Amusement Park Physics/Precalculus

World of Fun Amusement Park, Kansas City, MO

Ripcord

The Ripcord is an attraction where 1 to 3 riders are hoisted to the tower in the background of the image at the right. When one of the riders pulls the "ripcord" they swing through the twin towers in the foreground. The ride continues as they swing back and forth like a pendulum, gradually slowing until they can grab a rope from the attendents and swing to a stop. The image at the right shows the students at the top of the tower preparing the equipment. The two individuals on the left wore the CBL's on their backs. The two on the right triggered the CBL of on the individual to their right as shown below.

The Ripcord required working closely with park personnel to coordinate the data collection and ensure the safety of all individuals. LHS teachers Jerel Welker and James Rynearson discuss the setup with Worlds of Fun ride operators as the students are "suited up". Several practice sessions and much discussion about the procedure occurred prior to the actual ride. After several practice, it was decided to use two CBL's positioned on the students back. this would keep all of the equipment inside the suit and only the strap going around the students chest would have any pressure from the suit on it. The next discussion then led to triggering the CBL to start the equipment recording the data as there is no possibility of programing in a delay feature.

The CBL and Accelerometer were placed on the backs of the two individuals to the groups right. The individuals on the left side of the group would then reach to the individual on their right and trigger the CBL on the adjacent students back.

The images below show the students being hooked onto the cable and hoisted back toward the tower. You may note students have shifted to trigger the CBL's in the lower left image. Ride rules required them to lock arms before pulling the ripcord. Once this was accomplished, the ripcord was pulled the the swing began. After coming to a stop and unloading, the data is taken from the CBL and graphed. One will note a real life example of damped harmonic motion.

A larger view of the graph is shown below. The actual data is available in the file ripcord as a text file, TI-83 format or Vernier Graphical Analysis. All 3 axes of data are also available Graphical Analysis format. The data is also available in a TI-83 program with the warning that you may have to run the program in parts as most calculators do not have enough memory to run the program and install the data in the lists.

Assessment

The students analyzed this data to find various aspects. What types of mathematical models can be used to fit this data? Can you fit a model to the damped harmonic motion? What is the length of the pendulum based upon the data? Can you fit a model to the local maximums and local minimums?

Local Maximim and Local Minimum Models
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Several hints at finding a model.

• The pendulum will eventually swing to a stop where the acceleration measured by the accelerometer will be 9.8 m/s^2.

• Try finding an exponential regression for the local maximums and local minimimums.

• Is the midline of the sinusoid a constant? If not, how will this change the model?

The best fit we have accomplished at this time is shown in the images below.

Data Only
Data with Model

On the calculator, the above models appear to fit quite well. Looking at the model as shown in Graphical Analysis yields the following view. Here you get a better feel for the fit of the model.

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