ppt example great america project

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American Eagle First Hill

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Page 1: Ppt example great america project

American EagleFirst Hill

Page 2: Ppt example great america project

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.

Page 3: Ppt example great america project

Method 1 (Accel.)

Vertical acceleration graph from vest data (Y-accel. graph)

Acceleration =

-7.1 m/s2

Page 4: Ppt example great america project

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

Page 5: Ppt example great america project

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.)

Page 6: Ppt example great america project

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)

Page 7: Ppt example great america project

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

Page 8: Ppt example great america project

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

Page 9: Ppt example great america project

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

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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

Page 11: Ppt example great america project

Engineering & Height

Prediction: We estimated the drop to be 50 meters high because it seems to be about that high.

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Find height w/ altitude graph (vest data) Measurement at top minus measurement at

bottom to obtain height of coaster track

Method 1 (Engin. & Height)

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Method 1 (Altitude Graph)

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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)

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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

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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

Page 17: Ppt example great america project

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)

Page 18: Ppt example great america project

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

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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

Page 20: Ppt example great america project

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%.

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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

Page 22: Ppt example great america project

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

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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)

Page 24: Ppt example great america project

Method 1 (GPE)

Height (m)

Mass (kg)

35.87 52.27

GPE= mgΔyGPE= (52.27)(9.8)(35.87)GPE= 18,374.26 Joules

Page 25: Ppt example great america project

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

Page 26: Ppt example great america project

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

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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)

Page 28: Ppt example great america project

Method 2 (GPE)

Height (m) Mass (kg)

49 52.27

GPE= mgΔyGPE= (52.27)(9.8)(49)GPE= 24,843.9 Joules

Page 29: Ppt example great america project

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

Page 30: Ppt example great america project

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

Page 31: Ppt example great america project

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

Page 32: Ppt example great america project

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

Page 33: Ppt example great america project

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)

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Method 1 (Graph)

Page 35: Ppt example great america project

Y-acceleration=27.5 27.5/9.8=2.81 Fs=2.81Fg

Method 1

Page 36: Ppt example great america project

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

Page 37: Ppt example great america project

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

Page 38: Ppt example great america project

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

Page 39: Ppt example great america project

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)