Roller Coaster Physics

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Carden with his model “G Money.”

AP Physics 1 students were challenged to create a diagram and model of an original roller coaster design. The challenge required the students’ designs to exhibit realistic g forces, velocities, heights, and inclines. Students applied concepts of circular motion dynamics and energy conservation to calculate and label the velocity, centripetal acceleration, and g’s for at least three locations on the design. They also calculated and labeled the required energy to start the roller coaster.  The project required the roller coasters to have at least one hill and one loop, and maximum g’s were required to be less than 6 to maintain rider safety.

The creation of a model:

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Kendra and Leslie with their model of “No Clue.”

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SFOG-3-26-05-Superman-1

Physics Day at Six Flags Over Georgia

     The physics students of Sequoyah High School donned their datavests, probes, and sensors to explore real-world physics at the Six Flags Over Georgia Physics Day on April 27th.  Students discovered everything from maximum g’s on Goliath to the minimum velocity required to keep you in your seat on The MindBender. Nolan Williams discovered his apparent weight at the bottom of the most treacherous loop on SuperMan.  Here are his amazing results:

Apparent Weight on Superman

     The purpose of our experiment was to calculate the apparent weight at the bottom of the first loop on the roller coaster, Superman: Ultimate Flight. To find this value, we used data that we gathered from various instruments as we rode the ride. Our focus for the experiment is the bottom of first loop on the coaster. For a video of the roller coaster, see the YouTube video on the website.  The apparent weight will be the sum of the force of gravity and the centripetal force from the loop. Here is a free body diagram depicting the forces on us at the moment of interest:

Here’s a list of equipment needed for this lab: TI-84 Calculator with CBL Unit, One Dimensional Accelerometer, Digital Barometer, Instrument Holding Vest.

First, we set up the accelerometer and barometer in our instrument vest and attached them to the CBL unit. The accelerometer measured acceleration in the vertical direction and the barometer measured barometric pressure. The pressure could be used to determine altitude. We then set up the collection of our data inthe software DataMate. In DataMate, we set up the length of our experiment, the number of samples, and the time between samples. After setting up all the equipment, all we had to do was start the collection of the data on the CBL unit at the top of the first hill. The instruments then collected our data throughout the ride.

Here’s a sampling of our data:    The first column indciates time in seconds, the second column is acceleration (m/s/s) and the third column is barametric pressure (kPa).  The graph shows the rate of change in acceleration.

0                      9.31244                                   98.4212

0.75                 9.53653                                   98.4212

1.5                   9.31244                                   98.3831

2.25                 9.42448                                   98.4212

3                      9.53653                                   98.4212

3.75                 9.2004                                     98.4212

4.5                   10.5449                                   98.4212

5.25                 6.17524                                   98.3831

6                      0.797173                                 98.4212

6.75                 4.83072                                   98.3831

7.5                   9.87266                                   98.4212

8.25                 3.82233                                   98.4212

9                      -3.90864                                  98.4212

9.75                 14.5785                                   98.4212

10.5                 6.39932                                   98.3831

11.25               -4.13272                                  98.4212

12                    11.3292                                   98.3831

12.75               5.50298                                   98.4212

13.5                 -0.995514                                98.4212

14.25               7.40771                                   98.4212

15                    2.14169                                   98.4212

15.75               10.657                                     98.4212

16.5                 4.38255                                   98.4212

17.25               -3.90864                                  98.4212

18                    14.4664                                   98.3831

We analyzed the data as follows:

The goal of our experiment was to calculate the apparent weight of a person at the bottom of the first inverted loop on Superman: Ultimate Flight. To do so, we gathered data ourselves as we rode the coaster. After gathering the data we were able to analyze it and calculate the apparent weight. I calculated that my apparent weight at the bottom of the loop was about 396 pounds, compared to my actual weight of 160 pounds. That is about 2.5 times my normal weight! A possible source of error in our experiment could have been with the accelerometer we used. Our accelerometer only measured acceleration in one direction. The movement throughout the loop is mostly in the vertical direction, but there is some side to side movement. This means, the maximum acceleration we obtained may have not been the true maximum acceleration; however, because most of the movement in the loop is vertical, we can assume our data is fairly accurate and that riding an awesome rollercoaster like Superman is one really cool way to conduct a physics lab!

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