Amusement Park Physics

Using the Calculator Based Laboratory (CBL)

At the 1999 American Association of Physics Teachers Conference, Lincoln High Teachers Jerel Welker and James Rynearson were able to participate in a workshop designed to allow teachers the opportunity to experiment with various forms of data collection on amusement park rides. Using this opportunity to try various techniques with other colleagues from around the United States and Europe, they developed software and tested the techniques for collecting data on various amusement park rides. As time permits, some of these activities will be presented here. A popular attraction at various amusement parks around the country is a ride which is designed to simulate a "bungee jump". While various rides function differently, the data collected will be similar. The particular ride used here involves placing the passenger on the ride at the bottom of a tower and attaching the safety harness. The riders are mechanically lifted to the top of the tower.

	Once at the top of the tower, compressed air is used to propel the riders downward. The blue arrow on the images represent the magnitude and direction of the velocity at a given time. After the mechanism triggers the release of the "car", the car is accelerated downward.
	As the car proceeds toward the ground, the ride begins to slow the car down. At the point closest to the ground, the velocity for an instant is zero and....
	the car accelerates back towards the top of the tower. Friction and other forces result in a dampening of the velocity over time. As a result....
	the car doesn't reach the top of the tower before its velocity is zero and the object begins to fall again. This cycle is repeated several times before the ride is stopped and the passengers are allowed to disembark.

Data Collection

Equipment Required: 1 - TI 82, 83, or 83+ calculator 1 - TI CBL 1 - Vernier Single or Triple Axis Accelerometer The image of our "volunteer" at the right shows the CBL and calculator set up. The accelerometer is shown taped in the case at the lower right side of the image. The foam is cut out and the accelerometer is taped to the case. The accelerometer should be positioned so that the motion is in the direction indicated by the arrows on The wiring is run underneath the foam to the CBL on the left side of the case. The calculator has been positioned in the case for photographic purposes. Unfortunately, it hides the fact that a hole has been cut in the case so that the buttons on the CBL can be accessed without opening the case. To use the CBL, we program the CBL, remove the link cord and calculator. Close the case in the position shown and use a belt to strap the case securely to the chest. The user can start the CBL at any portion of the amusement park ride by pressing the Trigger button on the CBL. Software and instructions are available for the TI-83 calculator.

Accel (m/sec^2) vs. Time (sec)

The graph above contains the Acceleration vs Time data from one such amusement park ride. The data has been exported from the TI-83 Calculator into Graphical Analysis which is a software package produced by Vernier. As with any experiment, the calibration and understanding of the calibration is important. In this case, the accelerometer was calibrated so that the acceleration would read 9.8 meters per second squared (m/s^2) when the apparatus was not being accelerated (a reading of 9.8 m/s^2 would result from holding the accelerometer steady). As a result, a reading of zero m/s^2 would be free fall.

Some may prefer to refer to the acceleration in terms of a gravitational unit (G's). Using acceleration due to gravity on earth as 9.8 m/s^2, one can divide the acceleration by 9.8 m/s^2 and come up with a graph shown below in Gravitational Units. Here, a reading of 2G would be twice the amount of acceleration which would normally result from gravity.

To facilitate further discussion of the data, refer to the graph shown below.

In the region marked 'A', a red line has been drawn through the data. This horizontal line is the time period in which the accelerometer was at the top of the tower prior to the mechanical release of the platform. The baseline value demonstrates that the accelerometer was calibrated so that 9.8 m/s^2 was at rest (1 G). The end of the red line marks the time at which the platform was released. This point is slightly more than 5 seconds after the CBL was triggered.

The amusement park ride propels the rider down from the starting point at the top of the tower.The region of the graph marked point 'B' is data recorded during the descent. Note that 0.0 m/s^2 (0 G) would be freefall. In fact, one point recorded by the accelerometer was nearing -8.0 m/s^2 which is approaching (-1 G). As the ride drops down the tower, the velocity begins to slow until the velocity at the bottom of the tower is zero. In the region marked 'C' on the graph, the peak acceleration is required to change the direction of the ride as the car begins to accelerate upward.

A more detailed examination of the data is presented on the next page.