744262999999954E-3 -1.8879399000000009E-3- 2.0644469999999988E-3 -1.3332627000000002E-3 Time (s) Energy (j) Total Energy TE 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1000000000000001 1.1499999999999999 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.0499999999999998 2.1 2.15 2.2000000000000002 2.25 2.2999999999999998 2.35 2.4 2.4500000000000002 2.5 2.5499999999999998 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4 4.05 4.0999999999999996 4.1500000000000004 4.2 4.25 4.3 4.3499999999999996 4.4000000000000004 4.45 4.5 4.55 4.5999999999999996 4.6500000000000004 4.7 4.75 4.8 4.8499999999999996 4.9000000000000004 4.95 1.2719448445364869 1.2695389597192643 1.2685892011924174 1.2712827150840253 1.2814412627143061 1.2943663954477584 1.3086847557215817 1.321741678040919 1.3334705720388957 1.3350746275305647 1.3263762914584298 1.3158162554547737 1.3048729870526903 1.2908276679093904
- 19. 1.2807727423777651 1.2613419951825848 1.2479053073655002 1.2468561332251469 1.2446694879423779 1.2390428022010311 1.234669470404679 1.2342996669867639 1.2374784043051301 1.2394102054615297 1.242342462786717 1.2491566704296904 1.2572720213494299 1.2672164137998811 1.2792492742463109 1.2895083118903994 1.2981202400521212 1.3030160812753449 1.3035843570687757 1.3054748340410594 1.294362316619887 1.2828533014425298 1.269650569686128 1.2582899269121863 1.2493151356025771 1.2414813023409603 1.2316343899983508 1.2253805711062797 1.2248061769858527 1.2244101764597279 1.2238773430111418 1.223657913847731 1.2233517436189016 1.2283435482756548 1.2365409178792017 1.2413128811720193 1.2495765016205704 1.2604779642562594 1.2720897882951765 1.2770920217873605 1.2782372822533343 1.2805623579769376 1.2785860661081139 1.27339133085866 1.2655159070641957 1.2559218732587847 1.2463362206995279 1.2381410030408313 1.2328211358398369 1.2222228143303324 1.2154649590996653 1.2137458455089247 1.2121330352400177 1.2117388199107193 1.2121813948940785 1.2137532937388777 1.2170732796610764 1.2216967055675438 1.2271059390637997 1.2342755752859846 1.2424296415720892 1.2522685805563811 1.2568689783710789 1.2613467837076615 1.2586979229316992 1.2623526996249941 1.2592114351819432 1.2559493758811111 1.246239906594083 1.2376174266444688 1.2298229542659547 1.2228294011370482
- 20. 1.216806871480467 1.2120932649202094 1.2084690606172039 1.206485924105299 1.2058062179696276 1.2061248430233573 1.2075638669193407 1.2099856114312526 1.213393299157749 1.2179232490736933 1.2230998993937996 1.2296386367517371 1.2383503992503797 1.177140080855259 Time (s) Energy (j) 1 PHY 241 Fall 2018 PHY 241 Lab 6- Law of Conservation of Energy Introduction: Last week we spent significant effort understanding the forces and resulting acceleration of the cart in Figure 1 to the right. This week we want to keep the same experimental setup and focus our attention on the various Energies within this system. For example, because
- 21. objects are moving up and down, there must be Gravitational Potential Energy, GPE. Also, a spring is involved, so there must be Spring Potential Energy, SPE, as well. If we add ALL forms of energy involved in the system, we can also define a Total Energy, TE, �� = ��� + ��� + ⋯ . (1) The Total Energy is a very useful idea because the Law of Conservation of Energy promises us that the Total energy will behave in a very specific, simple way. The Law of Conservation of Energy states: “The total amount of energy in a system is a constant unless energy is transferred through the system boundary through Work, Heat, Electrical Transmission, etc.” This single statement gives us a series of concrete goals. A. Calculate, ��� and ��� for each time step at which we collected data. B. Plot each form of Energy over multiple bounces of the cart. Also add �� to the graph below. Does the behavior of the Total Energy agree with the Law of Conservation of energy stated
- 22. above? spring �2 � ����� Pulley Figure 1 H 0 0.2 0.4 0.6 0 0.2 0.4 0.6 0.8 1 E n e
- 23. rg y ( j) Time (s) All Energies? GPE SPE 2 PHY 241 Fall 2018 C. Plot �� over multiple bounces with the Energy axis “zoomed in” so you can evaluate the fluctuations in TE, similar to the “Is TE Constant?” graph below. Worry, ponder, and deliberate whether the changes in TE are due to Random Uncertainty, or some unaccounted form of Energy. D. If possible describe the Energy Transfer involved during your data run both qualitatively and quantitatively.
- 24. Equipment: (same as last experiment) CBR 2- connected directly to a computer using a USB cable Spring String with loop knots in each end Set of Masses Hook Cart Safety glasses Paperclip Pulley 2 m track Bubble level Computer with Logger Pro or Logger Lite and Excel. Procedure: 1) The central goal/question for this lab is: How does the Total Energy of our system change as the cart bounces back and forth multiple times? 2) Take some time to familiarize yourself with the accompanying spreadsheet. You should notice that there is a region for Initial Values. An important
- 25. part of this lab is figuring out 0 0.1 0.2 0.3 0.4 0.5 E n e rg y ( J) Time (s) Is TE Constant? TE 3 PHY 241 Fall 2018 what measurements you need to take to supplement the CBR measurements in order to calculate the energies required. Most likely, there are too many columns in the Initial Values and the Data Table. 3) Arrange your equipment to match Figure 1. Figure 2 shows a fast and easy way to connect
- 26. the different components. Make sure you place the CBR in a location where it can measure either the cart or the hanging mass as it moves. 4) When entering equations in E through L columns make sure you use: a. absolute references ($X$1) when using Initial Value cells. b. relative references (X1) when using Data Table cells. c. Refer to your Prelab for hints to improve the accuracy of your calculations. 5) Before leaving the classroom, make sure you email the data out to the entire group and the Teaching Assistant. Please use the subject “Lab 6 data- Section ###, Group ###.” 6) Also clean up your work station and returning small equipment to the appropriate storage. 7) Researcher: Use formulae (and the Word Equation Editor) to explicitly describe how the position data from the CBR was transformed into Stretch and Height data of the spring and hanging mass respectively. 8) Researcher: For each type of energy your group calculate in evaluating TE, provide a formula describing how your group calculated that energy.
- 27. For example, if you were to consider the work done by the friction inside the pulley you might write: “For each data time step, our group estimates that the friction inside the pulley does work on the system and reduces the total energy by Δ������� = −�ℎ������ ∙ ��������������� ∙ Δ����� , (2) Where ��������������� ≈ .1 � �2 (as given in the lab manual) and Δ����� is the distance the cart traveled between adjacent data points.” Notice that symbols are clearly labeled (using the “_” key in the Word Equation Editor to add subscripts to symbols) and new values like ��������������� get a bit of explanation. paperclip Figure 2
- 28. 4 PHY 241 Fall 2018 9) DA: Creating the two graphs described in the introduction and make sure they are properly formatted, including captions. 10) DA: Determine and report the approximate magnitude of the Random Uncertainty in your Total Energy measurement (with proper rounding and units). 11) PI: Calculate the energy transferred into/out of the system based on your data (a graph is a good way to visualize this calculation). Is this consistent with the acceleration of friction measurements you collected in Lab 3? Explain. 12) PI: Evaluate the Law of Conservation of Energy (as given in the intro of this lab manual) in light of your group’s data and analysis. Be as specific as possible in highlighting any deficiencies you see in the Law or in your data.