Lab 8 Condensed Completed Worksheet

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Dec 6, 2023

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Nick Smith PHY 202 Lab #8: Collisions Data and Results Sheet: You can record the momentum from the simulation instead of calculating it except for your sample calculation. Be sure to include the missing units in the tables. You may use your own tabulated results sheet if you prefer. Data: Trial 1: (e = 100%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 0.50 1.00 -1.25 m/s 2 1.50 -0.50 0.25 m/s Trial 2: (e = 100%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.00 2.00 -0.57 m/s 2 1.50 -1.00 2.43 m/s Trial 3: (e = 100%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.50 2.00 .50 m/s 2 1.50 0 2.5 m/s Trial 4: (e = 75%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.00 2.00 -0.25 m/s 2 1.50 -1.00 2.00 m/s Trial 5: (e = 50%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.00 2.00 .07 m/s 2 1.50 -1.00 1.57 m/s

Trial 6: (e = 25%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.00 2.00 .39 m/s 2 1.50 -1.00 1.14 m/s Trial 7: (e = 0%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 2.00 2.00 .71 m/s 2 1.50 -1.00 .71 m/s Trial 8: (e = 0%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 3.00 2.00 1.6 m/s 2 2.00 1.00 1.6 m/s Tabulated Results: “ Applied to a collision, the total momentum of the system before the collision is equal to the total momentum of the system after the collision. ” Trial 1: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 0.50 kg m/s 0.50 kg m/s 0.44J 0.44J 2 -0.75 kg m/s -0.75 kg m/s 0.44J 0.44J system -0.25 kg m/s -0.25 kg m/s 0% 0.88J 0.88J 0% Trial 2: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 4 kg m/s 4 kg m/s 4.75J 4.741 2 -1.50 kg m/s -1.50 kg m/s 4.75J 4.741 system 2.5 kg m/s 2.5 kg m/s 2.84% 9.5J 9.482J 0.18%

Trial 3: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 5 kg m/s 5 kg m/s 5J 5J 2 0 kg m/s 0 kg m/s 5J 5J system 5 kg m/s 5 kg m/s 0 % 10J 10J 0% Trial 4 : Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 4 kg m/s 4 kg m/s 4.75J 3.063J 2 -1.50 kg m/s -1.50 kg m/s 4.75J 3.063J system 2.5 kg m/s 2.5 kg m/s 0% 9.5J 6.126J 35.5% Trial 5: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 4 kg m/s 4 kg m/s 4.75J 1.86J 2 -1.50 kg m/s -1.50 kg m/s 4.75J 1.86J system 2.5 kg m/s 2.5 kg m/s 0% 9.5J 3.72J 60.9% Trial 6: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 4 kg m/s 4 kg m/s 4.73J 1.13J 2 -1.50 kg m/s -1.50 kg m/s 4.73J 1.13J system 2.5 kg m/s 2.5 kg m/s 0% 9.46J 2.26J 76.17% Trial 7: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 4 kg m/s 4 kg m/s 4.75J 0.89J 2 -1.50 kg m/s -1.50 kg m/s 4.75J 0.89J system 2.5 kg m/s 2.5 kg m/s 0% 9.5J 1.78J 81.2%

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Trial 8: Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 6 kg m/s 6 kg m/s 7J 6.4J 2 2 kg m/s 2 kg m/s 7J 6.4J system 8 kg m/s 8 kg m/s 0% 14J 12.8J 8.57% Sample Calculation : (e = 100%) Cart Mass (kg) Velocity before collision (m/s) Velocity after collision 1 1.25 2.00 -2.36 m/s 2 1.50 -2.00 1.64 m/s Sample Calculation : Cart or System p before p after % difference (p ) KE before KE after % change (KE) 1 2.5 kg m/s 2.5 kg m/s 5.49J 5.49J 2 -3 kg m/s -3 kg m/s 5.49J 5.49J system -0.5 kg m/s -0.5 kg m/s 0% 10.98J 10.98J 0% Coefficient of Restitution: e ¿ v 2 f − v 1 f v 1 i − v 2 i Trial Calculated e 0 ( sample ) 1 1 1 2 1 3 1 4 0.75 5 0.50 6 0.25 7 0 1) Sample Calculation – 1.64-(-2.36) / 2-(-2) = 4/4 = 1 2) 0.25-(-1.25) / 1-(-0.5) = 1.5/1.5 = 1 3) 2.43-(-0.57) / 2-(-1) = 3/3 = 1 4) 2.5-(0.50) / 2-(0) = 2/2 = 1 5) 2-(-0.25) / -1-(2) = 2.25/3 = 0.75 6) 1.57-(0.07) / 2-(-1) = 1.5/3 = 0.50 7) 1.14-(0.39) / 2-(-1) = 0.75/3 = 0.25 8) 0.71-(0.71) / 2-(-1) = 0/3 = 0

Questions: 1. Was Conservation of Momentum verified in this experiment? Explain, based on your results. Yes, conservation of momentum was verified in this experiment. In both elastic and inelastic collisions we can see consistently that pbefore = pafter excluding experimental error. 2. Did the KE change in ways that were expected? Explain, based on your results. Kinetic energy did change in ways that were expected, as we see the mass and speed change in each trial whether raised or lowered, KE is directly proportional to the mass and velocity at which the object is moving up to the point of collision. 3. Did the coefficients of restitution all within the expected ranges? Explain, based on your results. They did. As we see the ratio of speed at which the two objects separated after the collision to the speed in which they were approaching prior to colliding. We know perfectly elastic collisions have a coefficient of restitution of 1 and perfectly inelastic collisions have a coefficient of restitution of 0.

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