Lab Report 9

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Miami Dade College, Kendall *

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2053L

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Physics

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Apr 3, 2024

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Lab #9 Lab partner 1: Aaliyah Gonzalez ID: 6438902 Lab partner 2: Jade Ariel Rodriguez ID:6281288 Title: Momentum, Energy, and Collisions Preliminary Question Answers: 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 1 will come to rest after collision with ball 2. On the other hand, when ball 1 collides with ball 2, ball 2 will move with the same speed along the same line. 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?

- Both the momentum and the kinetic energy is conserved based on the graph from preliminary question 2. The initial momentum is m*v and the final momentum will also be m*v, therefore, momentum is conserved in this head on collision because there is no external force applied on the system. Similarly, velocity is the same between both ball 1 before collision and ball 2 after collision, therefore kinetic energy is conserved because KE=1/2m*v^2. Analysis: 1. For each run, determine the momentum ( mv ) of each cart before the collision, after the collision, and the total momentum before and after the collision. Calculate the ratio of the total momentum after the collision to the total momentum before the collision. Enter the values in Table 3. (Shown in table) 2. For each run, determine the kinetic energy ( KE = ½ mv 2 ) for each cart before and after the collision. Calculate the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision. Enter the values in Table 4. (Shown in table) 3. If the total momentum for a system is the same before and after the collision, we say that momentum is conserved . If momentum were conserved, what would be the ratio of the total momentum after the collision to the total momentum before the collision? - If momentum were conserved, the ratio of the total momentum after the collision to the total momentum before collision would be a 1:1 ratio because conserved momentum means that the total momentum before and after the collision is the same. 4. If the total kinetic energy for a system is the same before and after the collision, we say that kinetic energy is conserved . If kinetic energy were conserved, what would be the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision? - If kinetic energy were conserved, the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision should also be a 1:1 ratio. This is because KE being conserved means that the total KE is the same before and after the collision for the system. 5. Inspect the momentum ratios in Table 3. Even if momentum is conserved for a given collision, the measured values may not be exactly the same before and after due to measurement uncertainty. The ratio should be close to one, however. Is momentum conserved in your collisions? - For the most part, momentum was conserved in our collisions because most of our trials had a momentum ratio close to 1. However, trials 3 and 4 where it was dealing with the hook-and-pile runs, they had a momentum closer to 2. This might be due to the fact that these collisions were inelastic. This inelastic collision was due to the fact that the carts, once collided, were stuck together and continued

down the platform creating and internal friction, losing some of the intended conserved momentum. 6. Repeat the preceding question for the case of kinetic energy, using the kinetic energy ratios in Table 4. Is kinetic energy conserved in the magnetic bumper collisions? How about the hook-and-pile collisions? Is kinetic energy consumed in the third type of collision studies? Classify the three collision types as elastic, inelastic, or completely inelastic. - Kinetic energy was conserved slightly for our magnetic trials making this collision to be elastic since the carts repelled each other and cart 2 maintained the total KE of the system. Trials 3 and 4 did not maintain KE because once carts 1 and 2 collided, the stuck together creating a completely inelastic system which does not maintain/lowers the total KE of the system. Trials 5 and 6 slightly maintained the total KE of the system, however, this collision was a inelastic collision because cart 1 collided with cart 2 completely, however, they did not stick to each other. Cart 2 continued down the platform which resulted in these trials maintaining the total KE of the system slightly. 7. You may have learned that for elastic collisions , "approach speed" equals "separation speed." Check this by completing Table 5. (Shown in table) 8. If the last column in Table 5 contained a ratio greater than 1.0, it would imply that the combined kinetic energies of the carts had increased! What is the maximum value you found? - The maximum values we found were shown in trials 5 and 6 where the carts had an inelastic collision. The value for trial 5 was 2.175 and the value for trial 6 was 2.106. Our maximum ratio in table 5 was calculated to be for trial 5. Data Tables: Table 1 Mass of cart 1 (kg) 0.26185 kg Mass of cart 2 (kg) 0.2735 kg Positive direction for cart 1: Left Positive direction for cart 2: Left Table 2 Bumper Type Run number Velocity of cart 1 before collision (m/s) Velocity of cart 2 before collision (m/s) Velocity of cart 1 after collision (m/s) Velocity of cart 2 after collision (m/s) Part 1: Magnetic 1 -0.1211 0 0.02522 -0.1824

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Magnetic 2 -0.1198 0 0.005320 -0.1722 Part 2: Hook-and- pile 3 -0.1134 0 -0.1629 -0.1554 Hook-and-pile 4 -0.09727 0 -0.1259 -0.1433 Part 3: Both 5 -0.1050 0 -0.04192 -0.1234 Both 6 -0.1045 0 -0.01855 -0.1156 Table 3 Run numbe r Momentu m of cart 1 before collision (kg*m/s) Momentu m of cart 2 before collision (kg*m/s) Momentu m of cart 1 after collision (kg*m/s) Momentu m of cart 2 after collision (kg*m/s) Total momentu m before collision (kg*m/s) Total momentu m after collision (kg*m/s) Ratio of total momentum after/befor e 1 -0.0317 0 0.0066 -0.0499 -0.0317 -0.0433 1.366 2 -0.0314 0 0.00134 -0.0471 -0.0314 -0.04576 1.457 3 -0.0297 0 -0.0427 -0.0425 -0.0297 -0.0852 2.869 4 -0.0255 0 -0.0340 -0.0392 -0.0255 -0.0732 2.871 5 -0.0275 0 -0.0110 -0.0337 -0.0275 -0.0447 1.625 6 -0.0274 0 -0.0049 -0.0316 -0.0274 -0.0365 1.332 Table 4 Run number KE of cart 1 before collision (J) KE of cart 2 before collision (J) KE of cart 1 after collision (J) KE of cart 2 after collision (J) Total KE before collision (J) Total KE after collision (J) Ratio of total KE after/before 1 0.0019 0 0.000833 0.00455 0.0019 0.005383 2.833 2 0.00187 0 0.000003705 0.00406 0.00187 0.004063705 2.173 3 0.00168 0 0.00347 0.00330 0.00168 0.00677 4.030 4 0.00123 0 0.00208 0.00281 0.00123 0.00489 3.976 5 0.00144 0 0.00023 0.00208 0.00144 0.00231 1.604 6 0.00143 0 0.00004505 0.00183 0.00143 0.00188 1.315 Table 5 Run number Velocity of cart 1 before collision Velocity of cart 2 before collision Velocity of cart 1 after collision Velocity of cart 2 after collision Approach speed before collision Separation speed after collision (m/s) Ratio of speeds separation/approach

(m/s) (m/s) (m/s) (m/s) (m/s) 1 -0.1211 0 0.02522 -0.1824 -0.1211 -0.07859 0.6490 2 -0.1198 0 0.005320 -0.1722 -0.1198 -0.146 1.219 3 -0.1134 0 -0.1629 -0.1554 -0.1134 -0.1344 1.185 4 -0.09727 0 -0.1259 -0.1433 -0.09727 -0.120285 1.237 5 -0.1050 0 -0.04192 -0.1234 -0.1050 -0.2284 2.175 6 -0.1045 0 -0.01855 -0.1156 -0.1045 -0.2201 2.106 Graphs: Magnetic Graph: Both (Hook-and-pile and Magnetic):

*Forgot to take photo of hook-and-pile graph that we got for one of the trials and couldn’t retrieve since we continued the lab ☹ *Values for tables were negative because carts went to the right which were their negative direction

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