Lab2

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~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
~ Understanding the color code for PHYSICS PI Name:
~ Raw Data Formula that needs to be entered Open Response area DA Name:
~ Researcher Name:
~ Initial Values
~ start position(m) spring tension k initial 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:
~ 0.38 1.0191 26.313 0.405 0.036 0.3 0.32 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.
~ Data Table
~ Time (s) Position (m) Velocity (m/s) Acceleration (m/s^2) height ΔE of the Cart friction ΔE of the Pully friction KE (j) GPE (j) SPE (j) TE (j) Uncertainty of TE
~ 0.05 0.483884 -0.3006988889 -1.0532403704 0.301116 -0.0026301429 0.00037953 0.0355575949 0.88528104 0.3533568225 1.2719448445 0.0329796392
~ 0.1 0.471233 -0.3563794444 -0.9269337037 0.313767 -0.0044280621 0.00063897 0.0499452308 0.92247498 0.300907841 1.2695389597
~ 0.15 0.449934 -0.406891 -0.6562951852 0.335066 -0.004359663 0.0006291 0.0651065824 0.98509404 0.2221191418 1.2685892012
~ 0.2 0.428964 -0.4289138889 -0.2511468519 0.356036 -0.0046947978 0.00067746 0.0723450715 1.04674584 0.1562091413 1.2712827151
~ 0.25 0.406382 -0.43396 0.2389816049 0.378618 -0.0045866898 0.00066186 0.074057344 1.11313692 0.0981718285 1.2814412627
~ 0.3 0.38432 -0.4079805556 0.8088591975 0.40068 -0.0041110146 0.00059322 0.0654557286 1.1779992 0.0544292615 1.2943663954
~ 0.35 0.364546 -0.3543388889 1.430762037 0.420454 -0.0034263999 0.00049443 0.0493749159 1.23613476 0.0261070497 1.3086847557
~ 0.4 0.348065 -0.2722688889 2.1605138889 0.436935 -0.0027598725 0.00039825 0.0291517593 1.2845889 0.0103626412 1.321741678
~ 0.45 0.33479 -0.1374694444 2.7881462963 0.45021 -0.0005332635 0.00007695 0.0074315788 1.3236174 0.0028779068 1.333470572
~ 0.5 0.332225 0.0355811111 2.8166490741 0.452775 0.0016968798 -0.00024486 0.0004978606 1.3311585 0.0019662471 1.3350746275
~ 0.55 0.340387 0.172455 2.2622595679 0.444613 0.0023960475 -0.00034575 0.0116955409 1.30716222 0.0054682331 1.3263762915
~ 0.6 0.351912 0.2596511111 1.664441358 0.433088 0.0030698514 -0.00044298 0.0265124036 1.27327872 0.0133982605 1.3158162555
~ 0.65 0.366678 0.3305494444 1.1743141975 0.418322 0.0039415761 -0.00056877 0.0429676493 1.22986668 0.0286658517 1.3048729871
~ 0.7 0.385637 0.3791116667 0.649257716 0.399363 0.004089393 -0.0005901 0.0565201141 1.17412722 0.0566810408 1.2908276679
~ 0.75 0.405307 0.4050833333 -0.0183842593 0.379693 0.0049110138 -0.00070866 0.0645293784 1.11629742 0.0957435902 1.2807727424
~ 0.8 0.428929 0.3763166667 -0.6547648148 0.356071 0.0031490613 -0.00045441 0.0556897974 1.04684874 0.1561088065 1.2613419952
~ 0.85 0.444076 0.3203172222 -0.9679219136 0.340924 0.0031525956 -0.00045492 0.0403486781 1.00231656 0.2025423937 1.2479053074
~ 0.9 0.45924 0.2824111111 -1.3037003086 0.32576 0.0031347162 -0.00045234 0.031364061 0.9577344 0.255075296 1.2468561332
~ 0.95 0.474318 0.2049694444 -1.8323756173 0.310682 0.0016752582 -0.00024174 0.0165214051 0.91340508 0.3133094847 1.2446694879
~ 1 0.482376 0.0823438889 -2.047683642 0.302624 -0.0002594592 0.00003744 0.0026664379 0.88971456 0.3468838235 1.2390428022
~ 1.05 0.481128 -0.0215288889 -1.8623864197 0.303872 -0.0005476086 0.00007902 0.0001822686 0.89338368 0.3415721104 1.2346694704
~ 1.1 0.478494 -0.0958161111 -1.7413864197 0.306506 -0.0010916829 0.00015753 0.003610321 0.90112764 0.3304958589 1.234299667
~ 1.15 0.473243 -0.1923466667 -1.6359311728 0.311757 -0.0030336768 0.00043776 0.0145491647 0.91656558 0.3089595764 1.2374784043
~ 1.2 0.458651 -0.2744961111 -1.2621574074 0.326349 -0.0030482298 0.00043986 0.0296306462 0.95946606 0.252921869 1.2394102055
~ 1.25 0.443989 -0.3216461111 -0.8017003086 0.341011 -0.0037074807 0.00053499 0.0406841588 1.00257234 0.2022584547 1.2423424628
~ 1.3 0.426156 -0.3538605556 -0.3254012346 0.358844 -0.0039128859 0.00056463 0.0492417004 1.05500136 0.1482618659 1.2491566704
~ 1.35 0.407335 -0.3555838889 0.1728277778 0.377665 -0.0036642375 0.00052875 0.0497224915 1.1103351 0.1003499174 1.2572720213
~ 1.4 0.38971 -0.334885 0.6346429012 0.39529 -0.0034733853 0.00050121 0.0441021865 1.1621526 0.0639338026 1.2672164138
~ 1.45 0.373003 -0.2914622222 1.0701487654 0.411997 -0.0027923049 0.00040293 0.0334066768 1.21127118 0.0369607924 1.2792492742
~ 1.5 0.359572 -0.2247377778 1.4225070988 0.425428 -0.0020033244 0.00028908 0.0198619048 1.25075832 0.0206023315 1.2895083119
~ 1.55 0.349936 -0.1437522222 1.655679321 0.435064 -0.0010338867 0.00014919 0.0081263938 1.27908816 0.0117903829 1.2981202401
~ 1.6 0.344963 -0.0544127778 1.7753790123 0.440037 -0.0000648648 0.00000936 0.0011643151 1.29370878 0.008198491 1.3030160813
~ 1.65 0.344651 0.0341222222 1.8371030864 0.440349 0.0005908518 -0.00008526 0.0004578712 1.29462606 0.007994834 1.3035843571
~ 1.7 0.347493 0.1356594444 1.7380438272 0.437507 0.0023636151 -0.00034107 0.0072371704 1.28627058 0.0099445385 1.305474834
~ 1.75 0.358862 0.2221583333 1.3574725309 0.426138 0.0026157978 -0.00037746 0.0194085883 1.25284572 0.0198696705 1.2943623166
~ 1.8 0.371444 0.2736661111 0.9071200617 0.413556 0.0031885623 -0.00046011 0.0294517275 1.21585464 0.0348184817 1.2828533014
~ 1.85 0.386781 0.308165 0.5195774691 0.398219 0.0033509322 -0.00048354 0.0373452486 1.17076386 0.0586740688 1.2696505697
~ 1.9 0.402899 0.3248494444 0.1388074074 0.382101 0.0035056098 -0.00050586 0.0414985563 1.12337694 0.0904146808 1.2582899269
~ 1.95 0.419761 0.3253083333 -0.3005580247 0.365239 0.0034588323 -0.00049911 0.0416158825 1.07380266 0.1309368708 1.2493151356
~ 2 0.436398 0.3007988889 -0.8239222222 0.348602 0.0032247369 -0.00046533 0.0355812488 1.02488988 0.1782507666 1.2414813023
~ 2.05 0.451909 0.2363233333 -1.2146669753 0.333091 0.0017078985 -0.00024645 0.0219625083 0.97928754 0.2289228932 1.23163439
~ 2.1 0.460124 0.1646416667 -1.3440765432 0.324876 0.0014735952 -0.00021264 0.0106597799 0.95513544 0.258324396 1.2253805711
~ 2.15 0.467212 0.1065933333 -1.5138262346 0.317788 0.0010773378 -0.00015546 0.004468161 0.93429672 0.2851194181 1.224806177
~ 2.2 0.472394 0.0200088889 -1.7414253086 0.312606 -0.0004143447 0.00005979 0.0001574399 0.91906164 0.3055456513 1.2244101765
~ 2.25 0.470401 -0.0840894444 -1.6613095679 0.314599 -0.0016717239 0.00024123 0.0027806844 0.92492106 0.2976060925 1.223877343
~ 2.3 0.46236 -0.161155 -1.2991814815 0.32264 -0.0020465676 0.00029532 0.0102130698 0.9485616 0.2666344916 1.2236579138
~ 2.35 0.452516 -0.2047072222 -1.0418635803 0.332484 -0.0019457361 0.00028077 0.0164791597 0.97750296 0.2310345901 1.2233517436
~ 2.4 0.443157 -0.2613388889 -0.8302858025 0.341843 -0.0036066492 0.00052044 0.0268581943 1.00501842 0.1995531431 1.2283435483
~ 2.45 0.425809 -0.30233 -0.381504321 0.359191 -0.0031777515 0.00045855 0.0359443984 1.05602154 0.147294181 1.2365409179
~ 2.5 0.410524 -0.2989688889 0.0728169753 0.374476 -0.0030482298 0.00043986 0.0351496274 1.10095944 0.1078121835 1.2413128812
~ 2.55 0.395862 -0.2865572222 0.4096114198 0.389138 -0.0029182923 0.00042111 0.0322917401 1.14406572 0.0757162238 1.2495765016
~ 2.6 0.381825 -0.2636427778 0.8248132716 0.403175 -0.0028968786 0.00041802 0.02733383 1.1853345 0.0502884929 1.2604779643
~ 2.65 0.367891 -0.20868 1.2811824074 0.417109 -0.0017654868 0.00025476 0.0171249924 1.22630046 0.0301750627 1.2720897883
~ 2.7 0.359399 -0.1229233333 1.4946728395 0.425601 -0.0006305607 0.00009099 0.0059420649 1.25126694 0.0204225876 1.2770920218
~ 2.75 0.356366 -0.0466977778 1.4541135803 0.428634 -0.0002378376 0.00003432 0.0008575534 1.26018396 0.0173992865 1.2782372823
~ 2.8 0.355222 0.0211061111 1.3892358025 0.429778 0.0006054048 -0.00008736 0.0001751803 1.26354732 0.0163218129 1.280562358
~ 2.85 0.358134 0.0917672222 1.304462963 0.426866 0.0013511421 -0.00019497 0.003311646 1.25498604 0.019132208 1.2785860661
~ 2.9 0.364633 0.156155 1.1275962963 0.420367 0.0020031165 -0.00028905 0.009589159 1.23587898 0.0262091253 1.2733913309
~ 2.95 0.374268 0.2085244444 0.8626049383 0.410732 0.0024754653 -0.00035721 0.0170994711 1.20755208 0.0387461007 1.2655159071
~ 3 0.386175 0.2440033333 0.555512963 0.398825 0.0027453195 -0.00039615 0.0234131717 1.1725455 0.0576140321 1.2559218733
~ 3.05 0.39938 0.2634688889 0.2373737654 0.38562 0.002821203 -0.0004071 0.0272977851 1.1337228 0.0829015326 1.2463362207
~ 3.1 0.41295 0.268055 -0.106217284 0.37205 0.0027923049 -0.00040293 0.0282563822 1.093827 0.1136682459 1.238141003
~ 3.15 0.426381 0.2614905556 -0.5846169753 0.358619 0.0031563378 -0.00045546 0.0268893774 1.05433986 0.1488910206 1.2328211358
~ 3.2 0.441563 0.2080644444 -1.0142546296 0.343437 0.0012538449 -0.00018093 0.0170241122 1.00970478 0.1944210072 1.2222228143
~ 3.25 0.447594 0.142955 -1.1322330247 0.337406 0.0014771295 -0.00021315 0.0080365089 0.99197364 0.2141908307 1.2154649591
~ 3.3 0.454699 0.0931494444 -1.1833145062 0.330301 0.0006305607 -0.00009099 0.0034121591 0.97108494 0.2387091757 1.2137458455
~ 3.35 0.457732 0.0293472222 -1.2754067901 0.327268 0.000054054 -0.0000078 0.0003386903 0.96216792 0.249580171 1.2121330352
~ 3.4 0.457992 -0.0392994444 -1.270687037 0.327008 -0.0009295209 0.00013413 0.0006073535 0.96140352 0.2505233373 1.2117388199
~ 3.45 0.453521 -0.1039138889 -1.1403950617 0.331479 -0.0013619529 0.00019653 0.0042463514 0.97454826 0.2345522064 1.2121813949
~ 3.5 0.44697 -0.1550211111 -0.9472407407 0.33803 -0.0018771291 0.00027087 0.009450405 0.9938082 0.2121009478 1.2137532937
~ 3.55 0.437941 -0.20042 -0.7020361111 0.347059 -0.0024357564 0.00035148 0.0157961354 1.02035346 0.1830079607 1.2170732797
~ 3.6 0.426225 -0.228765 -0.3904608025 0.358775 -0.002496879 0.0003603 0.0205801195 1.0547985 0.1484546651 1.2216967056
~ 3.65 0.414215 -0.2387344444 -0.0841188272 0.370785 -0.0025688124 0.00037068 0.0224129436 1.0901079 0.1167832279 1.2271059391
~ 3.7 0.401859 -0.2348077778 0.1951438272 0.383141 -0.0023384592 0.00033744 0.0216817178 1.12643454 0.0881603367 1.2342755753
~ 3.75 0.390611 -0.2225533333 0.53315 0.394389 -0.0025112241 0.00036237 0.0194776671 1.15950366 0.0655971686 1.2424296416
~ 3.8 0.378532 -0.18565 0.9207731481 0.406468 -0.001607067 0.0002319 0.013553724 1.19501592 0.0450741035 1.2522685806
~ 3.85 0.370802 -0.1241361111 1.1673746914 0.414198 -0.0010376289 0.00014973 0.0060598937 1.21774212 0.0339548636 1.2568689784
~ 3.9 0.365811 -0.05531 1.1560126543 0.419189 0.0001370061 -0.00001977 0.0012030289 1.23241566 0.0276108587 1.2613467837
~ 3.95 0.36647 -0.0055911111 1.068712037 0.41853 -0.0002378376 0.00003432 0.0000122932 1.2304782 0.0284109473 1.2586979229
~ 4 0.365326 0.04252 1.108395679 0.419674 0.0009008307 -0.00012999 0.0007109765 1.23384156 0.0270293224 1.2623526996
~ 4.05 0.369659 0.1068544444 1.0986987654 0.415341 0.0013727637 -0.00019809 0.0044900783 1.22110254 0.0324441432 1.2592114352
~ 4.1 0.376262 0.16459 0.8609898148 0.408738 0.0022914738 -0.00033066 0.0106530906 1.20168972 0.0416457515 1.2559493759
~ 4.15 0.387284 0.1992661111 0.4877950617 0.397716 0.0020787921 -0.00029997 0.0156147711 1.16928504 0.0595612734 1.2462399066
~ 4.2 0.397283 0.2091461111 0.1687953704 0.387717 0.0022771287 -0.00032859 0.0172015792 1.13988798 0.0785793288 1.2376174266
~ 4.25 0.408236 0.2126072222 -0.0841799383 0.376764 0.0022555071 -0.00032547 0.01777562 1.10768616 0.1024311371 1.2298229543
~ 4.3 0.419085 0.2022877778 -0.3508240741 0.365915 0.002079 -0.0003 0.0160919257 1.0757901 0.1291683755 1.2228294011
~ 4.35 0.429085 0.1775227778 -0.6085432099 0.355915 0.0017149671 -0.00024747 0.0123930129 1.0463901 0.1565562615 1.2168068715
~ 4.4 0.437334 0.1400211111 -0.8291320988 0.347666 0.0013043646 -0.00018822 0.0077100247 1.02213804 0.1811290556 1.2120932649
~ 4.45 0.443608 0.0909177778 -0.9664089506 0.341392 0.0005943861 -0.00008577 0.0032506211 1.00369248 0.2010173434 1.2084690606
~ 4.5 0.446467 0.0392366667 -1.0109496914 0.338533 0.0001983366 -0.00002862 0.0006054147 0.99528702 0.2104237728 1.2064859241
~ 4.55 0.447421 -0.0112322222 -1.0119947531 0.337579 -0.0003927231 0.00005667 0.0000496135 0.99248226 0.2136103975 1.205806218
~ 4.6 0.445532 -0.0639233333 -0.9564330247 0.339468 -0.0009837828 0.00014196 0.0016068952 0.99803592 0.2073238506 1.206124843
~ 4.65 0.4408 -0.1110033333 -0.8115876543 0.3442 -0.0014230755 0.00020535 0.0048455243 1.011948 0.1919880682 1.2075638669
~ 4.7 0.433955 -0.1473661111 -0.6092401235 0.351045 -0.0017222436 0.00024852 0.0085401201 1.0320723 0.170846915 1.2099856114
~ 4.75 0.425671 -0.1729133333 -0.381677963 0.359329 -0.0019889793 0.00028701 0.0117577899 1.05642726 0.1469102185 1.2133932992
~ 4.8 0.416104 -0.1855927778 -0.1542960802 0.368896 -0.0019744263 0.00028491 0.0135453701 1.08455424 0.1215131553 1.2179232491
~ 4.85 0.406607 -0.1856661111 0.0230037346 0.378393 -0.0018879399 0.00027243 0.0135560766 1.11247542 0.0986839127 1.2230998994
~ 4.9 0.397526 -0.1829153333 0.1736963889 0.387474 -0.002064447 0.0002979 0.013157366 1.13917356 0.0790742577 1.2296386368
~ 4.95 0.387596 -0.1673136111 0.2988255864 0.397404 -0.0013332627 0.00019239 0.0110085793 1.16836776 0.0601149326 1.2383503993
~ 5 0.381183 -0.1468555556 0.3679026543 0.403817 -0.0792479457 0.01143549 0.0084810474 1.18722198 0.0492495091 1.1771400809

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 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 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 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 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 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 -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 -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 -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 -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 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 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)