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P1Lab08ImpulseWorksheet.xlsx

Worksheet

Physics I: Momentum & Impulse Worksheet
Class: UP1 Lab PHYS 2034 Names: Zachary Mann
Section: Section 1 Ashlynn Holt
Lab Group: Lab Group 15 Alwleed Almutair
Assignment Date: Tuesday, October 23
answer key: numbers text data
Table 1: Analytical Results for Impulse Trials
Trial 1 Trial 2 Trial 3 Trial 4
Mass of Cart, kg 506 1003 1500 1251
Impulse time, s 0.5 0.75 0.8 0.7
Initial Velocity, m/s 0.454 0.606 0.512 0.544
Final Velocity, m/s 0.302 0.430 0.386 0.416
Initial Momentum, kg m/s 229.724 607.818 768 680.544
Final Momentum, kg m/s 152.812 431.290 579 520.416
Change in Momentum, kg m/s 76.912 176.528 189 160.128
Total Measured Impulse, kg m/s 76.912 176.528 189 160.128
%Error between Momentum Change and Impulse 40.21 33.98 28.06 26.67

Data

Experimental Impulse Data
Trial 1 Trial 2 Trial 3 Trial 4
Experimental Data Selected Data Experimental Data Selected Data Experimental Data Selected Data Experimental Data Selected Data
Before Impulse After Impulse Before Impulse After Impulse Before Impulse After Impulse Before Impulse After Impulse
time (s) force (N) position (m) time (s) position (m) time (s) position (m) time (s) force (N) position (m) time (s) position (m) time (s) position (m) time (s) force (N) position (m) time (s) position (m) time (s) position (m) time (s) force (N) position (m) time (s) position (m) time (s) position (m)
-0.4610537772 0.1681210013 0.0333333333 0.033333 -0.249018 1.399986 -0.637637 0.033333 0.0282142587 -0.2131745 0.033333 -0.2131745 1.399986 -0.6577025 0.033333 0.0337828623 -0.256907 0.033333 -0.256907 1.433319 -0.585158 0.033333 0.0222744147 -0.185906 0.033333 -0.185906 1.466652 -0.5798415
-0.4539078724 0.1100361243 0.0666666667 0.066666 -0.2646245 1.433319 -0.627347 0.066666 0.0222744147 -0.2327255 0.066666 -0.2327255 1.433319 -0.6422675 0.066666 0.0222744147 -0.2735425 0.066666 -0.2735425 1.466652 -0.572467 0.066666 0.0222744147 -0.2039135 0.066666 -0.2039135 1.499985 -0.5661215
-0.4518212682 0.0455198687 0.1 0.099999 -0.279202 1.466652 -0.6168855 0.099999 0.0163345708 -0.2526195 0.099999 -0.2526195 1.466652 -0.6268325 0.099999 0.0222744147 -0.290521 0.099999 -0.290521 1.499985 -0.5596045 0.099999 0.0282142587 -0.2217495 0.099999 -0.2217495 1.533318 -0.5520585
-0.4521928553 0.0143634123 0.1333333333 0.133332 -0.294637 1.499985 -0.6065955 0.133332 0.0222744147 -0.2725135 0.133332 -0.2725135 1.499985 -0.610883 0.133332 0.0282142587 -0.306985 0.133332 -0.306985 1.533318 -0.5465705 0.133332 0.0222744147 -0.239414 0.133332 -0.239414 1.566651 -0.5379955
-0.4520499372 0.0143157724 0.1666666667 0.166665 -0.309386 1.533318 -0.5942475 0.166665 0.0222744147 -0.2920645 0.166665 -0.2920645 1.533318 -0.5956195 0.166665 0.0222744147 -0.3236205 0.166665 -0.3236205 1.566651 -0.5338795 0.166665 0.0222744147 -0.2553635 0.166665 -0.2553635 1.599984 -0.524447
-0.4509065924 0.0127912975 0.2 0.199998 -0.324821 1.566651 -0.584129 0.199998 0.0222744147 -0.312473 0.199998 -0.312473 1.566651 -0.5805275 0.199998 0.0222744147 -0.3407705 0.199998 -0.3407705 1.599984 -0.521017 0.199998 0.0222744147 -0.275429 0.199998 -0.275429 1.633317 -0.5105555
-0.4507636743 0.0017864941 0.2333333333 0.233331 -0.3393985 1.599984 -0.5736675 0.233331 0.0163345708 -0.332024 0.233331 -0.332024 1.599984 -0.563206 0.233331 0.0222744147 -0.3572345 0.233331 -0.3572345 1.633317 -0.507983 0.233331 0.0222744147 -0.2917215 0.233331 -0.2917215 1.66665 -0.496664
-0.4514782648 0.0019055937 0.2666666667 0.266664 -0.3548335 1.633317 -0.563549 0.266664 0.0222744147 -0.351918 0.266664 -0.351918 1.633317 -0.5479425 0.266664 0.0222744147 -0.37387 0.266664 -0.37387 1.66665 -0.495635 0.266664 0.0222744147 -0.3095575 0.266664 -0.3095575 1.699983 -0.4827725
-0.4501920019 -0.0229862236 0.3 0.299997 -0.3695825 1.66665 -0.553945 0.299997 0.0222744147 -0.3719835 0.299997 -0.3719835 1.66665 -0.5328505 0.299997 0.0222744147 -0.3908485 0.299997 -0.3908485 1.699983 -0.4827725 0.299997 0.0282142587 -0.329623 0.299997 -0.329623 1.733316 -0.4673375
-0.4504778381 -0.1127873252 0.3333333333 0.33333 -0.384846 1.699983 -0.543998 0.33333 0.0222744147 -0.3918775 0.33333 -0.3918775 1.699983 -0.518273 0.33333 0.0222744147 -0.409542 0.33333 -0.409542 1.733316 -0.467852 0.33333 0.0337828623 -0.3459155 0.33333 -0.3459155 1.766649 -0.453446
-0.4561945619 -0.2191432717 0.3666666667 0.366663 -0.3994235 1.733316 -0.533708 0.366663 0.0222744147 -0.4117715 0.366663 -0.4117715 1.733316 -0.5047245 0.366663 0.0222744147 -0.4241195 0.366663 -0.4241195 1.766649 -0.4556755 0.366663 0.0337828623 -0.3658095 0.366663 -0.3658095 1.799982 -0.439726
-0.471200962 -0.1507800989 0.4 0.399996 -0.4148585 1.766649 -0.5239325 0.399996 0.0222744147 -0.433895 0.399996 -0.433895 1.766649 -0.4913475 0.399996 0.0222744147 -0.443499 0.399996 -0.443499 1.799982 -0.442813 0.399996 0.0222744147 -0.3815875 0.399996 -0.3815875 1.833315 -0.4265205
-0.4729159792 0.0944459861 0.4333333333 0.433329 -0.4313225 1.799982 -0.514157 0.433329 0.0222744147 -0.4539605 0.433329 -0.4539605 1.799982 -0.477799 0.433329 0.0282142587 -0.4604775 0.433329 -0.4604775 1.833315 -0.4299505 0.433329 0.0222744147 -0.401653 0.433329 -0.401653 1.866648 -0.412629
-0.4597675143 0.2086625066 0.4666666667 0.466662 -0.446929 1.833315 -0.5043815 0.466662 0.0282142587 -0.4738545 0.466662 -0.4738545 1.833315 -0.464765 0.466662 0.0222744147 -0.4772845 0.466662 -0.4772845 1.866648 -0.4176025 0.466662 0.0282142587 -0.419832 0.466662 -0.419832 1.899981 -0.398909
-0.4527645276 0.14744531 0.5 0.499995 -0.461678 1.866648 -0.494606 0.499995 0.0163345708 -0.4940915 0.499995 -0.4940915 1.866648 -0.451731 0.499995 0.0282142587 -0.4940915 0.499995 -0.4940915 1.899981 -0.4049115 0.499995 0.0456625502 -0.4385255 0.499995 -0.4385255 1.933314 -0.3853605
-0.45033492 0.0701496669 0.5333333333 0.533328 -0.4769415 1.899981 -0.4851735 0.533328 0.0282142587 -0.5143285 0.533328 -0.5143285 1.899981 -0.4385255 0.533328 0.0337828623 -0.5112415 0.533328 -0.5112415 1.933314 -0.3922205 0.533328 0.0282142587 -0.4567045 0.533328 -0.4567045 1.966647 -0.372498
-0.4497632476 0.0314422955 0.5666666667 0.566661 -0.4916905 1.933314 -0.475398 0.566661 0.0222744147 -0.534051 0.566661 -0.534051 1.933314 -0.426006 0.566661 0.0337828623 -0.5294205 0.566661 -0.5294205 1.966647 -0.3798725 0.566661 0.0282142587 -0.4752265 0.566661 -0.4752265 1.99998 -0.359464
-0.4486199029 0.0122672592 0.6 0.599994 -0.506954 1.966647 -0.4659655 0.599994 0.0282142587 -0.554288 0.599994 -0.554288 1.966647 -0.4128005 0.599994 0.0456625502 -0.5465705 0.599994 -0.5465705 1.99998 -0.368039 0.599994 0.0337828623 -0.493234 0.599994 -0.493234
-0.4491915752 -0.0002381992 0.6333333333 0.633327 -0.5215315 1.99998 -0.4563615 0.633327 0.0222744147 -0.573839 0.633327 -0.573839 1.99998 -0.4004525 0.633327 0.0516023941 -0.563206 0.633327 -0.563206 0.633327 0.0222744147 -0.5132995 0.633327 -0.5132995
-0.4481911486 -0.03310969 0.6666666667 0.66666 -0.5369665 0.66666 0.0222744147 -0.596134 0.66666 -0.596134 0.66666 0.0872414577 -0.57967 0.66666 -0.57967 0.66666 0.0337828623 -0.53165 0.66666 -0.53165
-0.4496203295 -0.1092143371 0.7 0.699993 -0.5513725 0.699993 0.0222744147 -0.615685 0.699993 -0.615685 0.699993 0.388688537 -0.596134 0.699993 0.0337828623 -0.549486
-0.4549082991 -0.1742427209 0.7333333333 0.733326 -0.5668075 0.733326 0.0397227063 -0.635579 0.733326 -0.635579 0.733326 0.8557087658 -0.612598 0.733326 0.057542238 -0.567322
-0.466770501 -0.0796776352 0.7666666667 0.766659 -0.581385 0.766659 0.0694219259 -0.6556445 0.766659 -0.6556445 0.766659 1.4229638609 -0.6278615 0.766659 0.1050609895 -0.5849865
-0.4664846648 0.1791258047 0.8 0.799992 0.3946283809 -0.675367 0.799992 1.8899840897 -0.6422675 0.799992 0.512682779 -0.6031655
-0.4490486572 0.2950097196 0.8333333333 0.833325 1.0094022274 -0.694232 0.833325 2.2389499205 -0.655473 0.833325 1.0862489582 -0.620144
-0.44133108 0.2757155837 0.8666666667 0.866658 1.6535040533 -0.712411 0.866658 2.4813698007 -0.6666205 0.866658 1.6594438973 -0.636265
-0.4348997657 0.3799277374 0.9 0.899991 2.1383438139 -0.728189 0.899991 2.64657171 -0.6758815 0.899991 2.067436927 -0.6508425
-0.4228946456 0.7104291391 0.9333333333 0.933324 2.4754299568 -0.7417375 0.933324 2.7531176604 -0.683599 0.933324 2.3926433821 -0.6635335
-0.3940251903 1.264718697 0.9666666667 0.966657 2.6643912418 -0.7523705 0.966657 2.8180847034 -0.6885725 0.966657 2.6113038867 -0.673652
-0.3415742491 1.9189328229 1 0.99999 2.7709371922 -0.759745 0.99999 2.8359042352 -0.6913165 0.99999 2.7174785969 -0.6813695
-0.2636838868 2.4952558076 1.0333333333 1.033323 2.8299643912 -0.764204 1.033323 2.8121448595 -0.6926885 1.033323 2.8062050155 -0.6875435
-0.1692150255 2.8636308834 1.0666666667 1.066656 2.8121448595 -0.7664335 1.066656 2.7471778165 -0.691488 1.066656 2.8299643912 -0.6906305
-0.0663139965 2.9857079778 1.1 1.099989 2.7352981287 -0.7647185 1.099989 2.6350632624 -0.688401 1.099989 2.7943253277 -0.691145
0.0370157868 2.8400491618 1.1333333333 1.133322 2.581604667 -0.760431 1.133322 2.4813698007 -0.6837705 1.133322 2.7174785969 -0.6896015
0.1301983853 2.443090181 1.1666666667 1.166655 2.3688840064 -0.7533995 1.166655 2.2742177438 -0.677082 1.166655 2.581604667 -0.685314
0.2035153685 1.9052363684 1.2 1.199988 2.067436927 -0.743967 1.199988 2.0143495719 -0.6686785 1.199988 2.3748238503 -0.6789685
0.2575384087 1.3405851449 1.2333333333 1.233321 1.7010228048 -0.7317905 1.233321 1.7184710963 -0.658903 1.233321 2.0971361467 -0.6703935
0.2924104241 0.8042796272 1.2666666667 1.266654 1.228062732 -0.7187565 1.266654 1.3698765058 -0.64827 1.266654 1.7953178271 -0.660618
0.3077026604 0.390884901 1.3 1.299987 0.713894992 -0.703836 1.299987 0.9797030078 -0.6364365 1.299987 1.4114554133 -0.6487845
0.313133548 0.1545912863 1.3333333333 1.33332 0.3356011819 -0.6889155 1.33332 0.5835896659 -0.6237455 1.33332 0.9975225396 -0.6357505
0.3149914832 0.0398983674 1.3666666667 1.366653 0.1165694371 -0.673309 1.366653 0.3118418062 -0.611226 1.366653 0.5483218426 -0.6220305
0.3137052204 0.0198896339 1.4 1.399986 -0.0252443367 -0.6577025 1.399986 0.1165694371 -0.598192 1.399986 0.2587544511 -0.6083105
0.3135623023 0.0831315237 1.4333333333 1.433319 0.0222744147 -0.6422675 1.433319 0.0397227063 -0.585158 1.433319 0.0813016138 -0.594076
0.317564009 0.1713843304 1.4666666667 1.466652 0.0282142587 -0.6268325 1.466652 0.0397227063 -0.572467 1.466652 0.0397227063 -0.5798415
0.3311412281 0.0878955079 1.5 1.499985 0.0282142587 -0.610883 1.499985 0.0337828623 -0.5596045 1.499985 0.0397227063 -0.5661215
0.3297120471 -0.1635237566 1.5333333333 1.533318 0.0282142587 -0.5956195 1.533318 0.0282142587 -0.5465705 1.533318 0.0222744147 -0.5520585
0.3144198109 -0.2667831134 1.5666666667 1.566651 0.0222744147 -0.5805275 1.566651 0.0337828623 -0.5338795 1.566651 0.0282142587 -0.5379955
0.3072739061 -0.2260510488 1.6 1.599984 0.0282142587 -0.563206 1.599984 0.0282142587 -0.521017 1.599984 0.0222744147 -0.524447
0.2986988203 -0.1397038357 1.6333333333 1.633317 0.0222744147 -0.5479425 1.633317 0.0337828623 -0.507983 1.633317 0.0222744147 -0.5105555
0.296697967 -0.0232244228 1.6666666667 1.66665 0.0282142587 -0.5328505 1.66665 0.0337828623 -0.495635 1.66665 0.0282142587 -0.496664
0.3004138375 -0.001190996 1.7 1.699983 0.0163345708 -0.518273 1.699983 0.0337828623 -0.4827725 1.699983 0.0222744147 -0.4827725
0.2992704927 -0.0533566227 1.7333333333 1.733316 0.0044548829 -0.5047245 1.733316 0.0222744147 -0.467852 1.733316 0.0222744147 -0.4673375
0.2951258679 -0.0708642645 1.7666666667 1.766649 0.0103947269 -0.4913475 1.766649 0.0282142587 -0.4556755 1.766649 0.0222744147 -0.453446
0.2934108508 -0.0576442084 1.8 1.799982 -0.001484961 -0.477799 1.799982 0.0282142587 -0.442813 1.799982 0.0222744147 -0.439726
0.2921245879 -0.0578824076 1.8333333333 1.833315 0.0103947269 -0.464765 1.833315 0.0222744147 -0.4299505 1.833315 0.0222744147 -0.4265205
0.289266226 -0.0503195828 1.8666666667 1.866648 0.0222744147 -0.451731 1.866648 0.0282142587 -0.4176025 1.866648 0.0282142587 -0.412629
0.2882657993 -0.0306681481 1.9 1.899981 0.0516023941 -0.4385255 1.899981 0.0282142587 -0.4049115 1.899981 0.0222744147 -0.398909
0.2876941269 -0.0221882563 1.9333333333 1.933314 0.0222744147 -0.426006 1.933314 0.0282142587 -0.3922205 1.933314 0.0337828623 -0.3853605
0.2866222412 -0.0090515699 1.9666666667 1.966647 0.0163345708 -0.4128005 1.966647 0.0282142587 -0.3798725 1.966647 0.0222744147 -0.372498
0.2872653727 0.0058358806 2 1.99998 0.0222744147 -0.4004525 1.99998 0.0282142587 -0.368039 1.99998 0.0222744147 -0.359464
2.0333333333

Motion

Graphs of Cart in Motion
Figure 1: Position of Cart over Time with Linear Fits, Trial 1
Figure 2: Position of Cart over Time with Linear Fits, Trial 2
Figure 3: Position of Cart over Time with Linear Fits, Trial 3
Figure 4: Position of Cart over Time with Linear Fits, Trial 4

Force

Graphs of Force on Cart
Figure 5: Integrated Force on Cart over Time, Trial 1
Figure 6: Integrated Force on Cart over Time, Trial 2
Figure 7: Integrated Force on Cart over Time, Trial 3
Figure 8: Integrated Force on Cart over Time, Trial 4

Comparison

Comparisons:
Figure 9: Impulse Time over Mass
Figure 10: Impulse Time over Initial Velocity

Impulse Time Over Initial Velocity

Impulse time, s Trial 1 Trial 2 Trial 3 Trial 4 0.5 0.75 0.8 0.7 Initial Velocity, m/s Trial 1 Trial 2 Trial 3 Trial 4 0.45400000000000001 0.60599999999999998 0.51200000000000001 0.54400000000000004

Initial Velocity

Impulse Time

Impulse Time Over Mass

Mass of Cart, kg

Trial 1 Trial 2 Trial 3 Trial 4 506 1003 1500 1251 Impulse time, s

Trial 1 Trial 2 Trial 3 Trial 4 0.5 0.75 0.8 0.7

Impulse Time

Mass

Conclusion

Conclusion:

Overall, i believe the inteded purpose of this experiment was to demonstrate how a force acts upon an object when the mentioned object has a varying mass. The multiple trials allowed us to experience the varying changes in velocity and momentum, and showed us that something as simple as adding a block to a cart could change the rate at which that cart travels. During the lab i felt as if these trials were tedious and repetitive, but towards the end i was able to observe the multiple sets of data we had collected and it did an excellent job at showing us how the mass of the object is able to change the object's impulse. One possible source of error we could have encountered, aside from possible weighing errors or equipment malfunctions, was the starting position of the cart and the rate at which we allowed the cart to accelerate. While this was mostly accounted for by including the individual velocity and position for each trial, it does not change that it makes the data more difficult to compare directly. Other possible sources of error could include: an unleveled track, a frayed or aged rubber band, a track that is not smooth, and a loosening knot on the string that connects to the cart. All of these error sources are minor and can be accounted for with proper preparation, but the original error i mentioned involving the starting position would take more strenuous testing.