ranya rami ConservationOfMomentum (2)

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Arizona State University, Tempe *

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360

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Mechanical Engineering

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Oct 30, 2023

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1 PHY 113 – CONSERVATION OF MOMENTUM WORKSHEET Name: Partners: TA: SLN: Objective: Provide one or two sentences explaining the main objectives of the lab. to investigate simple elastic and inelastic collisions in one dimension in order to study the laws of conservation of momentum and conservation of energy

2 Predictions for Collisions: For the 4 collisions, the first two were inelastic and the last two were elastic. For all the collisions, sketch a diagram pre and post collision. Show the directions of the initial and final velocities of both carts and identify the masses, ! " and ! # , of each cart. Case 1: Inelastic $ % = $ ’ Case 2: Inelastic $ % ≠ $ ’ Case 3: Elastic $ % = $ ’ Case 4: Elastic $ % ≠ $ ’

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3 Experimental Data: Collision $ % $ ’ ) %* ) ’* ) %+ ) ’+ 1 2 3 4 Data Analysis: Momentum: Provide formulas and calculations for the following: initial momentums for carts 1 and 2 ( , "- and , #- ), final momentums ( , ". and , #. ), total momentum of the system before the collision ( , - ), total momentum of the system after the collision ( , . ), and the relative percent change of the total momentum for all the collisions using the exact data entered in your data table. Kinetic Energy: Below, provide formulas and calculations for the following: initial kinetic energies for carts 1 and 2 ( / "- and / #- ), final kinetic energies ( / ". and / #. ), total kinetic energy of the system before the collision ( / . ), total kinetic energy of the system after the collision ( / . ), and the relative percent change in kinetic energy using the exact data entered in your data table.

4 Results: Fill in the table below with the final results of your calculations in the data analysis section. Notice the units given are in SI. Collision 0 * [23 ∙ $ 5 ] 0 + [23 ∙ $ 5 ] 70 0 * ∙ %88[%] : * [;] : + [;] 7< : * ∙ %88[%] 1 2 3 4 Discussion and Conclusion: Divide your discussion into paragraphs. 1) Rephrase the objective in your own words. ( limit 2 sentences ) 2) Give a brief explanation of conservation of momentum. (limit 5 sentences) 3) Briefly describe how the experiment tests the conservation of momentum. ( limit 3- 5 sentences ) 4) Summarize the major results of the lab: Do the results support the conservation of momentum? Based on your data is kinetic energy conserved? If it is not always conserved, when is it? ( limit 5 sentences ) 5) What are the major sources of error in this lab experiment? Discuss all possible sources of error, statistical or systematic, and say which type they are. ( limit 3- 5 sentences ) 6) Conclude your discussion stating whether the objective of the lab has been achieved or not. ( limit 2- 3 sentences ) '

Objective The purpose of this experiment was to examine the conservation of energy and momentum in a system of two carts. To ascertain this, collisions between these carts with varying amounts of mass on each of them were conducted in both elastic and inelastic conditions. Despite the presence of friction in the experiment, a permissible margin of error allowed for a conclusion to be reached regarding whether momentum and kinetic energy were preserved. Two rolling carts on a track were used in the experiment, and they passed through two photogates that tracked their movement. By taking the slope of the Position vs. Time graph in the Data gathering interface and multiplying it by the position, the velocity was computed. The carts locked together during the inelastic collisions, changing the system's mass and velocity, and preventing kinetic energy from being conserved. Considering the majority of the data was precise and correct, it can be said that, when friction is taken into account, the Theory of Conservation of Momentum is valid. The Theory of Conservation of Energy also holds in the presence of inelastic collisions, as kinetic energy transforms into various types. Procedure: Two photogates, a track, two carts with magnets on one side and velcro on the other, data collection, a computer, and weights were the tools used in this experiment. On the desk it was mounted on, the track was leveled. Over the track, the photogates were placed, and they were connected to the computer-connected data collection interface. The two carts were positioned in the track's grooves. To set up the photogates, the experiment file was opened in the data collection interface. One of the carts was slid straight through each of the two photogates to calibrate the photogates. After that, the data collection interface's inputs were switched around, and the cart was pushed between the two photogates on the left. This was carried out slowly. Both a fast and moderate pace were repeated twice. To ascertain whether the rates were the same through each photogate, the velocity obtained from the photogates was employed in the v2/v1 formula. Because of friction, the cart moved through the second photogates slower than it did the first, as was to be expected. The carts had to have the proper amount of items before data could be collected. By directing one of the carts toward the other and causing them to collide on the track, data was gathered. By measuring how long each strip on top of the carts blocked the sensor, the photogates were able to determine their location. The data collection interface was used to graph the Position vs. Time graph. The slope of the Position vs. Time graph was used to calculate the carts' velocity. The photogates captured the positional shift. Position vs. Time graph based on data. To get the needed quantity, the slope of the Position vs. Time graph was calculated. The weight of each cart varied from part to part, among parts 2-1 and 2 and parts 2-3 and 4, the collision nature (elastic or inelastic) also varied. Discussion: The ratio of the speeds via both photogates coming from the right and left was noted for part 1. Because of friction, it is not unexpected that this velocity was larger than 1. In the absence of friction, the carts would simultaneously pass through both photogates, resulting in a ratio of 1. The ratio demonstrates how much the carts' speeds varied throughout the course of the duration that it took to move between the two photogates. The ratio of the carts' speeds between each photogate was more closely matched to one as they were pushed through the photogates more quickly. This is because friction was less noticeable at a faster speed over such a small distance. Since the cart would have traveled through both photogates at the same speed without being slowed down by friction (or track tilt), the theoretical value of the ratio of the velocities through the two photogates should equal 1. The relative percent of change for collision 1: 41.5%, collision 2: 88.6%, collision 3: 176% and collision 4: 21.1%. The lab could be improved by eliminating friction by tilting the track at the proper angle. The friction could essentially be reduced, enabling more precise results concerning speed, if the track could be tilted at an angle (ɵ) to make the cos(ɵ)*mass*gravity equals the frictional impact of kinetic friction. For part 2, the elastic collisions' relative velocity (Equation 6) was determined. When the masses were equal, these relative velocities were closest to -1. The ratio would always be -1 if there was no friction at all. In collisions between carts of different masses, the more hefty cart was subject to friction considerably more quickly and slowed down considerably more than when the weights were equal (and the carts were moving at the same speed). Momentum and kinetic energy changed fractionally for each trial, as was to be expected. However, the change in kinetic energy was always greater than the shift in momentum. As opposed to kinetic energy, which has velocity squared, which causes the overall change to get larger at a faster rate, momentum's equation is mass times velocity. The range of the change was -6% to 367%. The change in kinetic energy had to be under 20% to evaluate whether or not it

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was maintained. Friction contributed a small amount of error to the computation of these figures. The disparity caused by friction was visible when comparing the anticipated outcome of the ratio between the carts' final velocities and the actual value. The numbers' range demonstrates how friction affects the cart system. The ratio is lower at slower speeds because the force of friction has a greater impact on the carts. Both elastic and inelastic collisions preserve momentum, but only elastic collisions preserve kinetic energy. Only an external or net force operating on the system might prevent momentum from being maintained. Without any uncertainty, the lab's goal was accomplished. Except for a few statistical outliers, the four collisions were consistent with the theory. fractional shifts in kinetic energy and momentum. Momentum is conserved in every collision, while kinetic energy is only conserved in elastic collisions.