Lab 4: Conservation of Momentum ( The following is a modified version of the PASCO Conservation of Momentum lab, modified for PHYS 101 ) Group Members : Julia Louie Anthony Moore Sotero Casiano Luca Sirman 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. 2. Data Analysis: In this section, we will go over the various datasets and the parameters associated with each dataset. In order to get accurate results, multiple trials were run to collect data for each dataset. The datasets are available as text files on blackboard learn ( Important Note: when importing into excel, be sure to import the files as “tab delimited” or the column names will not correspond to the correct data). For both inelastic and elastic collision, we only want to look at the first collision between the carts! When looking 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 while P2 travels in ). Also, we only want to analyze the first collision that occurs between the carts. 2.1 Elastic Collisions: In each file, there will be data for “P1” and “P2”, this refers to cart 1 and cart 2. The combined mass of the cart and metal bars are given in the tables below – this indicates the total mass of P1 or P2. 2.1.1 Plotting the Data: To get started, we wish to v(t) for P1 and P2. The v(t) data for P1 and P2 should be overlaid in one plot. Overlaying the plots 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 by the number of velocities we added together. Using these calculations, we can determine if momentum and energy are conserved. Average Velocity of P1 before: 0.1229 m/s Average Velocity of P2 after: -0.002820 m/s Average Velocity of P2 before: 0.2011 m/s Average Velocity of P2 after:-0.2307 m/s

Average velocity of P1 before: 0.256 m/s P2 Before: 0.2097 m/s P1 After: 0.01778 m/s P2 After: -0.0183 m/s

Average Velocity of P1 Before: .126 m/s P2 Before: .161 m/s P1 After: .0077 m/s P2 After: -.0088 m/s 2.1.2 Dataset 1: For dataset 1, we have 3 files labeled “ Dataset1_Trial1.csv, Dataset1_Trial 2.csv, Dataset1_Trial3.csv ”. Using data from these files, file in the data below (include your plots as well). Be sure to include units where they are not given. Note v(t) refers to velocity vs. time. Remember to show all work - if your calculations are done in an excel sheet, the excel sheet should also be submitted. From “Dataset1_Trial1.csv”, overlay the position vs. time graphs of P1 and P2. In a few sentences, comment on the collision of carts P1 and P2 and the time that this occurs at. The cars collide at roughly 0.24 seconds. Table 2: P1 Data from v(t) -- USED MOMENTUM AND KINETIC ENERGY EQUATIONS Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy

Plot Average Initial Momentum Average Final Momentum Initial Momentum Standard Error Final Momentum Standard Error Average Initial Kinetic Energy Average Final Kinetic energy Initial Kinetic Energy Standard Error Final Kinetic Energy Standard Error v(t) 0.45 kg * m/s -0.585 kg * m/s 3.94% 2.48% 0.0730 J 0.1159 J 0.992% 1.75% Table 6: P2 Averages and Error Plot Average Initial Momentum Average Final Momentum Initial Momentum Standard Error Final Momentum Standard Error Average Initial Kinetic Energy Average Final Kinetic energy Initial Kinetic Energy Standard Error Final Kinetic Energy Standard Error v(t) -0.007k g * m/s 0.5 kg * m/s .54432 % 7.3918 % 0 J 0.1323 J 0.00544 % 3.21% 2.2 Inelastic Collisions: 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.

Average Velocity of P1 before

Trial: Mass (kg) Initial Velocity Final Velocity Initial Momentum Final Momentum Initial Kinetic Energy Final Kinetic Energy 1 3.5 - .19 m/s .02 m/s -.665 kg * m/s .07 kg * m/s .063 J .0007 J 2 3.5 -.2 m/s .03 m/s -.7 kg * m/s .105 kg * m/s .07J .00158 J 3.1 Analysis and Conclusion From the v(t) plots, calculate and compare momentum and energy by calculating the average momentum and energy for v(t). Calculate the standard error of these measurements. Comment on how these values compare. For error we used: Standard deviation / sqrt(N) * 100 where N is the number of trials and standard deviation is the sqrt(the sum of the difference between all our experimental values and average squared, divided by N). Table 11: P1 Averages and Error Plot Average Initial Momentum Average Final Momentum Initial Momentum Standard Error Final Momentum Standard Error Average Initial Kinetic Energy Average Final Kinetic energy Initial Kinetic Energy Standard Error Final Kinetic Energy Standard Error

v(t) .84 kg * m/s -.07 kg * m/s 5.25% 3.5% .101 J . 000888 J 4.62% 0.0411 % Table 12: P2 Averages and Error Plot Average Initial Momentum Average Final Momentum Initial Momentum Standard Error Final Momentum Standard Error Average Initial Kinetic Energy Average Final Kinetic energy Initial Kinetic Energy Standard Error Final Kinetic Energy Standard Error v(t) -.6825 kg * m/s .0875 kg * m/s 1.75% 1.75% .0665 J .00114 J 0.202% 0.0440% 3. Analysis Questions: 1. What experimental evidence do you have showing that momentum is conserved in inelastic and elastic collisions? We know that momentum is conserved because the sum of the momentum before the collision is roughly the same as the sum of the momentum after the collision for the system. This is the case with both datasets, meaning this occurs in both elastic and inelastic collisions. 2. How does your data support the conservation of kinetic energy in elastic collisions?