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- 1. American Eagle First Hill

2. Motion (Acceleration) Prediction: Acceleration = -7 m/s2 at bottom of hill b/c while the coaster is close to free fall, it does not go straight down so its acceleration would be smaller than - 9.8m/s2. 3. Method 1 (Accel.) Vertical acceleration graph from vest data (Y-accel. graph) Acceleration = -7.1 m/s2 4. Error Analysis/ Confidence We could have misread/misinterpreted the results on data studio Person who collected data could have shifted, thereby affecting the results We are confident in our data because aside from the results supporting our hypothesis, the vest data seems to be fairly consistent without any major bumps Errors that could have occurred include: 5. Measure cars and distance between cars in shoe lengths (shoe = .3m) Time how long it takes for the cars to pass a point on bottom and top of first drop Find velocity at top and bottom (V= x/t) Time how long it takes to get from top to bottom and divide difference in velocities by time (from top to bottom) to get acceleration. Method 2 (Accel.) 6. Car Lengt h (shoes ) Gap Lengt h (shoes ) Total Lengt h (m) Time to pass A (sec) Time to pass B (sec) Time from A to B (sec) Vel. At A (m/s) Vel. At B (m/s) Accel. (m/s2) Trial 1 8.5 2 15.15 2.49 .7 3.05 6.08 21.64 -5.101 Trial 2 8.25 2 14.775 2.43 .65 3.11 6.08 22.73 -5.354 Trial 3 8.5 2 15.15 2.51 .81 2.98 6.04 18.70 -4.248 Table (Method 2) 7. Method 2 (Math) TOTAL TRAIN LENGTH Trial 1- (8.5*.3)(5)+(2*.3)(4)= 15.15m Trial 2- (8.25*.3)(5)+(2*.3)(4)=14.775m Trial 3- (8.5*.3)(5)+(2*.3)(4)= 15.15m VELOCITY AT A (TOP) Trial 1- 15.15/2.49=6.08m/s Trial 2- 14.775/2.43=6.08m/s Trial 3- 15.15/2.51=6.04m/s VELOCITY AT B (BOTTOM) Trial 1- 15.15/.7=21.64m/s Trial 2- 14.775/.65= 22.73m/s Trial 3- 15.15/.81=18.70m/s ACCELERATION ON FIRST DROP Trial 1- (6.08-21.64)/3.05= -5.101m/s2 Trial 2- (6.08-22.73)/3.11= -5.354m/s2 Trial 3- (6.04-18.70)/2.98= - 4.248m/s2 Avrg. Accel. = -4.90 m/s2 Avrg. Time = 3.05 s 8. Error Analysis Errors that may have occurred: Time may have been measured incorrectly due to lack of perfect location for spotting first drop and lack fast reaction time-> time may have been a few seconds off Since a different shoe was used during actual experimentation, the total train length may have been affected, therefore affecting the velocity and acceleration The foot length may have not been the exact measurement 9. Confidence We are not confident with the data for this method because not only does it refute our hypothesis, the percent error is nearly %40 off. Since each method provided different results, we are not very confident in our data 10. Conclusion We hypothesized that the acceleration at the bottom of the hill would be -7 m/s2 While one of our methods resulted in an acceleration of -7.1 m/s2, our second method resulted in an acceleration of -4.9 m/s2, and therefore , our data does not support our hypothesis In order to improve our data, factors wed take in to consideration are: Find a location in which we can easily spot and time the first drop Use the same shoe during the prelab data collection and during the actual experimentation so no other factors are affected More trials could have been conducted 11. Engineering & Height Prediction: We estimated the drop to be 50 meters high because it seems to be about that high. 12. Find height w/ altitude graph (vest data) Measurement at top minus measurement at bottom to obtain height of coaster track Method 1 (Engin. & Height) 13. Method 1 (Altitude Graph) 14. Height at top= 38m Height at bottom= -11m (coaster starts above ground level) 38-(-11)= 49m 49TOTAL HEIGHT FROM TOP OF FIRST DROP Method 1 (Math) 15. Error Analysis/ Confidence Errors that could have occurred include: We could have misread/misinterpreted the graph, thereby affecting our results The person wearing the data vest could have not been sitting in an upright position and may have shifted while on the ride, therefore affecting the results 16. Confidence We are confident in our data for this method because not only does our results support our hypothesis, but it is difficult to get incorrect data while using the data vest 17. Triangulation Formula: (sin1)(sin2)/(sin(1-2))*B+ eye height *Find angles w/ horizontal accelerometer and baseline of 20m using 5m string to measure *Eye height= 1.47 (meter stick measurements) Method 2 (Engin. & Height) 18. 1 (degrees) 2 (degrees) Baseline (m) Eye Height (m) Height (m) Trial 1 25 20 20 1.47 34.64 Trial 2 23 20 20 1.47 52.539 Trial 3 24 17 20 1.47 20.95 Method 2 Triang. Chart Average Height: 35.87 m 19. Error Analysis Errors that could have occurred include: When we used the horizontal accelerometer, we may have not have been looking at the top of the drop While measuring the baseline, other students in line may have gotten in the way, and therefore our baseline may not have been exactly 20 m in a straight line When measuring our baseline, we may have not held the string to its fullest length, and therefore our baseline may have been less than 20 m While measuring the 1st and 2nd angle, we may have not looked at the exact point The measurements using the horizontal accelerometer may have been slightly off because not only did it measure every 5 degrees, the marbles occasionally got stuck in the tube 20. Confidence We are not confident with our data because not only do our results not support our hypothesis, the percent error is about 40%. 21. Conclusion We hypothesized that the height at the top of the first drop would be 50 m Our data does not support our hypothesis because although one of our methods resulted in 49 m, the second method resulted in 35.87 m In order to improve our results, factors we would consider include: Possibly conduct multiple trials with different eye heights as opposed to using one person for all three trials Measure the baseline and angles more carefully 22. Prediction: GPE at top of hill = KE at bottom because energy is conserved. Energy (GPE~KE) g-field GPE GPE Car Halfway Down Top KE g-field Car KE Bottom 23. Use height from engineering/height portion and plug that into GPE formula: GPE= mgy to find GPE at top of hill Use velocity value obtained from motion portion and mass of group member to find KE at bottom of hill using KE equation: KE= 1/2mv2 Method 1 (Energy) 24. Method 1 (GPE) Height (m) Mass (kg) 35.87 52.27 GPE= mgy GPE= (52.27)(9.8)(35.87) GPE= 18,374.26 Joules 25. Method 1 (KE) Velocity (m/s) Mass (kg) -14.95 52.27 kg KE= 1/2mv2 KE= 1/2(52.27)(-14.95)2 KE= 5,841.24 Joules V = at V = (-4.90)(3.05) V = -14.95 m/s 26. Error Analysis/ Confidence Errors that could have occurred include: The velocity and height that we found in the previous slides may have been incorrect, therefore affecting our results We are not confident in our data for this method because the GPE at the top of the drop is not at all similar to the KE at the bottom 27. Use the GPE and KE equations to find out GPE at top of hill and KE at bottom of hill Receive height value from vest data Receive velocity from area under acceleration graph from vest data Method 2 (Energy) 28. Method 2 (GPE) Height (m) Mass (kg) 49 52.27 GPE= mgy GPE= (52.27)(9.8)(49) GPE= 24,843.9 Joules 29. Method 2 (KE) Velocity (m/s) Mass (kg) -23.52 52.27 KE= 1/2mv2 KE= (52.27)(-23.52)2 KE= 14,457.6 Joules 30. Error Analysis/ Confidence Errors that could have occurred include: o The vest data we used could have been incorrect due to the fact the rider who collected this data may have shifted, therefore affecting our height and velocity o We could have misread the vest data, thereby affecting our results We are not confident in our data for this method because the GPE at the top of the drop is not at all similar to the KE at the bottom 31. Conclusion We hypothesized that the KE at the top of the hill would be equal to the GPE at the bottom of the hill Our data does not support our hypothesis because for each method we used, not one posed similar results for the KE at the top and the GPE at the bottom In order to improve the results of our experiment, factors we could consider include: Conduct more trials Measure angles and baseline more carefully-> could have affected the height we used Time the train more carefully to get a more accurate velocity 32. Forces Prediction: Bottom of hill/drop Fs will be about 2.5 times Fg because it takes a lot of force to change the motion of the roller coaster train and we estimate it to be about 2.5Fg. Y X Fs Fg 33. Use data vest Look at y-directional acceleration graph and find value at bottom of hill Divide by 9.8 to get the factor of Fg, because mass is constant, it can be ignored. Method 1 (Forces) 34. Method 1 (Graph) 35. Y-acceleration=27.5 27.5/9.8=2.81 Fs=2.81Fg Method 1 36. Error Analysis/ Confidence Errors that could have occurred include: The vest data could have been incorrect We could have misread the vest data We are not confident in our hypothesis b/c vest data is much more reliable than our hypothesis 37. Method 2 (F0rces) Use vertical accelerometer to get value for y-acceleration which is already in terms of Fg. Accelerometer Reading Trial 1 2.75 Fg Trial 2 2 Fg 38. Error Analysis/ Confidence We are relatively confident in our data because when we average all of our results, we end up with an average of Fs=2.52Fg, which is very close to our hypothesis of 2.5Fg. Some errors that could have occurred are: Difficulty to read accelerometer while on roller coaster. Bouncing spring Not enough trials to get a good average 39. Conclusion We hypothesized that the Fs at the bottom of the hill/ drop will be about 2.5 times Fg Our data does not support If we were to improve upon our data, factors we would take into consideration include: More carefully read the vertical accel