Conservation of Energy at Six Flags
OBJECTIVE: To use conservation of energy to predict the speed for “Batman the Ride” at Six Flags Great Adventure, Jackson, NJ.
INTRODUCTION:
“Batman the Ride” at Six Flags amusement park is an inverted, looping roller coaster. The roller coaster train consists of a series of 8 chairs suspended vertically from the track, as pictured below. A motor connected to a chain moves the train to the top of the hill, at constant speed. After the train reaches the top of the first hill, the only forces acting on it are gravity, the normal force from the track, friction, and air resistance.
METHOD:
You will being by using LoggerProto analyze the file “bathill.” Using Internet Explorer, navigate to the honors physics shared files folder (from either the school web site physics page or the Honors Physics I moodle page). Open the “Class Materials”, “videos”, and “Prepared” folders. Click on the “Library” tab above the picture of Mr. Ilyes. Click on the “Open with Explorer” button. Drag the “bathill” movie to a convenient location on your computer (such as the desktop). Alternatively, you may right click on your movie, select “Copy”, and then paste it to a convenient location. Open up LoggerPro and choose “Movie” from the “Insert” menu. Navigate to the location where you saved your movie. Select your movie, and click on "open."
Begin by marking the position of the top of the first chair in the first frame of the video. Try to locate it at the position of the “hole” above the chair (see below).
Next, advance the movie about 20 frames and mark a second position (again, at the “hole” above the first chair). Repeat this for a total of ten data points along the length of the hill.
Next, move the location of the origin to your first marked data point. Rotate the axes such that the x-axis is parallel to the track.
To scale the video, we will use the fact that the distance from the top of the first hill to the ground is 32 m. You will have to estimate the location of the ground, since it is not clearly visible beneath the first hill. Make sure you estimate where the ground would be in the plane of the first hill. This will be farther up the screen than the asphalt visible in the foreground.
Finally, plot a graph of horizontal position (X) vs. time. Determine the slope of the best-fit line, and print copies of the graph for each lab partner.
Next, you will use conservation of energy to predict the velocity of the train when it reaches the bottom of the first hill. To do this, note recall that the top of the first hill is 32 m above the ground, and note that the bottom of the first hill is 6.4 m above the ground. We will ignore non-conservative forces such as friction and air resistance.
To check your predicted velocity, you will measure the actual speed of the train at the bottom of the first hill. To do this, open a new LoggerPro window to analyze the file “batbottom”. Note that the train is nearly at the bottom of the first hill. Advance the movie until the train’s center of mass is located about six frames before the very bottom of the hill. Then mark the position of the “hole” above the last car in the train. Repeat this for about 4 or 5 additional positions, for which the train’s center of mass is located just before, at, or just after the bottom of the hill. Then move the origin to your first marked point and rotate the axes until the x-axis goes through as many of your marked points as possible. To scale the movie, use the fact that the distance from the top of the loop to the ground beneath it is 24.5 m (note that we are using a different scale than in the previous movie, since the motion is occurring in a different plane, closer to the camera). Again, you will have to estimate the location of the ground. Then plot a graph of horizontal position vs. time, as before, apply a linear fit, print the graph, and make note of the meaning of its slope.
DATA:
Slope of x-Position vs. Time Graph (climbing hill): ______m/s
Predicted Velocity of Train at Bottom of Hill: ______m/s
Slope of x-Position vs. Time Graph (bottom of hill): ______m/s
% Discrepancy: ______%
DATA TREATMENT:
- Predicted velocity of train at bottom of hill
- Include any additional calculations required to answer specific interpretations/analysis of errors questions with the answers to those questions
Interpretations:
- Based upon your measured velocity at the bottom of the hill, calculate the centripetal acceleration of one of the chairs (the radius of the bottom circular section of the track is 20 m). How many “g’s” does this represent?
- The radius of the loop gradually becomes smaller towards the top, with r = 5.5 m at the very top. Why wasn’t this radius used at the bottom? If it had been, how many g’s of acceleration would a rider experience there?
ANALYSIS OF ERRORS:
- Calculate the % discrepancy between your predicted and calculated speeds at the bottom of the hill.
- Based upon the predicted and measured velocities at the bottom of the hill, how many Joules of energy were lost by a 65.0 kg passenger on the train as he/she traveled from the top of the hill to the bottom? Also express this energy loss as a % loss (the percentage of the predicted energy that was lost by the rider).
- Based upon your answer to #2, do friction and air resistance appear to play a significant role over the portion of track examined? What if you were to use your data from the top of the first hill to predict the speed closer to the end of the ride? Would the % energy loss be the same, greater than, or less than the value calculated in #2? Justify your answer.
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