PHY 105M Lab 7 (1)

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University of Texas *

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105M

Subject

Chemistry

Date

Apr 29, 2024

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pdf

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4

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Method: For this lab, we were asked to take a closer inspection on collisions and how they are related to conservation laws. By producing several different experiments with different variations, we can observe how conservation laws can come into action through the process of collisions. For this experiment, we were asked to use a PASCO collision cart set up to make our discoveries and test the accuracy of the linear momentum equation ( 𝑃 = 𝑚 1 𝑣 1+ 𝑚 2 𝑣 2) and the mechanical energy equation ( 𝐸 =1/2 𝑚 1 𝑣 1+1/2 𝑚 2v2) Given this information, we were able to hypothesize that the collisions would allow conservation of energy, by testing the accuracy of the formulas and using them to prove our theory. To begin this experiment, we started out with 4 different experiment variations. These variations would measure different aspects of the collisions using different circumstances. Before we began, we aligned both the red and blue carts onto the PASCO setup. We also recorded that the weight of the cars was 0.275 +/- 0.005kg. After we calibrated and connected the setup to the carts, we began to set up our first experiment. We set up the blue and red carts so that they were free and their magnetic sides were facing each other. We started them at different sides of the track and gave both of the carts a push, resulting in a collision. In this case, the magnets were opposite poles so the carts rebounded on impact, creating a free elastic collision. Using the PASCO system, we were able to calculate the speed of the carts. We dissected the graph to find the initial velocity and final velocity points of the system before and after the collision (rebound) and collected the data. Table 1: Initial and Final Velocities of Collisions Mass (kg) Velocity 1, Blue (m/s) Mass (kg) Velocity 2, Red (m/s) E P Propagated Uncertainty of E Propagated Uncertainty of P Elastic Fixed Initial 0.275 +/- 0.005 0.081 +/- 0.001 0.275 +/- 0.005 0.878 +/- 0.001 0.1069 0.2637 0.0194 0.0213 Elastic Fixed Final 0.275 +/- 0.005 0.088 +/- 0.001 0.275 +/- 0.005 0.383 +/- 0.001 0.0212 0.1295 0.038 0.0213 Elastic Fixed Initial 0.275 +/- 0.005 0.935 +/- 0.001 0.275 +/- 0.005 0.707 +/- 0.001 0.1889 0.4515 0.254 0.121 Elastic Fixed Final 0.275 +/- 0.005 0.734 +/- 0.001 0.275 +/- 0.005 0.346 +/- 0.001 0.0905 0.2970 0.140 0.011 Elastic Fixed Initial 0.275 +/- 0.005 0.070 +/- 0.001 0.275 +/- 0.005 0.942 +/- 0.001 0.1226 0.2783 0.00223 0.009
Elastic Fixed Final 0.275 +/- 0.005 0.039 +/- 0.001 0.275 +/- 0.005 0.004 +/- 0.001 0.0002 0.0118 0.0001 0.0271 Elastic Fixed Initial 0.275 +/- 0.005 0.699 +/- 0.001 0.275 +/- 0.005 0.881 +/- 0.001 0.1739 0.4345 0.00231 0.288 Elastic Fixed Final 0.275 +/- 0.005 0.377 +/- 0.001 0.275 +/- 0.005 0.209 +/- 0.001 0.0255 0.1612 0.0039 0.822 Follow Up Elastic Fixed Initial 0.525 +/- 0.005 0.688 +/- 0.001 0.525 +/- 0.005 0.681 +/- 0.001 0.2459 0.7187 0.167 0.218 Follow Up Elastic Fixed Final 0.525 +/- 0.005 0.591 +/- 0.001 0.525 +/- 0.005 0.595 +/- 0.001 0.1846 0.6227 0.126 0.012 Table 2: T-score for the comparison between initial and final velocities of collisions -energy T-score (Energy) T-Score (E) T-Score (P) Elastic Fixed (i) v. Elastic Fixed 0.2497 1.4947 Elastic Free v. Elastic Free 23.8325 52.699 Inelastic Fixed v. inelastic Fixed 0.2095 —- Conclusion: Based on our data, our hypothesis is only partially correct, in that only of the two elastic collisions were conserved. Based on our t-scores, the only one that was under 1 was our free elastic collision (t=0.2497). Every other collision, fixed elastic, free inelastic, and fixed inelastic were above 1, which means they were not indistinguishable. Both inelastic collisions were accurate in our hypothesis but the fixed elastic collision was not correct in our hypothesis. That being said, that means that the only system that was conserved was the free elastic collision. All of the other three were not conserved. In our follow up, we found that the reaction was conserved, even with the increase in mass for both carts. The t-score was 0.2095 for the follow up free elastic collision and we found that it was also conserved. For other iterations of this lab, I think having carts of different masses instead of similar masses, will increase the accuracy of the experiment. Also, instead of colliding the carts by hand, using a mechanism that can propel the carts forward automatically would be more efficient. The PASCO models have a limit in terms of precision it can measure velocity, which is to three decimal places. In the future, a more powerful model can be applied, to measure to less uncertainty. When comparing to other groups, all of their t-scores were above the value of three, whereas ours only had half of then
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