Lab Report Momentum and Collision (Lab 8)

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Nov 24, 2024

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Course and Section PHYL ___________ Name of the Experiment _________________________________________________________ Your Name _________________________________________________________ J Number _________________________________________________________ Date Expt Performed _________________________________________________________ Your Lab Partners 1. ___________________________________________________ 2. ___________________________________________________ 3. ___________________________________________________ Your Lab Instructor _______________________________________________

PRE-LAB QUESTION Consider a head-on collision between a cue ball and a billiard ball initially at rest. Sketch a velocity-time graph for each ball for the interval shortly before until shortly after the collision. Justify your predictions for the final velocity of each billiard ball. Methods. The purpose of this experiment was to discover that an object in motion has kinetic energy. Momentum, p, is a property of the material that is associated to its mass and velocity which can be used to characterize it action, p = mv. And that an external factor causes an alteration in an item's momentum. If we regard two carts colliding as our systems, all energies they exert on each other are intrinsic to the system. In this lab, we will look at the motion of both carts before and after collisions to discover what influence, if there are any, these forces have on a system's momentum. We will conduct a three-part test. Part 1 is about elastic collisions, Part 2 is about inelastic collisions, and Part 3 is about explosions.

PROCEDURE 1. Attach the Motion Detectors to the brackets and position them at opposite ends of the Dynamics Track. 2. Your motion detectors have a switch, set each of them to Track. 3. Adjust the leveling screws on the feet as needed to level the track. To make sure the track is level, place a cart on the track and give it a gentle push. It should not slow more in one direction than in the other. 4. Connect both motion detectors to the interface and start the data-collection program. Make the necessary adjustments so that a velocity vs . time graph for each detector is shown in the graph window. 5. Make sure that each of your carts has the neodymium magnets at one end and the Velcro patches at the other. Place both carts, linked with their Velcro patches, in the center of the track. Zero both motion detectors and reverse the direction of one of them. 6. Begin collecting data, then gently push the linked carts towards one of the motion detectors (see Figure 1). Be sure to keep your hands out of the way of the motion detectors. Catch the carts before they run off the track. The velocity-time graphs from each detector should be nearly mirror images of one another; they will also show a slight decrease in velocity due to friction. Adjust the level of the track until this decrease appears to be nearly the same in both directions. Figure 1 Part 1 Elastic collisions 7. Reverse the carts so that their magnet ends face one another. Separate them by about 40 cm. Practice launching one cart toward the other so that at closest approach they exert forces on each other without touching. A jarring collision will not yield satisfactory data. 8. Place the target cart in the middle of the track. Position the other cart at least 20 cm in front of one of the motion detectors. 9. Start data collection. Then, when you hear the motion detectors clicking, launch one of the carts toward the other. Because momentum, like velocity, is a vector quantity,

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check to see if the signs of the velocities match your experimental setup. If necessary, reverse the direction of one or both sensors. 10. In this experiment you are concerned with changes in momentum due to the collisions of the carts. Some slowing due to friction is inevitable. To minimize the effect of frictional losses in your analysis, you should select short intervals of the velocity-time graphs just before and just after a collision. Then, choose Statistics from the Analyze menu and record the mean velocity of each cart for these intervals. 11. Collect data for up to six elastic collisions, varying the initial velocity and the mass of either cart. Try a collision in which both carts have an initial velocity, but different masses. Record your data in Table 1 and complete the rest of the table. [You may wish to use Logger Pro to help you record and analyze your data.] Part 2 Inelastic collisions 1. Reverse the carts so that the ends with the Velcro patches face one another. Practice launching one cart toward the other so that when they collide, the carts link smoothly and continue moving without a noticeable bounce. A jarring collision will not yield satisfactory data. 2. Collect data as before for at least three inelastic collisions, varying the initial velocity and the mass of either cart. Determine the velocity of the carts before and after the collision as you did in Part 1. Since both motion detectors provide velocity data after the collision, you will have to decide how to record the velocity of the linked carts. Record your data in Table II and complete the rest of the table. Part 3 Explosions 1. Place the carts in the center of the track with the plunger end of one cart facing the other. Depress and lock the mechanism on the plunger cart. Position the carts so that they are touching. 2. Begin data collection, then give a quick tap to the release pin with something hard, such as the support rod for a force sensor, as shown in Figure 2. Catch the carts before they run off the track. Figure 2

3. Repeat, varying the mass of either cart. Determine the velocity of the carts after the explosion as you did in Part 1. Record your data in Table III and complete the rest of the table. EVALUATION OF DATA Part 1 Elastic collisions 1. Use the tables below to help with your evaluation of the momentum before and after the collisions of the carts. DATA TABLE I (a) Data Piece of Metal-124.85g The cart- 246.77g Cart 1 Cart 2 Run Mass (kg) Initial velocity (m/s) Final velocity (m/s) Mass (kg) Initial velocity (m/s) Final velocity (m/s) 1 0.5146 0.257 0.23 0.5146 0 0.193 2 0.5146 0.18 0.009 0.5146 0 0.153 3 0.5146 0.247 0.039 0.2648 0 0.262 4 0.5146 0.22 0.027 0.2648 0 0.22 5 0.5146 0.194 0.014 0.2648 0 0.206 6 0.5146 0.24 0.036 0.2648 0 0.246 (b) Calculation of Linear Momentum Before After Ratio Ru n p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/ s) p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/ s) p after p before 1 0.132252 0 0.1322 522 0.011835 8 0.099317 8 0.1111 536 0.8404 66926 2 0.092628 0 0.0926 628 - 0.004631 4 0.078733 8 0.0741 026 0 3 0.127106 2 0 0.0127 1062 0.020069 4 0.069377 6 0.0894 47 0.7037 18623 4 0 0.1132 0.013894 0.056256 0.0721 0.6373

0.113212 12 2 502 01699 5 0.998324 0 0.9983 24 0.007204 4 0.545488 0.0617 532 0.6185 68721 6 0.023504 0 0.0235 04 0.018525 6 0.065140 8 0.0836 664 0.6774 36787 (c) Calculation of Kinetic energy E k , before E k , after 0.016994406 0.00972028 0.00833652 0.00604398 0.015697616 0.00947982 0.1245332 0.00659573 0.009683743 0.00566896 0.01482048 0.00834578 Another approach is to use Logger Pro to help you organize your calculations. 2. How does the total momentum of the system after the collision compare with that before the collision? Do your results agree with your expectations? Explain. For multiple runs, the total momentum after impact to momentum preceding collision ratio changes. Entire momentum after impact should have equaled total momentum before collision. This may contain an inaccuracy. 3. Calculate the total kinetic energy, E k = 1 2 mv 2 , of the system both before and after each of the collisions. How do these quantities compare? The system's start kinetic energy is the total of the initial kinetic energies of both cars, and the system's final kinetic energy is the sum of the final kinetic energies of both cars.

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Part 2 Inelastic collisions Use the tables below to help with your analysis of the momentum before and after the collision. DATA TABLE II (a) Data Cart 1 Cart 2 Run Mass (kg) Initial velocity (m/s) Final velocity (m/s) Mass (kg) Initial velocity (m/s) Final velocity (m/s) 1 0.514 6 0.32 0.145 0.2648 0 0.145 2 0.514 6 0.213 0.107 0.2648 0 0.176 3 0.514 6 0.472 0.293 0.2648 0 0.314 (b) Calculation of Linear Momentum Before After Ratio Ru n p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/ s) p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/s) p after p before 1 0.164672 0 0.1646 72 0.074617 0.038396 0.11301 3 0.68629 1537 2 0.109609 8 0 0.1096 098 0.055062 2 0.046604 8 0.10166 7 0.92753 5677 3 0.242891 2 0 0.2428 912 0.150777 8 0.083147 2 0.23392 5 0.96308 553

1. How does the total momentum of the system after the collision compare to that before the collision? Is the agreement in these inelastic collisions as good as that in the elastic collisions? Try to account for any differences. For multiple runs, the total momentum after impact to momentum before collision ratio changes. The ratios for all runs are less than one, indicating inelastic nature (collision). The ratio in this elastic collision ranges from 0.69 to 0.96. (Certain errors) 2. Calculate the total kinetic energy of the system both before and after each of the collisions. How do these quantities compare? E k , before E k , after 0.02634752 0.000819344 0.01167344 0.00704705 0.03514303 0.035140306 3. We have used “elastic” to describe collisions in which the objects bounce, and “inelastic” to describe collisions in which the objects stick. Based on your comparison of the kinetic energy before and after collisions, provide a more conceptual definition of these descriptors. The kinetic energy loss of a collision can be used to represent the nature of the impact. There is no kinetic energy loss in an elastic collision. In a relatively inelastic impact, the kinetic energy loss is maximal. Part 3 Explosions Use the tables below to help with your analysis of the momentum before and after the collision. DATA TABLE III Cart 1 Cart 2 Run Mass Initial Final Mass Initial Final

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(kg) velocity (m/s) velocity (m/s) (kg) velocity (m/s) velocity (m/s) 1 0.5146 0 -0.431 0.5146 0 0.417 2 0.5146 0 -0.447 0.5146 0 0.434 3 0.5146 0 -0.502 0.5146 0 0.446 Before After Ratio Ru n p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/s) p of cart 1 (kg-m/s) p of cart 2 (kg-m/s) p of system (kg-m/s) % diff 1 0 0 0 -0.2217926 0.214588 2 - 0.007204 4 100 2 0 0 0 -0.2300262 0.223336 4 - 0.006689 8 100 3 0 0 0 -0.2583292 0.229511 6 - 0.028817 8 100 1. How does the total momentum of the system after the explosion compare to that when the carts were stationary? Report any discrepancy as a percentage of the momentum of one of the carts. In an explosion, momentum is preserved. We disregard the gravity force because there is no external force occurring shortly after the explosion in this situation. As a result, the momentum will remain the unchanged after the explosion. 2. Calculate the total kinetic energy of the system both before and after each of the explosions. How do you account for the increase in kinetic energy? Ek, before Ek, after 0 0.09253795 0 0.09987885 0 0.11602172

Source of error. Because of the measurement instruments, this laboratory has a high rate of error, both random and systematic. Because of the unexpected cause of error, we had to move the carts to observe the data in this experiment, and we are not certain if our hand was in the path of the movement sensors, which produced the error, or not. This laboratory measurement apparatus levels to make up the gap between two carts may have some error due to the systematic cause of error. Conclusion. In summary, mobility is maintained in all collisions and is the equal before and after the contact, however there is no loss of energy in a flawlessly collision. In such an inelastic collision, many of the kinetic energy is converted to another kind of energy during the contact. Any major collision between things transforms some kinetic energy to internal energy and other types of energy. We discovered a high level of error in our data as a result of our trial.

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Lab Report Momentum and Collision (Lab 8)

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