Momentum, Energy and Collisions Temidayo Akinbi and Jacqueline Newland 12/14/18 Dr. Psaker Abstract For this experiment, we observed collisions between two carts, testing for the conservation of momentum. To set up this experiment we used a Vernier Dynamics track, a motion detector, two Vernier dynamic carts, Logger Pro and LabQuest. Next, we measured the masses of the dynamic carts and recorded them in the data table. Then, we set up the motion detector placing it 0.15 m away from the end of the dynamic track. For the bumper collisions in part I we repositioned the carts to that they were facing one another and then we started the collisions, collecting the data for the velocity vs time graph and position vs time graph. In trial one we found that the total momentum before the collision was 0.1527 kg*m/s for trial two it was 0.2201 kg*m/s for trial three it was 0.1698 kg*m/s and for trial four it was 0.2179 kg*m/s. We also found that in trial one the total momentum after collision was 0.1400 kg*m/s for trial two it was 0.2107 kg*m/s, for trial three it was 0.1554 kg*m/s and for trial four it was 0.2010 kg*m/s. Bringing the ratios for the total momentum before and after collision for trial one, two, three and four to 0.9168 kg*m/s, 0.9573kg*m/s, 0.9152 kg*m/s and 0.9224 kg*m/s. Since these ratios of the total momentum are close to 1 it tells us that the momentum was conserved in this experiment. We also found that the ratios for total kinetic energy for trials 1, 2, 3, and 4 were 0.8162 J, 1.002 J, 0.4187 J and 0.4244 J. Some potential sources of error include human error when resetting our collisions on the dynamic track we werenâ€™t consistently putting them the exact same distance apart which could have caused some variation in data. Preliminary Questions 1.) Consider a head-on collision between two identical billiard balls. Ball 1 is initially in motion toward ball 2, which is initially at rest. After the collision, ball 2 departs with the same velocity that ball 1 originally had. Disregard any friction between the balls and the surface. What happens to ball 1? What happens to ball 2? Ball one stops, the second ball moves with the same velocity as the first one. 2.) Sketch a position vs. time graph for each ball in Preliminary Question 1, starting with the time before the collision starts and ending a short time after the collision. 3.) Based on your graph from Preliminary Question 2, is momentum conserved in this collision? Is kinetic energy conserved? The momentum and kinetic energy are conserved in this collision. Since there are no external forces momentum and kinetic energy are conserved. Data Mass of cart 1(kg) 0.4987 Table 1 Mass of cart 2(kg) 0.5019 Table 2 Bumper type Run number Velocity of Velocity of Velocity of cart 1 before cart 2 before cart 1 after collision collisions collision (m/s) (m/s) (m/s) Part I 1 0.3062 0 0.0033 Bumper Bumper 2 0.4414 0 0.0170 Part II 3 0.3404 0 0.1538 Hook-andpile Hook-and4 0.4370 0 0.1999 pile Run number 1 2 3 4 Moment um of cart 1 before collision (kg*m/s) 0.1527 0.2201 0.1698 0.2179 Moment um of cart 2 before collision (kg*m/s) 0 0 0 0 Table 3 Moment Moment um of um of cart 1 cart 2 after after collision collision (kg*m/s) (kg*m/s) 0.0016 0.1384 0.0085 0.2022 0.0767 0.0787 0.0997 0.1013 Total moment um before collision (kg*m/s) 0.1527 0.2201 0.1698 0.2179 Velocity of cart 2 after collision (m/s) 0.2757 0.4028 0.1569 0.2019 Total moment um after collision (kg*m/s) 0.1400 0.2107 0.1554 0.2010 Ratio of total momentu m (after/bef ore) 0.9168 0.9573 0.9152 0.9224 Run number 1 2 3 4 KE of cart 1 before collision (J) 0.0234 0.0486 0.0289 0.0476 KE od cart 2 before collision (J) 0 0 0 0 Table 4 KE of KE of cart 1 cart 2 after after collision collision (J) (J) 2.715*10-6 0.0191 7.206*10-5 0.0407 0.0059 0.0062 0.0100 0.0102 Total KE before collision 0.0234 0.0486 0.0289 0.0476 Total KE after collision (J) 0.0191 0.0487 0.0121 0.0202 Ratio of total KE after/before 0.8162 1.002 0.4187 0.4244 Data Velocity vs time graph Figure 2. Velocity vs. Time graph of the two carts as they collide. Analysis 1. See Data Table 1 and 3. 2. See Data Table 4. 3. If momentum were conserved, the ratio of the total momentum after the collision to the total momentum before collision would be 1:1. 4. If kinetic energy were conserved, the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision would be 1:1. 5. Yes, momentum is conserved in our collision. We can come to this conclusion based on the fact all four of the trials had ratios very close to 1. The average percent difference between 1 and the average total momentum ratio is 7.48%. 6. Yes, kinetic energy is conserved in our completely inelastic collisions. Our four collisions were completely inelastic and since their ratios were very close to one, we can infer that kinetic energy was conserved. Recognizing that only two collisions were exactly inelastic one can make inferences about the other collisions. From the data, an inference can be made that the second two trials (Velcro to Velcro) can be classified as inelastic because they were both recorded in the 0.4 range. The first two trials (bumper to bumper) can be classified as completely inelastic because 1.0 and 0.8 are not close in the same range. References: GMU Reference By: https://mymasonportal.gmu.edu/webapps/blackboard/execute/content/file?cmd=view&content_i d=_4531146_1&course_id=_34409_1