PhysicsLAB
Video LAB: Looping Rollercoaster

This lab is based on the video entitled Corkscrew Loop: Looping Rollercoaster from the Direct Measurement Video Project hosted on the Science Education Research Center at Carleton College (SERC) website. The copyright for these videos belong to Independent School District 197 in Mendota Heights, Minnesota. The project is partially funded by a Science Foundation Grant #1245268 awarded in September 2013.

The following lab implementation was designed for use in my Honors Physics I class and only represents one method of analyzing the data provided in the video.
 
To open the video, choose the option of Gen 2 DVM Player. Before playing, note the following data presented on the screen:
  • length of entire train = 15.5 meters +/- 0.2 meters
  • length of one car = 2.45 meters +/- 0.1 meters
 
Also note that two measurement tools are presented along the bottom of the video, a protractor and a vertical ruler, as well as the option of playing the video at normal speed or in 8x slow motion. You should use the slow motion option when taking your meassurements.
First choose to overlay the protractor and "stretch it to match" the curvature of the inside of the track for the "lower approach loop." As you expand the size of the protractor some of it will move off the screen. Now choose the vertical ruler and measure the radius of the original approach. After lining up the zero of the ruler with the center of the protractor, you should obtain a value close to 15.5 meters. Take a moment to note that the top of the corkscrew lies below the center of the circle created by the approaching track. This relationship will be an important consideration when constructing your conclusions.
 
Now move the protractor and adjust its size to match the inside track of the top of the corkscrew. The "x-axis" of the protractor should line up with the vertical trusses which are supporting the corkscrew. Now move the vertical ruler and measure the circle's radius.
 
Now play the video several times to acquaint yourself with the scenario that was filmed.
 
At how many frames per seconds was the film analyzed (8x slow motion)? 

What is the radius of the top semicircular section of the corkscrew in meters? 

What is the length of track along the top of the semicircle of the corkscrew in meters? 

On frames+730, the train completely fills the top semicircle of the corkscrew. Using the fact that there are six "equal length" cars in the train, estimate your value for the length of one car. 

Is your value for the length of a car within the tolerances stated on the video? Support your answer (yes or no) numerically.
 

Sample Data Collection
 
 
Now you are going to obtain three average values for the speed of the lead car as it moves through the top semicircle. Once again load the protractor and adjust its size to inscribe the upper circular section of the corksrew. Looking closely at the protractor you will see white markings every 30º. 
 
We will begin with a sample calculation for the speed at 180º. To do this, we will take measurements that bracket 180º: one at 210º and the other at 150º. On frames+375 the passengers in the front seat of the front car reach the 210º mark on the protractor while on frames+455 they reach the 150º mark on the protractor.
 
How many seconds pass between these two positions? 

How far did the passengers travel between these two position? Remember that you know the diameter to the top semicircle so you can calculate its circumference. The distance between the 210º and the 150º marks represents 1/6th of that circumference. 

What was their average speed during this interval? 

 
The average speed of the car between 210º and 150º can be represented as a secant connecting those two positions. As can be seen in the diagram, the slope of the red secant approaches the slope of the car's instantaneous velocity, the blue tangent, at 180º.

Using this fact, calculate the centripetal acceleration experienced by the passengers in the first car as it passed the left truss in frames+416.
 

Refer to the following information for the next six questions.

Repeat the same process for 90º using 120º and 60º as your bracket.
At what frame number were the passengers in the front seat of the first car passing through the 120º mark? 

At what frame number were the passengers in the front seat of the first car passing through the 60º mark? 

How many seconds pass between these two positions? 

How far did the passengers travel between these two position? 

What was their average speed during this interval? 

Calculate the centripetal acceleration experienced by the passengers in the first car as it passed through the top of the semicircle in frames+566. 

Refer to the following information for the next six questions.

Repeat the same process for 0º using 30º and 330º as your bracket.
At what frame number were the passengers in the front seat of the first car passing through the 30º mark? 

At what frame number were the passengers in the front seat of the first car passing through the 330º mark? 

How many seconds pass between these two positions? 

How far did the passengers travel between these two position? 

What was their average speed during this interval? 

Calculate the centripetal acceleration experienced by the passengers in the first car as it passed the right truss in frames+763. 

 
Conclusions
 
Before getting onto the rollercoaster, what would be the magnitude of the normal force supporting a 40-kg passenger as he stands in line on a flat surface? 

Once the 40-kg passenger is on the rollercoaster and moving through the top semicircular section of the corkscrew, what were the magnitudes of the normal forces he experienced when

(a) as his car first entered the upper semi-circle (180º)? 

(b) his car passed through the top of the loop's turn (90º)? 

(c) as his car exited the upper semi-circle (0º)? 

Explain why the passenger did not experience "apparently weightlessness" as he moved through the 90º position.
 

Calculate the kinetic energy of a 40-kg passenger as he passed through the 180º position. Consider the x-axis between the left and right trusses to be the "zero level" for determining any changes in the potential energy for the top semicircle. 180º is located on one side of the "zero level." 

Calculate the total mechanical energy of a 40-kg passenger as he passed through the 90º position. Remember that the "zero level" for changes in potential energy through the top semicircle of the corkscrew is the line connecting the left and right trusses. 

Calculate the kinetic energy of a 40-kg passenger as he passes through the 0º position. 

Did the passenger's trip through the top semicircle of the corkscrew conserve mechanical energy?
 
If not, during which transition (the approach from 180º to 90º or recession from 90º to 0º) was more energy lost?