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Two carts (red and blue) are facing each other with their plunger sides. The carts weigh approximately 0.240 kg, and the blue cart has an additional 0.25 kg mass on top. With a small stick, the button that ejects the plunger (no matter which cart) is hit. Both carts will move away from each other. This experiment simulates an explosion, and the data for the single run is provided. a) Is the momentum of the system conserved? b) Plot the center of mass of the system (xcm = (m1x1 + m2x2)/(m1 + m2)) as a function of time and discuss the results. (hint: x1 and x2 can be directly implemented from the position sensor data; the answer to this question ties very closely to the reason behind the symmetry of fireworks)

Two carts (red and blue) are facing each other with their plunger sides. The carts weigh approximately 0.240 kg, and the blue cart has an additional 0.25 kg mass on top. With a small stick, the button that ejects the plunger (no matter which cart) is hit. Both carts will move away from each other. This experiment simulates an explosion, and the data for the single run is provided. a) Is the momentum of the system conserved? b) Plot the center of mass of the system (xcm = (m1x1 + m2x2)/(m1 + m2)) as a function of time and discuss the results. (hint: x1 and x2 can be directly implemented from the position sensor data; the answer to this question ties very closely to the reason behind the symmetry of fireworks)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Two carts (red and blue) are facing each other with their plunger sides. The carts weigh approximately 0.240 kg, and the blue cart has an additional 0.25 kg mass on top. With a small stick, the button that ejects the plunger (no matter which cart) is hit. Both carts will move away from each other. This experiment simulates an explosion, and the data for the single run is provided.

a) Is the momentum of the system conserved?

b) Plot the center of mass of the system (xcm = (m1x1 + m2x2)/(m1 + m2)) as a function of time and discuss the results. (hint: x1 and x2 can be directly implemented from the position sensor data; the answer to this question ties very closely to the reason behind the symmetry of fireworks)

time (s) position blue speed blue position red speed red time (s) position blue speed blue position red speed red 4.28 4.78 -0.2152 -0.479 0.4168 0.971 4.3 -0.016 0.005 4.8 -0.2248 -0.48 0.4363 0.97 4.32 -0.097 0.09 4.82 -0.2344 -0.481 0.4556 0.97 4.34 -0.0019 -0.244 6.06E-04 0.326 4.84 -0.2441 -0.48 0.475 0.971 4.36 -0.0097 -0.393 0.0102 0.639 4.86 -0.2537 -0.478 0.4945 0.972 4.38 -0.0195 -0.479 0.029 0.876 4.88 -0.2631 -0.476 0.5139 0.971 4.4 -0.0296 -0.498 0.0483 0.962 4.9 -0.2727 -0.476 0.5333 0.97 4.42 -0.0395 -0.498 0.0677 0.968 4.92 -0.2822 -0.476 0.5527 0.97 4.44 -0.0495 -0.497 0.0869 0.969 4.94 -0.2918 -0.475 0.5721 0.97 4.46 -0.0594 -0.496 0.1065 0.969 4.96 -0.3012 -0.474 0.5915 0.97 4.48 -0.0694 -0.495 0.1257 0.969 4.98 -0.3107 -0.473 0.6109 0.97 4.5 -0.0792 -0.494 0.1452 0.969 5 -0.3201 -0.473 0.6303 0.97 4.52 -0.0891 -0.492 0.1646 0.969 5.02 -0.3296 -0.473 0.6497 0.97 4.54 -0.0989 -0.49 0.184 0.969 5.04 -0.339 -0.473 0.6691 0.97 4.56 -0.1087 -0.488 0.2032 0.97 5.06 -0.3485 -0.472 0.6885 0.97 4.58 -0.1185 -0.488 0.2228 0.97 5.08 -0.358 -0.47 0.7079 0.969 4.6 -0.1282 -0.488 0.2422 0.97 5.1 -0.3673 -0.469 0.7273 0.968 4.62 -0.138 -0.487 0.2614 0.969 5.12 -0.3766 -0.469 0.7466 0.968 4.64 -0.1477 -0.486 0.281 0.97 5.14 -0.3861 -0.469 0.766 0.968 4.66 -0.1574 -0.485 0.3002 0.971 5.16 -0.3954 -0.468 0.7854 0.968 4.68 -0.1671 -0.484 0.3198 0.971 5.18 -0.4048 -0.467 0.8047 0.968 4.7 -0.1768 -0.483 0.3392 0.971 5.2 -0.4141 -0.467 0.8241 0.968 4.72 -0.1864 -0.482 0.3586 0.97 5.22 -0.4234 -0.467 0.8435 0.967 4.74 -0.1961 -0.481 0.378 0.97 5.24 -0.4328 -0.467 0.8628 0.966 4.76 -0.2057 -0.48 0.3974 0.971 5.26 -0.4421 -0.466 0.8821 0.966
Transcribed Image Text:time (s) position blue speed blue position red speed red time (s) position blue speed blue position red speed red 4.28 4.78 -0.2152 -0.479 0.4168 0.971 4.3 -0.016 0.005 4.8 -0.2248 -0.48 0.4363 0.97 4.32 -0.097 0.09 4.82 -0.2344 -0.481 0.4556 0.97 4.34 -0.0019 -0.244 6.06E-04 0.326 4.84 -0.2441 -0.48 0.475 0.971 4.36 -0.0097 -0.393 0.0102 0.639 4.86 -0.2537 -0.478 0.4945 0.972 4.38 -0.0195 -0.479 0.029 0.876 4.88 -0.2631 -0.476 0.5139 0.971 4.4 -0.0296 -0.498 0.0483 0.962 4.9 -0.2727 -0.476 0.5333 0.97 4.42 -0.0395 -0.498 0.0677 0.968 4.92 -0.2822 -0.476 0.5527 0.97 4.44 -0.0495 -0.497 0.0869 0.969 4.94 -0.2918 -0.475 0.5721 0.97 4.46 -0.0594 -0.496 0.1065 0.969 4.96 -0.3012 -0.474 0.5915 0.97 4.48 -0.0694 -0.495 0.1257 0.969 4.98 -0.3107 -0.473 0.6109 0.97 4.5 -0.0792 -0.494 0.1452 0.969 5 -0.3201 -0.473 0.6303 0.97 4.52 -0.0891 -0.492 0.1646 0.969 5.02 -0.3296 -0.473 0.6497 0.97 4.54 -0.0989 -0.49 0.184 0.969 5.04 -0.339 -0.473 0.6691 0.97 4.56 -0.1087 -0.488 0.2032 0.97 5.06 -0.3485 -0.472 0.6885 0.97 4.58 -0.1185 -0.488 0.2228 0.97 5.08 -0.358 -0.47 0.7079 0.969 4.6 -0.1282 -0.488 0.2422 0.97 5.1 -0.3673 -0.469 0.7273 0.968 4.62 -0.138 -0.487 0.2614 0.969 5.12 -0.3766 -0.469 0.7466 0.968 4.64 -0.1477 -0.486 0.281 0.97 5.14 -0.3861 -0.469 0.766 0.968 4.66 -0.1574 -0.485 0.3002 0.971 5.16 -0.3954 -0.468 0.7854 0.968 4.68 -0.1671 -0.484 0.3198 0.971 5.18 -0.4048 -0.467 0.8047 0.968 4.7 -0.1768 -0.483 0.3392 0.971 5.2 -0.4141 -0.467 0.8241 0.968 4.72 -0.1864 -0.482 0.3586 0.97 5.22 -0.4234 -0.467 0.8435 0.967 4.74 -0.1961 -0.481 0.378 0.97 5.24 -0.4328 -0.467 0.8628 0.966 4.76 -0.2057 -0.48 0.3974 0.971 5.26 -0.4421 -0.466 0.8821 0.966
time (s) position blue speed blue position red speed red time (s) position blue speed blue position red speed red 5.28 -0.4515 -0.465 0.9015 0.966 5.84 -0.7067 -0.448 1.4413 0.931 5.3 -0.4607 -0.464 0.9207 0.965 5.86 -0.7157 -0.448 1.4618 0.959 5.32 -0.47 -0.463 0.94 0.964 5.88 -0.7247 -0.447 1.4809 0.969 5.34 -0.4792 -0.462 0.9593 0.964 5.9 -0.7335 -0.446 1.5 0.958 5.36 -0.4884 -0.461 0.9786 0.964 5.92 -0.7425 -0.445 1.5194 0.951 5.38 -0.4977 -0.461 0.9979 0.964 5.94 -0.7513 -0.445 1.5382 0.936 5.4 -0.5069 -0.461 1.0171 0.964 5.96 -0.7602 -0.445 1.5568 0.922 5.42 -0.5161 -0.461 1.0364 0.962 5.98 -0.7692 -0.445 1.575 0.915 5.44 -0.5253 -0.46 1.0557 0.951 6. -0.778 -0.443 1.5933 0.91 5.46 -0.5345 -0.459 1.0747 0.937 6.02 -0.7869 -0.441 1.6115 0.909 5.48 -0.5436 -0.459 1.0929 0.938 6.04 -0.7956 -0.441 1.6295 0.909 5.5 -0.5528 -0.459 1.1116 0.955 6.06 -0.8045 -0.442 1.6478 0.909 5.52 -0.5621 -0.458 1.1314 0.979 6.08 -0.8133 -0.442 1.666 0.91 5.54 -0.5711 -0.457 1.1509 .997 6.1 -0.822: -0.441 1.6841 5.56 -0.5802 -0.456 1.1712 1.007 6.12 -0.8309 -0.441 1.7025 0.719 5.58 -0.5895 -0.455 1.1915 1.014 6.14 -0.8397 -0.441 1.7199 0.339 5.6 -0.5984 -0.454 1.2117 1.008 6.16 -0.8486 -0.441 1.7166 -0.072 5.62 -0.6075 -0.454 1.232 0.998 6.18 -0.8573 -0.44 1.7106 -0.305 5.64 -0.6166 -0.454 1.2517 0.986 6.2 -0.8662 -0.439 1.7031 -0.339 5.66 -0.6257 -0.453 1.2713 0.969 6.22 -0.8749 -0.438 1.6967 -0.333 5.68 -0.6347 -0.453 1.2907 0.945 6.24 -0.8836 -0.437 1.6899 -0.322 5.7 -0.6438 -0.453 1.3093 0.93 6.26 -0.8924 -0.436 1.6838 -0.315 5.72 -0.6529 -0.452 1.3271 0.942 6.28 -0.9011 -0.435 1.6773 -0.308 5.74 -0.6618 -0.451 1.3465 0.97 6.3 -0.9097 -0.435 1.6715 -0.312 5.76 -0.6708 -0.451 1.3665 0.993 6.32 -0.9184 -0.436 1.6653 -0.324 5.78 -0.6799 -0.45 1.3863 0.983 6.34 -0.9272 -0.437 1.6584 -0.34 5.8 -0.6889 -0.448 1.4065 0.942 6.36 -0.9359 -0.436 1.6515 -0.347 5.82 -0.6977 -0.447 1.4245 0.92 6.38 -0.9446 -0.435 1.6446 -0.347
Transcribed Image Text:time (s) position blue speed blue position red speed red time (s) position blue speed blue position red speed red 5.28 -0.4515 -0.465 0.9015 0.966 5.84 -0.7067 -0.448 1.4413 0.931 5.3 -0.4607 -0.464 0.9207 0.965 5.86 -0.7157 -0.448 1.4618 0.959 5.32 -0.47 -0.463 0.94 0.964 5.88 -0.7247 -0.447 1.4809 0.969 5.34 -0.4792 -0.462 0.9593 0.964 5.9 -0.7335 -0.446 1.5 0.958 5.36 -0.4884 -0.461 0.9786 0.964 5.92 -0.7425 -0.445 1.5194 0.951 5.38 -0.4977 -0.461 0.9979 0.964 5.94 -0.7513 -0.445 1.5382 0.936 5.4 -0.5069 -0.461 1.0171 0.964 5.96 -0.7602 -0.445 1.5568 0.922 5.42 -0.5161 -0.461 1.0364 0.962 5.98 -0.7692 -0.445 1.575 0.915 5.44 -0.5253 -0.46 1.0557 0.951 6. -0.778 -0.443 1.5933 0.91 5.46 -0.5345 -0.459 1.0747 0.937 6.02 -0.7869 -0.441 1.6115 0.909 5.48 -0.5436 -0.459 1.0929 0.938 6.04 -0.7956 -0.441 1.6295 0.909 5.5 -0.5528 -0.459 1.1116 0.955 6.06 -0.8045 -0.442 1.6478 0.909 5.52 -0.5621 -0.458 1.1314 0.979 6.08 -0.8133 -0.442 1.666 0.91 5.54 -0.5711 -0.457 1.1509 .997 6.1 -0.822: -0.441 1.6841 5.56 -0.5802 -0.456 1.1712 1.007 6.12 -0.8309 -0.441 1.7025 0.719 5.58 -0.5895 -0.455 1.1915 1.014 6.14 -0.8397 -0.441 1.7199 0.339 5.6 -0.5984 -0.454 1.2117 1.008 6.16 -0.8486 -0.441 1.7166 -0.072 5.62 -0.6075 -0.454 1.232 0.998 6.18 -0.8573 -0.44 1.7106 -0.305 5.64 -0.6166 -0.454 1.2517 0.986 6.2 -0.8662 -0.439 1.7031 -0.339 5.66 -0.6257 -0.453 1.2713 0.969 6.22 -0.8749 -0.438 1.6967 -0.333 5.68 -0.6347 -0.453 1.2907 0.945 6.24 -0.8836 -0.437 1.6899 -0.322 5.7 -0.6438 -0.453 1.3093 0.93 6.26 -0.8924 -0.436 1.6838 -0.315 5.72 -0.6529 -0.452 1.3271 0.942 6.28 -0.9011 -0.435 1.6773 -0.308 5.74 -0.6618 -0.451 1.3465 0.97 6.3 -0.9097 -0.435 1.6715 -0.312 5.76 -0.6708 -0.451 1.3665 0.993 6.32 -0.9184 -0.436 1.6653 -0.324 5.78 -0.6799 -0.45 1.3863 0.983 6.34 -0.9272 -0.437 1.6584 -0.34 5.8 -0.6889 -0.448 1.4065 0.942 6.36 -0.9359 -0.436 1.6515 -0.347 5.82 -0.6977 -0.447 1.4245 0.92 6.38 -0.9446 -0.435 1.6446 -0.347
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