Post on 14-Jun-2015
transcript
American EagleFirst Hill
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.
Method 1 (Accel.)
Vertical acceleration graph from vest data (Y-accel. graph)
Acceleration =
-7.1 m/s2
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:
Percent Error: *100
|−7−(−7.1)−7.1 |∗100=1.4
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= Δx/Δt) 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.)
Car Length (shoes)
Gap Length (shoes)
Total Length (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)
Method 2 (Math)
TOTAL TRAIN LENGTHTrial 1- (8.5*.3)(5)+(2*.3)(4)= 15.15mTrial 2- (8.25*.3)(5)+(2*.3)(4)=14.775mTrial 3- (8.5*.3)(5)+(2*.3)(4)= 15.15mVELOCITY AT A (TOP)Trial 1- 15.15/2.49=6.08m/sTrial 2- 14.775/2.43=6.08m/sTrial 3- 15.15/2.51=6.04m/sVELOCITY AT B (BOTTOM)Trial 1- 15.15/.7=21.64m/sTrial 2- 14.775/.65= 22.73m/sTrial 3- 15.15/.81=18.70m/s
ACCELERATION ON FIRST DROPTrial 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
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
Confidence
Percent Error: *100
|−7−(−4.9)−4.9 |∗100=%42.86
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
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 we’d 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
Engineering & Height
Prediction: We estimated the drop to be 50 meters high because it seems to be about that high.
Find height w/ altitude graph (vest data) Measurement at top minus measurement at
bottom to obtain height of coaster track
Method 1 (Engin. & Height)
Method 1 (Altitude Graph)
Height at top= 38mHeight at bottom= -11m (coaster starts above ground level)38-(-11)= 49m 49TOTAL HEIGHT FROM TOP OF FIRST DROP
Method 1 (Math)
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
Confidence
Percent Error: *100
|50−4949 |∗100=%2.04
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
Triangulation Formula: (sinӨ1)(sinӨ2)/(sin(Ө1-Ө2))*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)
Ө1 (degrees)
Ө2 (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
Error AnalysisErrors 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
Confidence
Percent Error: *100
|50−35.8735.87 |∗100=%39.39
We are not confident with our data because not only do our results not support our hypothesis, the percent error is about 40%.
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
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
Use height from engineering/height portion and plug that into GPE formula: GPE= mgΔy 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)
Method 1 (GPE)
Height (m)
Mass (kg)
35.87 52.27
GPE= mgΔyGPE= (52.27)(9.8)(35.87)GPE= 18,374.26 Joules
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 = atV = (-4.90)(3.05)V = -14.95 m/s
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
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)
Method 2 (GPE)
Height (m) Mass (kg)
49 52.27
GPE= mgΔyGPE= (52.27)(9.8)(49)GPE= 24,843.9 Joules
Method 2 (KE)
Velocity (m/s)
Mass (kg)
-23.52 52.27
KE= 1/2mv2
KE= ½(52.27)(-23.52)2
KE= 14,457.6 Joules
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
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
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
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)
Method 1 (Graph)
Y-acceleration=27.5 27.5/9.8=2.81 Fs=2.81Fg
Method 1
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
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
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
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
accelerometer Conduct more trials (even if that means
going on the ride more than 2 times)