PHYS 101 Lab 4 Worksheet v010522(1)

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1 PHYS 101 - Conservation of Momentum Worksheet Group Members : Sam Macris - sm4797 ___________________________ Jenny Yoy – jy584 Freya Aidoo- fea26 Before starting the lab be sure to watch the videos on blackboard. As always, be sure to show all work/plots in order to receive full credit. 1. Data Analysis: In this section, we will go over the various datasets and the parameters associated with each dataset. For both inelastic and elastic collisions, we focus on the time around the collision between the carts! Note: When looking at the velocity of P1 and P2 in the files below, multiply the velocity of P2 by -1. This accounts for the fact that P1 and P2 travel in opposite directions when they collide but only one direction can be positive, and the other direction must be negative (i.e. P1 travels in +𝑥^ while P2 travels in −𝑥^ ). Also, we only want to analyze the first collision that occurs between the carts. 2.1 Elastic Collisions: Begin by investigating how momentum and kinetic energy behave in an elastic collision. Ensure that the carts are aligned such that the magnetic sides are facing each other . You may look at different initial conditions for the collision. Some examples for you to choose from are, but are not limited to: - Cart 2 at rest, both carts have the same mass or different masses (place 250 g on one cart) - Carts move in opposite directions (i.e., towards each other) with same/different mass - Carts move in the same direction with one faster than the other (may be more challenging) 2.1.1 Plotting the Data: To get started, we wish to see the v ( t ) graphs for P1 and P2. Using the motion sensors and the computer output, record the v ( t ) graphs for the motion you chose in 2.1. The v ( t ) data for P1 and P2 should be overlaid in one plot. Overlaying the plot allows us to compare the positions and velocity of each cart. From the v ( t ) plots calculate the average velocity for before and after the collision. We can calculate the average velocity by summing up the velocities over a certain interval of time and dividing them by the number of velocities we added together. Using these calculations, we can determine if momentum and energy are conserved.
2 1. In a few sentences, comment on the collision of carts P1 and P2 and the time that this occurs. The collision was very strong and prominent. Cart 1 was able to push a force that made cart 2 be pushed all the way to the end of the track.
3 Table 2: P1 Data from v ( t ) (Cart 2 at rest, Cart 1 collides, equal mass) Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy 1 0.50 0.214 0 0.107 0 0.0114 0 2 0.50 0.290 0 -0.145 0 0.0210 0 Table 3: P2 Data from v ( t ) Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy 1 0.50 0 0.191 0 0.0955 0 0.00912 2 0.50 0 0.170 0 -0.0850 0 0.00723 Now, we will calculate the change in momentum and energy of the carts. Comment on how these values compare. Table 4: P1 Change in momentum and energy Trial Initial Momentum Final Momentum Change in momentum Initial Kinetic Energy Final Kinetic energy Change in Kinetic Energy 1 0.107 0 -0.107 0.0114 0 -0.0114 2 -0.145 0 0.145 0.0210 0 -0.0210 Table 5: P2 Change in momentum and energy Trial Initial Momentum Final Momentum Change in momentum Initial Kinetic Energy Final Kinetic energy Change in Kinetic Energy 1 0 0.0955 0.0955 0 0.00912 -0.00912 2 0 -0.0850 -0.0850 0 0.00723 -0.00723 2. For trial 1: compare the change in momentum that cart 1 and cart 2 experienced, what do you notice about the change in momentum? What do you notice about the sum of the change in momenta? What would you expect the change in momentum to be for the system? Repeat for trial 2. Is this what you would expect from an ELASTIC collision? 3. For trial 1 and trial 2, comment on the change in kinetic energy before and after the collision (make sure to investigate the TOTAL energy before/after). Is this what you would expect for an ELASTIC collision?
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4 2.2 Inelastic Collisions: Turn the carts around to make their non-magnetic sides face each other. Follow the same instructions as section 2.1 and 2.1.1 to fill in the plots below. Be sure to include all plots, fits and work. 4. In a few sentences, comment on the collision of carts P1 and P2 and the time that this occurs. The collision was very slow, and the carts seemed to stay attached to each other when they came into contact. (Cart 1 into Cart 2 at rest. Equal mass. Inelastic) Table 6: P1 Data from v ( t ) Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy 1 0.500 0.375 0.190 0.188 0.0950 0.0352
5 2 0.500 0.349 0.154 0.175 Table 7: P2 Data from v ( t ) Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy 1 0.500 0 0.190 2 0.500 0 0.154 3.1 Analysis and Conclusion Now, we will calculate the change in momentum and energy of the carts. Comment on how these values compare. Table 8: P1 Momentum and Energy Trial Initial Momentum Final Momentum Change in momentum Initial Kinetic Energy Final Kinetic energy Change in Kinetic Energy 1 2 Table 9: P2 Momentum and Energy Trial Initial Momentum Final Momentum Change in momentum Initial Kinetic Energy Final Kinetic energy Change in Kinetic Energy 1 2
6 5. For trial 1: compare the change in momentum that cart 1 and cart 2 experienced, what do you notice about the change in momenta? What do you notice about the sum of the change in momenta? What would you expect the change in momentum to be for the system? Repeat for trial 2. Is this what you would expect from an INELASTIC collision? 6. For trial 1 and trial 2, comment on the change in kinetic energy before and after the collision (make sure to investigate the TOTAL energy before/after). Is this what you would expect for an INELASTIC collision? 4. Analysis Questions: 1. What experimental evidence do you have showing that momentum is conserved in inelastic and elastic collisions? 2. How does your data support the conservation of kinetic energy in elastic collisions? 3. How does your data support the non-conservation of kinetic energy in inelastic collisions? 4. Why is kinetic energy not conserved in inelastic collisions? Where is the energy lost? 5. In what situations is momentum not conserved? Briefly discuss one example.
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