Physics of Roller Coasters - Complete Toolkit

Objectives

1. To use energy principles and energy bar charts to explain the changes in speed of a car that traverses a roller coaster track.
2. To use kinetic and potential energy equations to predict the speed of a roller coaster car at a particular height on the track if given the initial height of the first drop.
3. To construct free-body diagrams for riders along curved sections of the track (dips and hills, banked turns, , loop tops, and loop bottoms) and to explain the relative magnitudes of the individual forces at such locations along the track.
4. To use the concepts of inertia and centripetal force to explain the sensations that riders have along curved sections of a roller coaster track.
5. To use circular motion equations and Newton's second law to mathematically analyze curved sections of the track, relating the rider speed, radius of curvature, mass, and individual force values to one another.

 

Readings from The Physics Classroom Tutorial

 

Interactive Simulations

1. Roller Coaster Model
     
   This interactive simulation allows students to explore energy and forces associated with the motion of a roller coaster car. The model window represents the forces (Fgrav and Fnorm) the velocity by vector arrows and represents kinetic energy, potential energy, and the total mechanical energy by bar charts. The speed of the car at each position along the track is indicated by a digital display. Students can explore a straight-line inclined plane, a loop and a section of track with a series of hills and dips. The last two explorations include the ability to modify the shape of the loop or of the hills and dips.
   
   
   
    
2. Roller Coaster Design 
   
   The Roller Coaster Design Interactive provides an engaging walk-through of the variables that affect the thrill and safety of a roller coaster design. Factors affecting speed, accelerations, normal force and the number of Gs are presented in an understandable language. Students then design a loop top, a loop bottom, a hill top, and a hill bottom and view how design parameters such as heights and radii affect the experience and safety of the riders. The Interactive comes with two different activities. One activity is designed to support classrooms that are using the Interactive as part of a roller coaster design activity. The second activity has been designed to support classrooms that are using the Interactive to promote science reasoning skills.
   
   
   
    
3. Open Source Physics:  Roller Coaster Model and Lesson Plan
   
   This Java model created by a high school teacher simulates motion along a constrained path and lets students explore numerous concepts associated with roller coaster physics: conservation of energy, reaction forces, and friction. Choose from 5 track configurations or create your own. Energy bar graphs show changing levels of kinetic/potential energy. You can set initial speed or add friction. Don’t miss the lesson plan and student guide! Oh….you can easily access the source code to set your own parameters
   
   
   
   
   
    
4. PhET Energy Skate Park
   
   If your classroom computers are Java enabled, this popular PhET simulation provides a robust environment to explore conservation of energy in skateboarding. Though it’s not a roller coaster system, many design issues are similar to those faced by ride designers. You can build ramps, jumps, and loops. You can add friction, change the rider’s mass, and view kinetic, potential, and thermal energy in bar graphs or pie charts. We especially like the auto-generated Energy vs. Position graphs and the tool to change gravitational constant. What would the motion be like on Jupiter or the moon?
   
   
   Teachers:  Don’t miss the set of 35 Power Point slides that go with the “Energy Skate Park” simulation  --  Veteran HS physics teacher Trish Loeblein created a great set of clicker questions to gauge student understanding of conservation of energy concepts. Includes questions AND answer key about skating ramps and roller coasters. 
   
   
     

 

Video and Animations

 

Labs and Investigations

Minds On Physics Internet Modules:

The Minds On Physics Internet Modules are a collection of interactive questioning modules that target a student’s conceptual understanding. Each question is accompanied by detailed help that addresses the various components of the question.

1. Work and Energy module, Ass’t WE3 -  Kinetic and Potential Energy
    
2. Work and Energy module, Ass’t WE4 -  Total Mechanical Energy
    
3. Work and Energy module, Ass’t WE6 -  Work-Energy Bar Chart Analysis
    
4.  Work and Energy module, Ass’t WE8 -  Energy Conservation - Math Analysis
    
5. Circular Motion module, Ass’t CG3 -  Centripetal Force and Inertia
    
6. Circular Motion module, Ass’t CG4 -  Centripetal Force Requirement
    
7. Circular Motion module, Ass’t CG5 -  Mathematical Analysis of Circular Motion

 
 

 

Concept Building Exercises:

1. The Curriculum Corner, Work, Energy and Power, Energy
    
2. The Curriculum Corner, Work, Energy and Power, Energy Concepts
    
3. The Curriculum Corner, Work, Energy and Power, Work-Energy Bar Charts
    
4. The Curriculum Corner, Circular Motion, Circular Motion and Inertia
    
5. The Curriculum Corner, Circular Motion, Centripetal Force Requirement
    
6. The Curriculum Corner, Circular Motion, Mathematics of Circular Motion
   
   Links:
   http://www.physicsclassroom.com/curriculum/energy
   
   http://www.physicsclassroom.com/curriculum/circles

 

 

Problem-Solving Exercises:

1. The Calculator Pad, Work, Energy and Power, Problems #12 - #18
    
2. The Calculator Pad, Circular Motion and Gravitation, Problems #1 - #15
   
   Links:
   http://www.physicsclassroom.com/calcpad/energy/problems
   
   http://www.physicsclassroom.com/calcpad/circgrav/problems

 
 

Science Reasoning Activities:

1. The Science Reasoning Center – Circular Motion Section - Weightlessness Training
    
2. The Science Reasoning Center – Circular Motion Section - Roller Coaster Loops
   
   Link: http://www.physicsclassroom.com/reasoning/circularmotion

 

Real Life Connections:

1. A Century of Screams – Multimedia History of the Roller Coaster (PBS)
   
   Did you know there were 1500+ roller coasters in the U.S. by the late-1920’s? The introduction of electric winches to pull cars up a hill transformed roller coasters into “scream machines” with steeper drops, tighter curves and dizzying speeds. But some of these retro wooden coasters were so dangerous they frequently resulted in injury or even fatality. Roller coasters fell out of favor in the 1930’s. Walt Disney is credited with reviving the roller coaster with the Matterhorn ride built at Disneyland in 1959 – the first tubular steel roller coaster in the world. This resource from PBS gives a great overview of roller coaster history and a glimpse of the early technologies.
   
   
   
    
2. Roller Coaster Safety: Accident Analysis
   
   Don’t forget about the study of system failure – it’s an important part of the engineering process and often overlooked in high school physics. Early roller coaster designs (see resource above) experienced failure mostly due to flawed track design, unsafe initial velocities, or untrained ride operators. WHAT ABOUT NOW?  The Physics Classroom took a dive into roller coaster disasters in the past decade. We learned that a surprising number of accidents were due to failures in passenger restraint systems or collisions caused by stalled cars.
   
   THE TASK:  Watch the videos below about two catastrophic roller coaster accidents – one in June 2015 that involved a collision, and one in 2013 involving a failed passenger seat belt. Both roller coasters were designed by Gerstlauer Amusement Rides of Germany. Conduct a web quest to find out what caused the failures and build an argument about who should be held liable – the manufacturer, the theme park, or perhaps the rider(s)?  Teachers: this will not be a simple task for students and will require more than a Google search. This will be a test of their internet mining skills and their ability to assess an accident within the context of engineering design. 
    
   Video 1:  BBC News – Smiler Roller Coaster Crash, June 201
    http://www.bbc.com/news/uk-england-stoke-staffordshire-32987550
    
   Video 2: Fox News – Deadly Fall from “Texas Giant” Roller Coaster, July 2013
   http://www.fox4news.com/story/22889634/six-flags-woman-died-while-riding-texas-giant
    
   Supplement:  Fort Worth Star Telegram – Battle over Liability in Texas Giant Fatality
   http://www.star-telegram.com/news/business/article3865021.html

Common Misconceptions:

1. The Thrill is in the Speed
   
   Students often falsely believe that the thrill of a roller coaster ride is due to how fast riders move. While speed may be a contributor to rider thrill, it is not the sole contributor. In fact, speed by itself does not lead to any sense of thrill. Many amusement park goers move faster on their trip down the highway to the amusement park than they move once they arrive at the park. If thrill were due to speed along, such thrill-seekers should continue driving on the highway and save themselves some money. The thrill of a ride is associated with changes in speed and direction. It is these changes that lead to accelerations and the changes in seat force that make amusement park rides so exciting. The thrill comes from accelerations and rapid changes in accelerations and the associated changes in the normal forces experienced by riders.

 

 

 

Standards:

A. Next Generation Science Standards (NGSS)

• HS-PS3-1   Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. 

• HS-PS2.A.i  Newton’s Second Law accurately predicts changes in the motion of macroscopic objects.
• HS-PS2.A.ii   Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object.

• HS-PS3.B.i   Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.
• HSPS3.B.iii   Mathematical expressions, which quantify how the stored energy in a system depends on its configuration and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior

• High School:  Systems can be designed to cause a desired effect.

• High School:  When investigating or describing a system, the boundaries and initial conditions of the system need to be defined.
• High School:  Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models.
• High School:  Models (e.g. physical, mathematical, computer models) can be used to simulate systems and interactions – including energy, matter, and information flows – within and between systems at different scales.

• High School:  Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of , and within that system.
• High School:  Energy cannot be created or destroyed – it only moves between one place and another place, between objects and/or fields, or between systems.

• High School:  Investigating or designing new systems or structures requires a detailed examination of the properties of different materials, the structures of different compounds, and connections of components to reveal its function and/or solve a problem.