ANALYSIS 1. Perform the momentum and energy calculations for the data tables using a spreadsheet. a. 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 your data table. b. Determine the kinetic energy (1/2 mv-) 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 your data table. 2. For the system of cart 1 for each type of collision, does the momentum of cart 1 increase, decrease, or remain the same? Provide evidence. 3. For the system of cart 2 for each type of collision, does the momentum of cart 2 increase, decrease, or remain the same? Provide evidence. 4. For the system of cart 1/cart 2 for each type of collision, does the momentum of cart1/cart 2 system increase, decrease, or remain the same? Provide evidence. 5. For the system of cart 1 for each type of collision, does the kinetic energy of cart 1 increase, decrease, or remain the same? Provide evidence. 6. For the system of cart 2 for each type of collision, does the kinetic energy of cart 2 increase, decrease, or remain the same? Provide evidence. 7. For the system of cart 1/cart 2 for each type of collision, does the kinetic energy of cart 1/cart 2 system increase, decrease, or remain the same? Provide evidence. 8. Inspect the momentum ratios. 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? 9. Repeat the preceding question for the case of kinetic energy. Is kinetic energy restored in the magnetic bumper collisions? How about the Velcro collisions and plunger? Classify the four collision types as elastic, inelastic, completely inelastic, or super elastic. EXTENSIONS 1. Using the magnetic bumpers, consider other combinations of cart mass by adding weight to one cart. Are momentum or energy conserved in these collisions? 2. Using the magnetic bumpers, consider other combinations of initial velocities. Begin with having both carts moving toward one another initially. Are momentum and energy conserved in these collisions? 18 - 4 Physics with VernierA TABLE Mass of cart 1 (kg) 45 Mass of cart 2 (kg) 5 Kg Run number Initial Velocity | Initial Velocity Final Final Velocity of cart 1 of cart 2 Velocity of of cart 2 (m/s) (m/s) cart 1 (m/s) (m/s) 1 0 O 2 0 . 3108 3 3968 0 2039 . 2420 4 - 3055 0 1490 , 2227 5 1. 34 75 0 :0793 . 3581 6 .2556 0 :0724 2847 7 0 0 - 1206 1580 00 0 0 51277 1788 Run Initial Initial Final Final Initial Total Final Total Ratio of number Momentum Momentum Momentum Momentum momentum momentum total of cart 1 of cart of cart of cart 2 (kg.m/s) (kg.m/s) momentum (kg.m/s) 2(kg.m/s) 1 (kg.m/s) (kg.m/s after/before 1 0 2 0 3 0 4 0 5 0 6 0 7 0 o o 3 Run Initial KE of Initial KE of Final KE of Final KE of Initial Total Final Total Ratio of number cart 1 cart 2 cart 1 cart 2 KE KE total KE ( J ) ( J ) ( J ) ( J ) ( J ) ( J ) after/before 1 0 2 0 3 0 4 0 5 0 6 0 V 0 0 8 0 0 Physics with Vernier 18 - 3Callof (body) X V fx 2 F G H D E A B C n1 n2 0.45 0.5 v1i v2i v1f v2f run 0.3997 0 0 0.4456 2 0.2827 0 0 0.3108 3 0.3969 0 0.2039 0.242 0.3055 0 0.199 0.2227 0.3475 0 0.0793 0,3581 OUT 0.2556 0 0.0724 0.2847 10 0 0 -0.1206 0.158 11 8 0 0 -0.1277 0,1788 12 13 run pli p2i p1f p2f pt1 otf ratio 14 1 0.179865 0 0.2228 0.179865 0.2228 1.238707 15 2 0.127215 O 0 0.1554 0.127215 0.1554 1.221554 16 3 0.178605 0 0.091755 0.121 0.178605 0.212755 1.191204 17 4 0.137475 0 0.08955 0.11135 0.137475 0.2009 1.461357 18 5 0.156375 0 0.035685 0.17905 0.156375 0.214735 1.373205 19 6 0.11502 O 0.03258 0.14235 0.11502 0.17493 1.520866 20 0 -0.05427 0.079 0 0.02473 21 8 0 0 -0.05747 0.0894 0 0.031935 22 23 24 25 26 27 28 E Sheet1 + Calculation Mode: Automatic Workbook StatisticsCompute 0o Momentum, Energy and Collisions Collisions are classified as elastic (kinetic energy is the same before and after the collision), inelastic (kinetic energy is lost) or completely inelastic (the objects stick together after collision) Sometimes collisions are described as super-elastic if kinetic energy is gained. In this experiment you can observe these types of collisions. OBJECTIVES . Observe collisions between two cartsand measure the momentum of each cart. . Measure energy changes during different types of collisions. . Classify collisions as elastic, inelastic, or completely inelastic. MATERIALS computers dynamics cart track Vernier computer interface two low-friction dynamics carts with Logger Pro magnetic and VelcroTM bumpers two Vernier Motion Detectors PRELIMINARY QUESTIONS 1. Consider a head-on collision between two billiard balls. One is initially at rest and the other moves toward it. Sketch a position vs. time graph for each ball, starting with time before the collision and ending a short time afterward. 2. As you have drawn the graph, is momentum conserved in this collision? Is kinetic energy conserved? PROCEDURE 1. Measure the masses of your carts and record them in your data table. Label the carts as cart 1 and cart 2. 2. Set up the track so that it is horizontal. Test this by releasing a cart on the track from rest. The cart should not move. 3. Practice creating gentle collisions by placing cart 2 at rest in the middle of the track, and release cart 1 so it rolls toward the first cart, magnetic bumper toward magnetic bumper. The carts should smoothly repel one another without physically touching. 4. Place a Motion Detector at each end of the track, allowing for the 0.40 m minimum distance between detector and cart. Connect the Motion Detectors to the DIG/SONIC 1 and DIG/SONIC 2 channels of the interface. 5. Open the file "18 Momentum Energy Coll" from the Physics with Vernier folder. 6. Click _ Collect to begin taking data. Repeat the collision you practiced above and use the position graphs to verify that the Motion Detectors can track each cart properly throughout Physics with Vernier 18 - 1Computer 18 the entire range of motion. You may need to adjust the position of one or both of the Motion Detectors. 7. Place the two carts at rest in the middle of the track, with their Velcro bumpers toward one another and in contact. Keep your hands clear of the carts and click 8 zero ]. Select both sensors and click OK . This procedure will establish the same coordinate system for both Motion Detectors. Verify that the zeroing was successful by clicking _ collect] and allowing the still-linked carts to roll slowly across the track. The graphs for each Motion Detector should be nearly the same. If not, repeat the zeroing process Part 1: Magnetic Bumpers 8. Reposition the carts so the magnetic bumpers are facing one another. Click D Collect to begin taking data and repeat the collision you practiced in Step 3. Make sure you keep your hands out of the way of the Motion Detectors after you push the cart. 9. From the velocity graphs you can determine an average velocity before and after the collision for each cart. To measure the average velocity during a time interval, drag the cursor across the interval. Click the Statistics button to read the average value. Measure the average velocity for each cart, before and after collision, and enter the four values in the data table. Delete the statistics box. 10. Repeat Step 9 as a second run with the magnetic bumpers, recording the velocities in the data table. Part II: Velcro Bumpers 11. Change the collision by turning the carts so the Velcro bumpers face one another. The carts should stick together after collision. Practice making the new collision, again starting with cart 2 at rest. 12. Click D Collect] to begin taking data and repeat the new collision. Using the procedure in Step 9, measure and record the cart velocities in your data table 13. Repeat the previous step as a second run with the Velcro bumpers. Part III: Velcro to Magnetic Bumpers 14. Face the Velcro bumper on one cart to the magnetic bumper on the other. The carts will not stick, but they will not smoothly bounce apart either. Practice this collision, again starting with cart 2 at rest. 15. Click D collect] to begin data collection and repeat the new collision. Using the procedure in Step 9, measure and record the cart velocities in your data table 16. Repeat the previous step as a second run with the Velcro to magnetic bumpers. Part IV: Velcro Bumpers to Plunger Face the Velcro bumper on one cart to the plunger on the other. The plunger spring should be compressed and locked before the collision, but then released during the collision. Practice this collision, again starting with both carts at rest 18. Click D collect to begin data collection and repeat the new collision. Using the procedure in Step 9, measure and record the cart velocities in your data table. 19. Repeat the previous step as a second run with the Velcro bumper to plunger. 18 - 2