# The Physics of Roller Coasters

## Basic Research Questions

Your role as researcher for this project involves acquiring a wealth of technical information about the physics of a variety of amusement park rides, particularly roller coaster rides. The process of conducting a literature search should yield some basic information about the motion of a roller coaster car and its occupants in terms of concepts such as speed, acceleration (both linear and centripetal), net forces, normal forces, friction forces, momentum, and energy (KE, PE, TME); when finished, you should be able to conceptually and mathematically describe the motion of occupants on roller coaster rides and other amusement park rides. Some basic topics for research and ultimate discussion have been listed below to assist you in the initial stages of your literature search. The role of this listing is to provide an initial framework for your literature search and not a conclusive list of topics to be discussed. Your group is expected to go beyond these topics, exploring diverse areas of individual interest about the physics of roller coasters and amusement park rides.

1. Describe Newton's laws of motion and explain how each individual law can be used to explain the motion of an object on roller coaster rides.
2. Perform free-body diagram analyses for roller coaster car occupants at strategic locations along track (e.g., on inclines, on straight level sections, at the bottom of loops and the top of loops, on banked curves, during braking sections, at the top and bottom of small dips, etc.); combine the FBDs with Newton's second law to predict the normal forces experienced by riders and relate such predictions to the actual experiences of riders.
3. Use kinematic equations and estimations of distance and acceleration to predict the final speeds of roller coaster cars during a linear section of track (e.g., on constant-angle inclines and in the final braking section of the track.
4. Define work and energy and use the work-energy theorem to trace the presence of different types of energy for a roller coaster car during a typical roller coaster ride; use work and energy to perform sample calculations for a roller coaster ride.
5. Relate kinetic and potential energy to speed and height and use specific equations to calculate the actual speed and given heights during a sample roller coaster ride (a sketch of the ride with pertinent information should be included).
6. Describe work-energy bar charts and use such charts to describe energy transformations during roller coaster rides.
7. Describe the motion characteristics of objects moving in circles (or near circles) and relate such characteristics to the motion of coaster riders through vertical loops and horizontal curves; use mathematical equations to make predictions about the relations between speed, radius, acceleration, net force and individual force values.
8. Conduct a free-body diagram analyses for objects on inclined sections of track (such as on vertical drops and banked curves) and explain how force vectors can be resolved to facilitate a determination of the net force and accleration for such sections.
9. Explain what is meant by g-forces and explain the underlying physics which explain the various g-force phenomenon during a roller coaster ride.
10. Explain the cause of weightless sensations and relate such sensations of weightlessness to the normal forces experienced by roller coaster riders during specific sections of a roller coaster ride.
11. Explain how and why roller coaster designers use projectile mathematics to design the trajectories of small dips and relate such designs to the weightless sensations experienced by riders; use a diagram and sample numbers to illustrate the usefulness of such calculations.
12. Describe what a clothoid loop is and explain why it is used in place of the traditional circular loop.
13. Describe some rotational motion principles and apply such principles to explain the motion experienced by riders in either roller coaster rides or other amusement park rides.
14. Explain what is known about the physiological symptoms experienced by roller coaster riders and relate specific symptoms to the motion characteristics of roller coaster rides.
15. Conduct a comparison between roller coaster rides and other amusement park rides in terms of the underlying physics and the related physiological experience of the riders.
16. Explain the methods used and questions asked by roller coaster designers and safety engineers in the process of designing roller coaster rides.
17. Retrieve specific statistics about various roller coaster rides, specifically record-breaking rides; make meaning of such statistics by relating values of heights, speeds, and angle measurements to the physics of motion.
18. Describe the history of roller coaster rides and some of the early disasters which resulted from phaulty physics.

## Other GBS Resources

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Questions and comments can be sent to Tom Henderson.