Roller+Coaster+Project

=**Six Flags Great Adventure Assignment**= By: Garrett Almeida and Hella Talas

ACTIVITY A: The First Drop of a Roller Coaster

Name of roller coaster ride: **"El Toro"**

1) Estimate distances and angles and 2) Measure time

3) Diagrams

FBD of Car on Way Up First Hill:



FBD of Car on Way Down First Hill:



FBD of Car at Bottom of First Hill:



FBD of Mass on String on Way Up:

FBD of Mass on String on Way Down: FBD of Mass on String at Bottom: c. Labeled sketch of relevant portion of the roller coaster (top and side views) Side View:

Top View:

d. Take a clear side view picture Side View of Drop:

Side View of Entire Coaster:

e. Take a short video of the relevant segment for future reference media type="file" key="Movie on 2012-05-28 at 20.25.mov" width="300" height="300"

4) Graphs a. Create d vs. t, v vs. t and a vs. t graph for the motion this segment of the ride.

b. Create a thrill vs. acceleration graph for this segment of the ride. 5) Evaluate a. Safety: What features were in place? "El Toro" has a number of safety features. Firstly, there are height restrictions. You must be at least forty eight inches tall in order to ride. In addition, there was a seat belt and a bar restraining the rider. This would prevent him from being tossed around. There are also emergency brakes in the event of a necessary stop.

b. Describe the weight sensations on the way up, on the way down, and at the bottom of the first hill: did you feel lighter, heavier, or normal? At the top I felt lightest. As we went down, I felt as though I was getting progressively heavier. The weight sensation at the bottom of the hill was when I felt the heaviest.

c. Describe the excitement level: on the way up, on the way down, and at the bottom of the first hill. On the way up, there was not much excitement, just anxiety. On the way down the excitement level kept on building. At the bottom, the excitement level was the highest because one experiences the most g's.

d. Describe the thrill factors that may contribute to those feelings (besides the #g’s) The slow climb started the thrill factor. It really began to kick in when we traveled down the hill and the wind traveled against our faces. The faster we went the more thrill I experienced. Also, the fact that we sat in the first row contributed to a more thrilling experience.

1) Calculate Experimental Values a. Speed at bottom of the first hill b. Acceleration down the first hill c. Power needed to get up the hill 2) Calculate Theoretical Values a. Speed at bottom of the first hill b. Acceleration down the first hill c. Power needed to get up the hill 3) Evaluate Accuracy of the 3 calculations above. Percent Error Calculations Velocity This calculation was very accurate as the percent error was just 1.33%. Generally, anything below 10% is considered accurate.

Acceleration This calculation was wildly off. With 33% error it is fair to say that this is not accurate.

Power As this value is still over 10%, it is also considered to be not accurate. The calculations for acceleration and power are not very accurate, however that of speed is very, very close.

4) Evaluate Safety a. Calculate #g’s on the way down the hill and at the bottom of the hill b. Were #g’s within safe limits? The g's were within safe limits. The value we got, .51, is well under 3 and 4 g's. It is therefore safe for a human being.

c. Was there correlation between #g’s and excitement level? Explain, providing evidence. Yes there was. This is because the excitement level was at its highest at the bottom of the hill and that is where the most g's are, .61. The further down the hill, the more g's and more excitement.

5) Thinking about Physics a) Explain the behavior of the mass on the string. Did the FBD of the car correlate to that of the mass? Why or why not? No they did not. They both have weight acting on them however the mass has tension puling at it in a horizontal direction and the cart has normal force acting on it in the vertical direction.

b) Did the #g’s correlate to the sensation of weight? Yes, the g's correlated to the sensation to weight. The more the g's the heavier I felt. This is why I felt as though I was getting heavier as I went down the hill.

c) Discuss the graphs that you created and why they curve the way that they do. __D vs. T__: The car was moving at a constant speed so the diagonal line symbolizes. Then the speed increases at a certain rate going down the hill 9not constant) and that is why we see an increasing half of a parabola. __V vs. T__: The cart went up the hill at the same positive speed through out and this is symbolized by the straight line above the x axis. Then the velocity got progressively higher as it went down the hill; this is symbolized by the diagonal line. __A vs. T:__ The cart did not have an acceleration as it maintained a constant speed going up the hill however it maintained a positive, steady acceleration going down the hill. This is drawn in the graph. __Thrill vs. Acceleration__: Going up the hill, there was little thrill but it increased as anxiety settled in. The thrill went way up as the cart continued down the hill. There are symbolized by progressively positive diagonal lines, both of different slopes.

ACTIVITY B: A Vertical Loop of a Roller Coaster

Name of roller coaster ride: **"Green Lantern"**

PART A: At the park: 1) Estimate distances and angles and 2) Measure time

3) Diagrams a. FBD of car or rider at top position b. FBD of mass on a string at top position

c. Labeled sketch of roller coaster (top and side views) Side- Top-

d. Take a clear side view picture

e. Take a short video of the relevant segment media type="file" key="Movie on 2012-05-28 at 20.31

4) Graphs a. Create v vs. t, Fc vs. t and a vs. t graph for the motion this segment of the ride. b. Create a thrill vs. acceleration graph for this segment of the ride.

5) Evaluate a. Describe the safety features on this coaster. There is an emergency brake on this ride. Also, there is a height restriction of fifty four inches. Although this ride does not have seats, it restrains you with a thick metal bar.

b. Describe the excitement level that you felt at the top, side and bottom of the loop. I had the most excitement at the top of the loop because it was incredible to riding upside down. At a close second was the bottom of the loop because the speed increased a lot at the bottom. The sides were less exciting but still thrilling.

c. Describe the thrill factors that may contribute to those feelings (besides the #g’s) The twists and turns made this particular coaster thrilling. The size was also a thrill factor. The three loops were phenomenal and made the ride more enjoyable. Lastly, the ride required you to stand, not sit down, and this made it even more interesting and thrilling.

d. Describe the weight sensations at the top, side and bottom of the loop.: did you feel lighter, heavier, or normal? I felt heaviest at the bottom of the loop. The bottom left me with a heavy sensation, whereas the top made me feel fairly light. The side made me feel slightly lighter but almost normal.

PART B) Back at School



3) Evaluate Safety a. #g’s were within safe limits? The ride is indeed safe as it has only 1.08 g's. This is much less than 3 g's and it is therefore safe for us to ride.

b. Was there correlation between #g’s and excitement level? Explain, providing evidence. Generally speaking, this is true, however on this ride I did not feel that way. I feel as though I got the most thrill from being at the top of the loop (with less g's) as opposed to the bottom of the loop. This is my opinion.

4) Thinking about the Physics a) Explain the behavior of the mass on the string. Did the FBD of the car correlate to that of the mass? Why or why not? The FBDs do correlate in that both forces acting on the mass and the car acted downward. The only difference is the forces. The mass had weight and tension acting downward, while the cart had weight and normal force acting downward.

b) Did the #g’s correlate to the sensation of weight? Yes. The more the g's the heavier one felt, while if less g's were acting on you, you would feel lighter.

c) Discuss the graphs that you created and why they curve the way that they do. __V vs. T__: The velocity decreases on its way to the top of loop but does not reach 0 (other wise the roller coaster would fall) and then, it will pick up speed from the top of the loop back to the bottom, thus the v shape. __Fc vs. T__: When the coaster is descending down the first hill (before entering the loop) there is no centripetal force. Therefore, the graph is initially a horizontal line at zero. The following can be explained with the equation Fc = (mv^2)/r. At the bottom of the loop, the velocity is greatest. Therefore, the centripetal force is greatest (mass = constant; radius = constant). At the top of the loop, the velocity is smallest. Therefore, the centripetal force is smallest. The graph is shaped like a parabola because of the v^2 relationship in the Fc = (mv^2)/r equation. __A vs. T__: The acceleration begins negative at a steady rate as the coaster slows down towards the top of the loop. The acceleration then becomes positive and remains at a steady rate as it comes down the loop. Thus it is a change from a steady negative to a steady positive acceleration. __Thrill vs. A__: Once again, my opinion was that I felt the most thrill at the top of the loop when I was completely upside down. The bottom of the loop quite as thrilling but definitely enjoyable. It may just be because I went on El Toro first, but the bottom of the loop was not as thrilling an experience for me.

PART C: A Rotating Ride (either Vertical or Horizontal)

Name of rotating ride: **"Taz's Tornado"**

PART A: At the park: 1) Estimate distances and angles and 2) Measure time

3) Diagrams a. FBD of car or rider (at max and min height, if vertical). b. FBD of mass on a string at various positions (at max and min height, if vertical). c. Labeled sketch of ride (top and side views) Side - Top -

d. Take a clear side view picture

4) Graphs a. Create Fc vs. t and a vs. t graph for the motion this segment of the ride.

b. Create a thrill vs. acceleration graph for this segment of the ride.

5) Evaluate a. Describe the safety features of this ride The chair is made with a bar to prevent one from falling out. There is an emergency brake.

b. Describe the excitement level that you felt at the min and max height (if vertical), or at max speed (if horizontal) There was no change in thrill. I was unmoved by this ride because it was more of a child's ride. It was boring from start to finish. It had little thrill.

c. Describe the thrill factors that may contribute to those feelings (besides the #g’s) This ride was not very exciting, however it did have some thrill factors. The elevation made it seem as though one was flying. The new perspective added to the thrill.

d. Describe the weight sensations at the top, side and bottom of the loop.: did you feel lighter, heavier, or normal? The weight sensation was the same regardless of the position. I felt lighter when the ride was going at max speed.