A cautionary note: though this is called an experiment, it was really just a high school independent study project, whose goal was to learn how to do experiments and write them up, rather than coming up with new and exciting science.
Daniel Dickinson and Rick Martin
To verify that momentum is conserved, using a variety of situations.
i) explosions - one dimensional
ii) collisions - one dimensional
iii) couplings - one dimensional
iv) angular
We expect that our experiments will show that momentum is conserved.
air track 2 sets of photogates 2 air track gliders SuperCHAMP system variety of masses 2 velcro couplers springs electronic balance 5cm x 5cm paper cards masking tape and string rotating disc 2 discs of different sizes metal bar 4 retort stands
Momentum before = Mass * Velocity before Momentum after = Mass * Velocity after Total momentum before = momentum of glider 1 before + momentum of glider 2 before Total momentum after = momentum of glider 1 after + momentum of glider 2 after Absolute difference = | momentum before - momentum after | Percent error = Absolute Difference / momentum before * 100 Table 1 A = Trial B = Mass of glider 1 in kg C = Velocity of glider 1 before collision, coupling, or explosion in m/s D = Velocity of glider 1 after collision, coupling, or explosion in m/s E = Momentum of glider 1 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F =============================================================== Collisions, both moving 1 0.23295 0.7474 -0.4044 0.174107 -0.094205 2 0.23295 0.6720 -0.5456 0.156542 -0.127098 3 0.23295 0.6702 -0.4735 0.156123 -0.110302 4 0.23295 0.6083 -0.4854 0.141703 -0.113074 5 0.23295 0.7102 -0.3520 0.165441 -0.081998 1 0.25317 0.7547 -0.3266 0.191067 -0.082685 2 0.25317 0.6333 -0.2459 0.160333 -0.062255 3 0.25317 0.559 -0.3851 0.141750 -0.097496 4 0.25317 0.5869 -0.2931 0.148585 -0.074204 5 0.25317 0.5485 -0.2665 0.138864 -0.067470 1 0.28322 0.7559 0.3407 0.214086 0.096493 2 0.28322 0.5653 0.3962 0.096493 0.112212 3 0.28322 0.6812 0.2023 0.160104 0.057295 4 0.28322 0.6414 0.2068 0.112212 0.058570 5 0.28322 0.5787 0.1390 0.192929 0.039300 Table 2 A = Trial Number B = Mass of glider 2 in kg C = Velocity of glider 2 before collision, coupling, or explosion in m/s D = Velocity of glider 2 after collision, coupling, or explosion in m/s E = Momentum of glider 2 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F ================================================================= Collisions, both moving 1 0.23295 -0.4958 0.6028 -0.11550 0.140422 2 0.23295 -0.6321 0.5181 -0.14725 0.120691 3 0.23295 -0.5747 0.5155 -0.13388 0.120086 4 0.23295 -0.5734 0.4850 -0.13357 0.112981 5 0.23295 -0.4223 0.5834 -0.09837 0.135903 1 0.23295 -0.4699 0.6680 -0.10946 0.155611 2 0.23295 -0.3775 0.5757 -0.08794 0.134109 3 0.23295 -0.5181 0.4801 -0.12069 0.111839 4 0.23295 -0.4290 0.5211 -0.09994 0.121390 5 0.23295 -0.3934 0.4936 -0.09164 0.114984 1 0.23295 0.6169 0.7491 0.14371 0.174503 2 0.23295 0.6435 0.5727 0.17450 0.133410 3 0.23295 0.5238 0.6689 0.14990 0.155820 4 0.23295 0.5038 0.6333 0.13341 0.147527 5 0.23295 0.4452 0.5631 0.12202 0.131174 Table 3 A = Trial Number B = Total momentum before in kg.m/s C = Total momentum after in kg.m/s D = Absolute value of difference in momentums E = Percent Error A B C D E ===================================================== Collisions, both moving 1 0.058610 0.04622 0.01239294 21.14 2 0.009295 0.00641 0.00288858 31.08 3 0.022247 0.00978 0.0124628 56.02 4 0.008130 0.00009 0.00803677 98.85 5 0.067066 0.05390 0.01316168 19.62 1 0.081604 0.07293 0.00867892 10.64 2 0.072394 0.07185 0.00053912 0.74 3 0.021058 0.01434 0.00671496 31.89 4 0.048650 0.04719 0.00146381 3.01 5 0.047221 0.04751 0.00029310 0.62 1 0.357793 0.27100 0.08679695 24.26 2 0.270996 0.24562 0.02537367 9.36 3 0.310008 0.21312 0.09689193 31.25 4 0.245622 0.20610 0.03952510 16.09 5 0.314949 0.17054 0.14440695 45.85 Table 4 A = Trial B = Mass of glider 1 in kg C = Velocity of glider 1 before collision, coupling, or explosion in m/s D = Velocity of glider 1 after collision, coupling, or explosion in m/s E = Momentum of glider 1 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F =============================================================== Collisions, one stopped 1 0.23295 0.8264 0.0000 0.192510 0.000000 2 0.23295 0.7639 0.0000 0.177951 0.000000 3 0.23295 0.8591 0.0000 0.200127 0.000000 4 0.23295 0.6935 0.0000 0.161551 0.000000 5 0.23295 0.7337 0.0000 0.170915 0.000000 1 0.28322 1.0140 0.0000 0.287185 0.000000 2 0.28322 0.6920 0.0000 0.195988 0.000000 3 0.28322 0.7616 0.0000 0.215700 0.000000 4 0.28322 0.6757 0.0000 0.191372 0.000000 5 0.28322 0.6246 0.0000 0.176899 0.000000 1 0.23295 0.8584 0.0000 0.199964 0.000000 2 0.23295 0.7639 0.0000 0.177951 0.000000 3 0.23295 0.9363 0.0000 0.218111 0.000000 4 0.23295 1.1390 0.0000 0.265330 0.000000 5 0.23295 0.8306 0.0000 0.193488 0.000000 Table 5 A = Trial Number B = Mass of glider 2 in kg C = Velocity of glider 2 before collision, coupling, or explosion in m/s D = Velocity of glider 2 after collision, coupling, or explosion in m/s E = Momentum of glider 2 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F ================================================================= Collisions, one stopped 1 0.23295 0.0000 0.7418 0.000000 0.172802 2 0.23295 0.0000 0.6831 0.000000 0.159128 3 0.23295 0.0000 0.7722 0.000000 0.179884 4 0.23295 0.0000 0.6211 0.000000 0.144685 5 0.23295 0.0000 0.6588 0.000000 0.153467 1 0.23295 0.0000 1.0050 0.000000 0.234115 2 0.23295 0.0000 0.6725 0.000000 0.156659 3 0.23295 0.0000 0.7413 0.000000 0.172686 4 0.23295 0.0000 0.6720 0.000000 0.156542 5 0.23295 0.0000 0.6017 0.000000 0.140166 1 0.28322 0.0000 0.6854 0.000000 0.194119 2 0.28322 0.0000 0.6035 0.000000 0.170923 3 0.28322 0.0000 0.7491 0.000000 0.212160 4 0.28322 0.0000 0.9200 0.000000 0.260562 5 0.28322 0.0000 0.6540 0.000000 0.185226 Table 6 A = Trial Number B = Total momentum before in kg.m/s C = Total momentum after in kg.m/s D = Absolute value of difference in momentums E = Percent Error A B C D E ===================================================== Collisions, one stopped 1 0.192510 0.172802 0.019708 10.24 2 0.177951 0.159128 0.018822 10.58 3 0.200127 0.179884 0.020243 10.12 4 0.161551 0.144685 0.016866 10.44 5 0.170915 0.153467 0.017448 10.21 1 0.287185 0.234115 0.053070 18.48 2 0.195988 0.156659 0.039329 20.07 3 0.215700 0.172686 0.043015 19.94 4 0.191372 0.156542 0.034829 18.20 5 0.176899 0.140166 0.036733 20.77 1 0.199964 0.194119 0.005845 2.92 2 0.177951 0.170923 0.007027 3.95 3 0.218111 0.212160 0.005951 2.73 4 0.265330 0.260562 0.004768 1.80 5 0.193488 0.185226 0.008262 4.27 Table 7 A = Trial B = Mass of glider 1 in kg C = Velocity of glider 1 before collision, coupling, or explosion in m/s D = Velocity of glider 1 after collision, coupling, or explosion in m/s E = Momentum of glider 1 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F =============================================================== Couplings, both moving 1 0.23295 0.3440 0.0000 0.080135 0.000000 2 0.23295 0.4864 0.0000 0.113307 0.000000 3 0.23295 0.4978 0.0000 0.115963 0.000000 4 0.23295 0.4292 0.0000 0.099982 0.000000 5 0.23295 0.5869 0.0000 0.136718 0.000000 Table 8 A = Trial Number B = Mass of glider 2 in kg C = Velocity of glider 2 before collision, coupling, or explosion in kg.m/s D = Velocity of glider 2 after collision, coupling, or explosion in kg.m/s E = Momentum of glider 2 before in kg.m/s F = Momentum of glider 2 after in kg.m/s A B C D E F ================================================================= Couplings, both moving 1 0.23295 0.3310 0.00000 -0.077106 0.000000 2 0.23295 -0.4902 0.00000 -0.114192 0.000000 3 0.23295 -0.4785 0.00000 -0.111467 0.000000 4 0.23295 -0.4543 0.00000 -0.105829 0.000000 5 0.23295 -0.6472 0.00000 -0.150765 0.000000 Table 9 A = Trial Number B = Total momentum before in kg.m/s C = Total momentum after in kg.m/s D = Absolute value of difference in momentums E = Percent Error A B C D E ========================================================== Couplings, both moving 1 0.003028 0.000000 0.003028 7.75 2 -0.000885 0.000000 0.000885 11.43 3 0.004496 0.000000 0.004496 11.19 4 -0.005847 0.000000 0.005847 10.64 5 -0.014047 0.000000 0.014047 15.18 Table 10 Lost to data corruption Table 11 Explosions, different masses 1 0.27946 0.0000 0.2139 0.000000 0.059776 2 0.27946 0.0000 0.1749 0.000000 0.048878 3 0.27946 0.0000 0.2904 0.000000 0.081155 Table 12 A = Trial Number B = Total momentum before in kg.m/s C = Total momentum after in kg.m/s D = Absolute value of difference in momentums E = Percent Error A B C D E ===================================================== Explosions, equal masses 1 0.000000 -0.014777 0.014777 5.04 2 0.000000 -0.012828 0.012828 7.92 3 0.000000 -0.015395 0.015395 7.07 Explosions, different masses 1 0.000000 -0.021270 0.021270 6.24 2 0.000000 -0.050798 0.050798 5.40 3 0.000000 -0.025280 0.025280 8.35
Moment of Inertia = Sum of all m.r2's Angular Momentum = Angular Velocity * Moment of Inertia Absolute Difference = Angular momentum before - Angular momentum after Percent Error = Absolute Difference / Angular momentum before * 100 Table 1 Object Mass(g) Radius(cm) mr2(kg.m2) ========================================================== original disc 712.05 12.75 0.000908 large disc 743.41 12.75 0.000948 metal bar 621.74 14.05 0.000874 small disc 107.48 5.60 0.000060 masses(1) 200.55 3.50 0.000070 masses(2) 300.55 5.60 0.000168 Table 2 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia Before in kg.m2 D = Angular Momentum before in rad.kg.m2/s A B C D ============================================== Original disc + large disc, trial 1 1 17.47 0.00090786 0.015860 2 16.99 0.00090786 0.015425 3 16.47 0.00090786 0.014953 4 15.99 0.00090786 0.014517 5 15.33 0.00090786 0.013918 Original disc + large disc, trial 2 1 18.83 0.00090786 0.017095 2 18.56 0.00090786 0.016850 3 18.23 0.00090786 0.016550 4 17.94 0.00090786 0.016287 5 17.66 0.00090786 0.016033 Original disc + large disc, trial 3 1 10.61 0.00090786 0.009632 2 10.45 0.00090786 0.009487 3 10.27 0.00090786 0.009324 4 10.06 0.00090786 0.009133 5 9.852 0.00090786 0.008944 Table 3 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia After in kg.m2 D = Angular Momentum after in rad.kg.m2/s A B C D ============================================== Original disc + large disc, trial 1 1 6.49 0.00185571 0.012047 2 6.15 0.00185571 0.011403 3 5.81 0.00185571 0.010787 4 5.46 0.00185571 0.010128 5 5.08 0.00185571 0.009429 Original disc + large disc, trial 2 1 7.00 0.00185571 0.012997 2 6.72 0.00185571 0.012461 3 6.41 0.00185571 0.011895 4 6.09 0.00185571 0.011309 5 5.75 0.00185571 0.010663 Original disc + large disc, trial 3 1 4.302 0.00185571 0.007983 2 4.057 0.00185571 0.007529 3 3.816 0.00185571 0.007081 4 3.566 0.00185571 0.006617 5 3.305 0.00185571 0.006133 Table 4 A = Trial B = Average Angular Momentum before in rad.kg.m2/s C = Average Angular Momentum after in rad.kg.m2/s D = Absolute Difference E = Percent Error A B C D E ============================================== Original Disc + big mass 1 0.014934 0.010759 0.004175 27.96 2 0.016563 0.011865 0.004698 28.36 3 0.009304 0.007069 0.002235 24.03 Table 5 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia Before in kg.m2 D = Angular Momentum before in rad.kg.m2/s A B C D ============================================== Original disc + metal bar, trial 1 1 17.53 0.00090786 0.015915 2 17.52 0.00090786 0.015906 3 17.25 0.00090786 0.015661 4 16.96 0.00090786 0.015397 5 16.75 0.00090786 0.015207 Original disc + metal bar, trial 2 1 16.94 0.00090786 0.015379 2 16.96 0.00090786 0.015397 3 16.76 0.00090786 0.015216 4 16.54 0.00090786 0.015016 5 16.29 0.00090786 0.014789 Original disc + metal bar, trial 3 1 14.12 0.00090786 0.012819 2 13.69 0.00090786 0.012429 3 13.45 0.00090786 0.012211 4 13.20 0.00090786 0.011984 5 12.92 0.00090786 0.011730 Table 6 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia After in kg.m2 D = Angular Momentum after in rad.kg.m2/s A B C D ============================================== Original disc + metal bar, trial 1 1 9.409000 0.00178141 0.016761 2 7.662000 0.00178141 0.013649 3 6.098000 0.00178141 0.010863 4 5.159000 0.00178141 0.009190 5 4.837000 0.00178141 0.008617 Original disc + metal bar, trial 2 1 5.146 0.00178141 0.009167 2 4.805 0.00178141 0.008560 3 4.489 0.00178141 0.007997 4 4.153 0.00178141 0.007398 5 3.867 0.00178141 0.006889 Original disc + metal bar, trial 3 1 6.526 0.00178141 0.011625 2 4.866 0.00178141 0.008668 3 3.991 0.00178141 0.007110 4 3.615 0.00178141 0.006440 5 3.104 0.00178141 0.005529 Table 7 A = Trial B = Average Angular Momentum before in rad.kg.m2/s C = Average Angular Momentum after in rad.kg.m2/s D = Absolute Difference E = Percent Error A B C D E ============================================== Original disc + metal bar 1 0.015617 0.011816 0.003800 24.34 2 0.015160 0.008002 0.007157 47.21 3 0.012234 0.007875 0.004359 35.64 Table 8 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia Before in kg.m2 D = Angular Momentum before in rad.kg.m2/s A B C D ============================================== Original disc, small disc, and masses(1), trial 1 1 15.10 0.00090786 0.013709 2 14.80 0.00090786 0.013436 3 14.30 0.00090786 0.012982 4 13.74 0.00090786 0.012474 5 13.44 0.00090786 0.012202 Original disc, small disc, and masses(1), trial 2 1 17.70 0.00090786 0.016069 2 17.51 0.00090786 0.015897 3 17.30 0.00090786 0.015706 4 17.12 0.00090786 0.015543 5 16.94 0.00090786 0.015379 Original disc, small disc, and masses(1), trial 3 1 16.23 0.00090786 0.014735 2 16.05 0.00090786 0.014571 3 15.81 0.00090786 0.014353 4 15.60 0.00090786 0.014163 5 15.41 0.00090786 0.013990 Table 9 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia After in kg.m2 D = Angular Momentum after in rad.kg.m2/s A B C D ============================================== Original disc, small disc, and masses(1), trial 1 1 11.76 0.00096805 0.011384 2 11.45 0.00096805 0.011084 3 11.12 0.00096805 0.010765 4 10.83 0.00096805 0.010484 5 10.54 0.00096805 0.010203 Original disc, small disc, and masses(1), trial 2 1 14.60 0.00096805 0.014134 2 14.37 0.00096805 0.013911 3 14.16 0.00096805 0.013708 4 13.90 0.00096805 0.013456 5 13.63 0.00096805 0.013195 Original disc, small disc, and masses(1), trial 3 1 13.28 0.00103825 0.013788 2 12.98 0.00103825 0.013476 3 12.67 0.00103825 0.013155 4 12.36 0.00103825 0.012833 5 12.07 0.00103825 0.012532 Table 10 A = Trial B = Average Angular Momentum before in rad.kg.m2/s C = Average Angular Momentum after in rad.kg.m2/s D = Absolute Difference E = Percent Error A B C D E ============================================== Original disc, small disc, and masses(1) 1 0.012961 0.010784 0.002176 16.79 2 0.015719 0.013681 0.002038 12.97 3 0.014362 0.013157 0.001205 8.40 Table 11 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia Before in kg.m2 D = Angular Momentum before in rad.kg.m2/s Original disc, small disc, and masses(2), trial 1 1 10.30 0.00090786 0.009351 2 10.13 0.00090786 0.009197 3 9.97 0.00090786 0.009052 Original disc, small disc, and masses(2), trial 2 1 17.54 0.00090786 0.015924 2 17.38 0.00090786 0.015779 3 17.19 0.00090786 0.015606 4 16.97 0.00090786 0.015406 5 16.75 0.00090786 0.015207 Original disc, small disc, and masses(2), trial 3 1 19.11 0.00090786 0.017349 2 18.95 0.00090786 0.017204 3 18.77 0.00090786 0.017041 4 18.57 0.00090786 0.016859 5 18.37 0.00090786 0.016677 Table 12 A = Reading B = Angular Velocity(rad/s) C = Moment of Inertia After in kg.m2 D = Angular Momentum after in rad.kg.m2/s A B C D ============================================== Original disc, small disc, and masses(2), trial 1 1 8.43 0.00113636 0.009574 2 8.27 0.00113636 0.009400 3 8.12 0.00113636 0.009224 Original disc, small disc, and masses(2), trial 2 1 13.55 0.00113636 0.015398 2 13.29 0.00113636 0.015102 3 13.02 0.00113636 0.014795 4 12.74 0.00113636 0.014477 5 12.48 0.00113636 0.014182 Original disc, small disc, and masses(2), trial 3 1 15.28 0.00113636 0.017364 2 15.1 0.00113636 0.017159 3 14.9 0.00113636 0.016932 4 14.67 0.00113636 0.016670 5 14.43 0.00113636 0.016398 Table 13 A = Trial B = Average Angular Momentum before in rad.kg.m2/s C = Average Angular Momentum after in rad.kg.m2/s D = Absolute Difference E = Percent Error A B C D E ============================================== Original disc, small disc, and masses(2) 1 0.009200 0.009399 0.000199 2.17 2 0.015584 0.014791 0.000793 5.09 3 0.017026 0.016904 0.000121 0.71
The results obtained in all cases tested proved that momentum is conserved. This was found to be true for both linear and angular momentum situations. Therefore our hypothesis was correct.
© 1992-2006 Daniel Dickinson <cshore@wightman.ca>
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