Lab 7

Arizona State University General Physics 113 Lab Report #7: Momentum & Collisions Lab Group 2: Kaya Horonenko Samantha Mullins Kayla Nguyen Lab TA: Sreekanth Thatikonda Lab Section: M & W 12:30-3 pm

I. Objective Observe momentum and collisions to determine if kinetic energy is conserved in the system. Momentum is the force or speed of an object, and is the product of the mass and velocity of the object. Kinetic energy is energy an object possesses due to its motion. In an elastic collision, kinetic energy is conserved, while in an inelastic collision, kinetic energy is transformed into different types of energy. II. Materials/Procedures To begin the experiment, open the Logger Pro app and keep the velocity v time graph. Mass both of the carts and record in the data table. First, the sensors must be tested to ensure they are set up correctly. Make sure cart one is facing the other with the magnet side. Place cart two in the center of the track and cart one at the end of the track (about 20cm from the motion detector). Collect in Logger Pro and gently push cart one toward cart two. Make sure the velocity v time graph records one of the carts in the negative and continue. If it is not, the direction of the sensor must be reversed. In order to do that, select “Experiment”, “Set Up Sensors”, “Labquest 1”, and to the right of the lab quest picture will be “DIG/Sonic”. Click on the picture of one of the motion detectors and select “Reverse Direction”. To begin part one of the experiment, place cart two in the center of the track and cart one 20 cm away from the motion detectors. Begin data collection and gently push cart one to cart two. Determine on the velocity v time graph which colored line corresponds to the cart and record it in the data table. Then highlight the portion of the velocity v time where cart one was moving at a constant velocity before the collision and where cart two was moving at a constant velocity after the collision. Take a screenshot and record the mean for all velocity values in the data table. Then determine momentum and kinetic energy of each cart. Repeat for 5 trials.

Table 2 . Part I - Prior to Collision Cart 1 Cart 2 Total System V 1i ( ? ? ) P 1i (Ns) KE 1i (J) V 2i ( ? ? ) P 2i (Ns) KE 2i (J) P i (Ns) KE i (J) Trial 1 0.487 0.243 0.059 0 0 0 0.243 0.059 Trial 2 0.478 0.239 0.057 0 0 0 0.239 0.057 Trial 3 0.558 0.279 0.078 0 0 0 0.279 0.078 Trial 4 0.550 0.275 0.076 0 0 0 0.275 0.076 Trial 5 0.595 0.297 0.088 0 0 0 0.297 0.088 Average: 0.267 0.072 Table 3 . Part I After Collision Cart 1 Cart 2 Total System V 1f ( ? ? ) P 1f (Ns) KE 1f (J) V 2f ( ? ? ) P 2f (Ns) KE 2f (J) P f (Ns) KE f (J) Trial 1 0 0 0 0.534 0.267 0.071 0.267 0.071 Trial 2 0 0 0 0.475 0.237 0.056 0.237 0.056 Trial 3 0 0 0 0.533 0.266 0.071 0.266 0.071 Trial 4 0 0 0 0.570 0.285 0.081 0.285 0.081 Trial 5 0 0 0 0.588 0.294 0.086 0.294 0.086 Average: 0.270 0.073 Figure 1. Velocity vs. Time (s) of Magnetic Repulsion Collision (Part I): This graph depicts ( ? ? ) the velocity on the y-axis vs. the time in seconds on the x-axis of Trial 1.

Table 4 . Part II - Prior to Collision Cart 1 Cart 2 Total System V 1i ( ? ? ) P 1i (Ns) KE 1i (J) V 2i ( ? ? ) P 2i (Ns) KE 2i (J) P i (Ns) KE i (J) Trial 1 0.530 0.265 0.070 0 0 0 0.265 0.070 Trial 2 0.529 0.264 0.070 0 0 0 0.264 0.070 Trial 3 0.571 0.285 0.081 0 0 0 0.285 0.081 Trial 4 0.730 0.365 0.133 0 0 0 0.365 0.133 Trial 5 0.577 0.288 0.083 0 0 0 0.288 0.083 Average: 0.294 0.087

Cart 1 Cart 2 Total System V 1i ( ? ? ) P 1i (Ns) KE 1i (J) V 2i ( ? ? ) P 2i (Ns) KE 2i (J) P i (Ns) KE i (J) Trial 1 0 0 0 0 0 0 0 0 Trial 2 0 0 0 0 0 0 0 0 Trial 3 0 0 0 0 0 0 0 0 Trial 4 0 0 0 0 0 0 0 0 Trial 5 0 0 0 0 0 0 0 0 Average 0 0 Table 7 . Part III - After Collision Cart 1 Cart 2 Total System V 1f ( ? ? ) P 1f (Ns) KE 1f (J) V 2f ( ? ? ) P 2f (Ns) KE 2f (J) P f (Ns) KE f (J) Trial 1 -0.516 -0.258 0.067 0.349 0.174 0.030 -0.083 0.097 Trial 2 -0.520 -0.260 0.067 0.483 0.241 0.058 -0.018 0.126 Trial 3 -0.500 -0.250 0.062 0.476 0.238 0.057 -0.012 0.119 Trial 4 -0.523 -0.261 0.068 0.438 0.219 0.048 -0.042 0.116 Trial 5 -0.516 -0.258 0.067 0.479 0.239 0.057 -0.018 0.124 Average: -0.035 0.116 Figure 3. Velocity vs. Time (s) Trial One of Explosive Collision (Part III): This graph ( ? ? ) shows the velocity on the y-axis and the time in seconds on the x-axis.

IV. Calculations Momentum Equation for Magnetic Repulsion 1. f f ?₁?₁ᵢ + ?₂?₂ᵢ = ?₁?₁ + ?₂?₂ a. Remove values where velocity is 0 ( and f ) ?₂ᵢ ?₁ 2. = f ?₁?₁ᵢ ?₂?₂ Kinetic Energy Equation for Magnetic Repulsion 1. = f ² f ² 1 2 ?₁?₁ᵢ² + 1 2 ?₂?₂ᵢ² 1 2 ?₁?₁ + 1 2 ?₂?₂ a. Remove values where velocity is 0 ( and f ) ?₂ᵢ ?₁ 2. = f ² 1 2 ?₁?₁ᵢ² 1 2 ?₂?₂ Momentum Change for Magnetic Repulsion - Experimental Change: f ∆? = ? − ?ᵢ - Theoretical Change: ∆? = 0 Kinetic Energy Change for Magnetic Repulsion

2. = f ² f ² 0 1 2 ?₁?₁ + 1 2 ?₂?₂ Momentum Change for Explosion - Experimental change in momentum: f ∆? = ? − ?ᵢ - Theoretical change in momentum: ∆? = 0 Percent Error Calculations Equation for Percent Error: 𝑇ℎ?????𝑖𝑐𝑎? 𝑉𝑎??? − 𝐸𝑥???𝑖????𝑎? 𝑉𝑎??? 𝐸𝑥???𝑖????𝑎? 𝑉𝑎??? 𝑥 100 ∆? − 0 | | 𝑥 100% = ? ? − ? 𝑖 | | 𝑥 100% △𝑇 − 0 | | 𝑥 100 = 𝑇 ? − 𝑇 𝑖 | | 𝑥 100% Sample Calculations: 𝑃 ?𝑎?𝑖? = 𝑃 ? 𝑃 𝑖 ≃ 1 → % 𝐸???? = 𝑃 ?𝑎?𝑖? − 1 1 | | | | | | 𝑥 100 1. Part I △ P Percent Error = = 1.011 − 1 1 | | | | 𝑥 100 1. 12% a. 𝑃 ?𝑎?𝑖? = 0.270 0.267 = 1. 011 2. Part II △ P Percent Error = = 0.925 − 1 1 | | | | 𝑥 100 7. 48 | |% a. 𝑃 ?𝑎?𝑖? = 0.073 0.0717 = 1. 011 𝑇 ?𝑎?𝑖? = 𝑇 ? 𝑇 𝑖 ≃ 1 → % 𝐸???? = 𝑇 ?𝑎?𝑖? − 1 1 | | | | | | 𝑥 100 1. Part I △ T Percent Error = = 0.928 − 1 1 | | | | 𝑥 100 7. 22% | | 2. 𝑃 ?𝑎?𝑖? = 0.272 0.294 = 0. 925 V. Discussion/Conclusion

The goal of this lab was to observe different types of collisions and if kinetic energy was conserved in the system after the collision of the two objects. In this lab, two carts were used in various forms of collisions to observe the resulting kinetic energy conservation. For the magnetic repulsion collision, the theoretical momentum change is △ P = 0 since the system is expected to be a conserved system. The experimental momentum change is 1.011 . The percent error for the momentum change in the magnetic repulsion collision was ??·? ? 1.12%. The theoretical kinetic energy change is △ T = 0, since the system is expected to be conservative. The experimental kinetic energy change was 0.925 J. The percent error for the kinetic energy change in the magnetic repulsion collision was 7.22%. For the velcro collision, the theoretical momentum change is △ P = 0 for the same reasoning as the prior collision. The experimental change in momentum was 0.928 . The ??·? ? percent error for the change in momentum in the velcro collision was 7.48%. The theoretical momentum change for the explosion collision is △ P = 0 . Values for the experimental change in momentum were not able to be calculated, as a would not be 𝑃 ?𝑎?𝑖? possible since the denominator would be 0. The values of the initial and final velocities before and after the collision found for both carts affected the momentum and kinetic energy values. The equation for momentum is , ? = ?? and from this equation it can be seen that velocity is directly proportional to momentum. Therefore, an increase/decrease in velocity will lead to an increase/decrease in momentum. Further, the equation for kinetic energy is , which shows that kinetic energy is 𝐾 = 1 2 ??² directly proportional to the square of v, resulting in the same relationship as described above.The initial and final velocities of each cart, which were the independent variables, affected the initial

energy values for the system. This error is due to an error in the experimental method, and could be fixed with a specified force to push the cart, such as “gently” or “aggressively.” Another source of error for this lab is that the system is assumed to be closed for each collision. For example, the track is assumed to be frictionless, however in reality there is likely to be slight friction between the wheels of the carts and the track. Therefore, some kinetic energy would be transferred into thermal energy, since friction causes an increase in temperature between two objects. This error is due to an idealization in the theory. A way to fix this in the lab would be to create a truly frictionless surface, however this is not an achievable goal, therefore a close-to-frictionless track is acceptable. Overall, the lab was successful as conservation of kinetic energy was observed between two different types of collisions, elastic and inelastic. Additionally, the lab portrayed the principle of momentum conservation in any type of collision.