Summary
Students design, build and test model roller coasters using foam tubing, toothpicks and masking tape. As if they are engineers, teams compete to create the winning design based on costs and aesthetics. Guided by three worksheets, students prototype, test, evaluate and finalize their ideas, all while integrating energy concepts. The goal is to understand the basics of engineering design associated with kinetic and potential energy to create optimal roller coasters. The marble (roller coaster car) starts with potential energy that is converted to kinetic energy as it moves along the track. The diameter of the loops that the marble traverses without falling out depends on the kinetic energy obtained by the marble.Engineering Connection
Mechanical and civil engineers are involved in the design of roller coasters. Engineers must understand how the basic physics concepts of energy apply to successful roller coasters. The challenge is to make the roller coasters fast and fun, without compromising structural integrity, which is critical for ride safety.
Learning Objectives
After this activity, students should be able to:
 Identify situations in which kinetic energy is transformed into potential energy and vice versa.
 Identify key steps in the engineering design process.
 Model, test, evaluate and modify a design.
 Invent a product to meet a need.
 Create a prototype and final model, taking design criteria into consideration.
 Use science, math, and engineering principles to design and optimize a product.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards  Science
NGSS Performance Expectation  

MSETS11. Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions. (Grades 6  8) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Define a design problem that can be solved through the development of an object, tool, process or system and includes multiple criteria and constraints, including scientific knowledge that may limit possible solutions. Alignment agreement:  The more precisely a design task's criteria and constraints can be defined, the more likely it is that the designed solution will be successful. Specification of constraints includes consideration of scientific principles and other relevant knowledge that is likely to limit possible solutions. Alignment agreement:  All human activity draws on natural resources and has both short and longterm consequences, positive as well as negative, for the health of people and the natural environment. Alignment agreement: The uses of technologies and any limitations on their use are driven by individual or societal needs, desires, and values; by the findings of scientific research; and by differences in such factors as climate, natural resources, and economic conditions.Alignment agreement: 
NGSS Performance Expectation  

MSETS14. Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved. (Grades 6  8) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Develop a model to generate data to test ideas about designed systems, including those representing inputs and outputs. Alignment agreement:  Models of all kinds are important for testing solutions. Alignment agreement: The iterative process of testing the most promising solutions and modifying what is proposed on the basis of the test results leads to greater refinement and ultimately to an optimal solution.Alignment agreement: 
NGSS Performance Expectation  

MSPS32. Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. (Grades 6  8) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Develop a model to describe unobservable mechanisms. Alignment agreement:  A system of objects may also contain stored (potential) energy, depending on their relative positions. Alignment agreement: When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object.Alignment agreement:  Models can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matter flows within systems. Alignment agreement: 
NGSS Performance Expectation  

MSPS35. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object. (Grades 6  8) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Construct, use, and present oral and written arguments supported by empirical evidence and scientific reasoning to support or refute an explanation or a model for a phenomenon. Alignment agreement: Science knowledge is based upon logical and conceptual connections between evidence and explanations.Alignment agreement:  When the motion energy of an object changes, there is inevitably some other change in energy at the same time. Alignment agreement:  Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). Alignment agreement: 
Common Core State Standards  Math

Reason abstractly and quantitatively.
(Grades
K 
12)
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Do you agree with this alignment?

Fluently divide multidigit numbers using the standard algorithm.
(Grade
6)
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Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.
(Grade
6)
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Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
(Grade
6)
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Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
(Grade
8)
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International Technology and Engineering Educators Association  Technology

Students will develop an understanding of the attributes of design.
(Grades
K 
12)
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Students will develop an understanding of engineering design.
(Grades
K 
12)
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Students will develop an understanding of the role of troubleshooting, research and development, invention and innovation, and experimentation in problem solving.
(Grades
K 
12)
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Students will develop abilities to apply the design process.
(Grades
K 
12)
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Students will develop an understanding of the relationships among technologies and the connections between technology and other fields of study.
(Grades
K 
12)
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Modeling, testing, evaluating, and modifying are used to transform ideas into practical solutions.
(Grades
6 
8)
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State Standards
Massachusetts  Math

Reason abstractly and quantitatively.
(Grades
K 
12)
More Details
Do you agree with this alignment?

Fluently divide multidigit numbers using the standard algorithm.
(Grade
6)
More Details
Do you agree with this alignment?

Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.
(Grade
6)
More Details
Do you agree with this alignment?

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
(Grade
6)
More Details
Do you agree with this alignment?

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
(Grade
8)
More Details
Do you agree with this alignment?
Massachusetts  Science

Differentiate between potential and kinetic energy. Identify situations where kinetic energy is transformed into potential energy and vice versa.
(Grades
6 
8)
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Do you agree with this alignment?

Identify and explain the steps of the engineering design process, i.e., identify the need or problem, research the problem, develop possible solutions, select the best possible solution(s), construct a prototype, test and evaluate, communicate the solution(s), and redesign.
(Grades
6 
8)
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Describe and explain the purpose of a given prototype.
(Grades
6 
8)
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Materials List
To share with the entire class:
 57 6foot lengths of foam pipe insulation tubing, cut in half lengthwise per group
 2 rolls masking tape
 2 boxes round toothpicks (~20 per group)
 16 mm marbles (5 per group)
Each group needs:
 container to catch marbles
 flexible tape measure
 scissors and ruler
 2 differentcolored stickers, one marked "P," the other "K"
 Worksheet 1: Reference Diagram
 Worksheet 2: Design and Building Guidelines
 Worksheet 3: Cost and Evaluation Sheet
Worksheets and Attachments
Visit [www.teachengineering.org/activities/view/wpi_amusement_park_ride] to print or download.More Curriculum Like This
Students explore the physics exploited by engineers in designing today's roller coasters, including potential and kinetic energy, friction and gravity. During the associated activity, students design, build and analyze model roller coasters they make using foam tubing and marbles (as the cars).
High school students learn how engineers mathematically design roller coaster paths using the approach that a curved path can be approximated by a sequence of many short inclines. They apply basic calculus and the workenergy theorem for nonconservative forces to quantify the friction along a curve...
Students build their own smallscale model roller coasters using pipe insulation and marbles, and then analyze them using physics principles learned in the associated lesson. They examine conversions between kinetic and potential energy and frictional effects to design roller coasters that are compl...
Build a small roller coaster prototype out of foam pipe wrap insulation and marbles, but apply calculus and physics in the design! This realworld engineering challenge applies practical mathematics to test smallsized models on a real track.
Introduction/Motivation
The city of Wahoo wants to build a new roller coaster ride on their town common as part of the celebration of their 300th year. For consistency with the round number, they want a design to be as "loopy" as possible while keeping cost to a minimum. They are looking for engineering designs that optimize the ratio (material costs/inches of loop diameter) and are aesthetically pleasing (look good!). Every section of a roller coaster has different characteristics. Some portions have very light turns while others have more gentle curves and turns. Each scenario has its limits for whether or not it will work.
Procedure
Background
Roller coasters at amusement parks utilize potential energy and kinetic energy. Typically, a motor pulls up the roller coaster car to gain its initial potential energy. Once at the peak point, no motors are connected to the car in any way. The car begins its winding and looping decent along a track that has been designed to safely convert potential energy into kinetic energy while making it a thrilling ride.
If the car goes through a loopdeloop and does not have enough kinetic energy, it will not stay on the track as it reaches the peak of the loop. Kinetic energy is measured as KE=(mv^{2})/2, where m is the mass of the object and v is the velocity. Potential energy is measured as PE=mgh, where m is the mass, g is the gravitational force, and h is the distance above the reference point where the mass starts.
Ideally, all the potential energy is converted to kinetic energy, but in reality, this never holds true, since some of the energy is lost to friction. Because of the loss of energy, the peak of the loops must be lower than the initial starting point of the car. See Worksheet 3 for a reference diagram.
With the Students
Part 1: Preliminary Design and Testing
 Show Worksheet 1: Reference Diagram as an overhead transparency OR make copies and distribute as a student handout. Discuss the energy concepts illustrated on the worksheet.
 Hand out Worksheet 2: Design and Building Guidelines to all students. Review the task, design criteria and scoring.
 Discuss the engineering design process (refer to the figure below) and how engineers use it to design structures like roller coasters.
 Divide the class into groups of three students each.
 Give each group 1 marble, a container to catch the marble, 1 foam piece, 1 toothpick, and a onefoot piece of masking tape.
 Have each team design and test a preliminary prototype using the provided materials.
 As they test, advise the groups to plan their final designs and the amount of materials that they will need. Have them sketch their ideas on paper and fill in quantities of materials on Worksheet 3: Cost and Evaluation Sheet.
 After 20 minutes, have students return the materials from the preliminary prototypes and obtain the materials they listed on Worksheet 3 from the "store." If this is done at two separate class times, the materials can be ready for students when they arrive for the second meeting.
Part 2: Final Design and Testing
 Permit additional materials to be purchased during the first phase of design and testing, about 30 minutes. Once materials have been obtained from the store, they may not be returned or exchanged.
 Give teams 10 minutes to finalize their designs. Give each group 1 "P" sticker and 1 "K" sticker. Remind groups to use the stickers to mark the places on their roller coasters that have the greatest kinetic and potential energy.
 When time is up, have groups step back from their roller coasters. Test each roller coaster individually by having a team member release the marble to run through it. Remember, each roller coaster must be able to stand alone and the marble must travel completely from start to finish. Permit at least two tries per coaster, though more testing can be done if time allows.
 Identify an "aesthetic rating." Have each group look at all of the roller coaster designs and come up with an aesthetic rating, such as 16 if six groups, with 1 being the best. Based on the group responses, the leader announces the ratings.
 Have groups measure the diameter of each loop in the roller coaster and total the cost of purchased materials in Worksheet 3.
 Have students compute the loop diameter to cost ratio, then add the aesthetic ranking.
 After all groups have completed the tests, come to a consensus as a class about the results. Lead a discussion on observations about effective and noneffective solutions. Was there a stronger design/construction that seemed to work? How did potential and kinetic energy play a role? Along with justifying the best design, did your group consider structural integrity? Is the ride safe?
Vocabulary/Definitions
gravitational force: Force exerted between the Earth and an object that attracts the object toward the Earth.
kinetic energy: Energy associated with motion of an object.
potential energy: Energy an object has because of its relative location.
Assessment
PreActivity Assessment
Discussion: Observe student participation in class discussion on potential and kinetic energy.
Activity Embedded Assessment
Observation: Observe student participation and contribution within groups during the preliminary and final design stages.
Circumferece: Have students calculate the circumference of the loops (assuming they are true circles) using the measured diameter.
PostActivity Assessment
Estimating Velocity: Have students estimate the velocity at the point where the kinetic energy is the highest (the lowest point of the track). Start by estimating the potential energy at the start (PE = m*g*h ) and then assume that all of this energy is converted to kinetic energy. Solve the equation KE = (1/2)mv^{2} for the velocity. Note: if you set the two equal (m*g*h = (1/2) mv^{2}), you do not need to measure the mass of the ball!
Graph: As a class, create a scatter plot of the maximum height of each track vs. calculated theoretical velocity. Discuss the relationship between the variables.
Recap: Assign students to individually describe their roller coaster designs with sketches, explaining what worked and what did not work. Review their recaps to gauge their depth of comprehension.
Making Sense: Have students reflect about the science phenomena they explored and/or the science and engineering skills they used by completing the Making Sense Assessment.
Investigating Questions
 Where is the potential energy greatest in your system? (Answer: It is greatest at the highest location.)
 Why do most roller coasters have corkscrew turns instead of loopdeloops? (Answer: It takes a lot of kinetic energy to make it all the way around a loopdeloop. Corkscrew turns [twisty downhill turns] simply use the potential energy to gain speed through the turn.)
 How must the track be designed to keep the car in corkscrew turns? (Answer: The track must be at an angle, tilting forward, instead of level to the ground.)
Activity Extensions
Have students research either the history or safety of roller coasters. When was the first loopdeloop introduced?
Have students calculate the potential energy of the marble at several locations along their tracks.
Activity Scaling
For upperlevel students, assign the activity extensions. Also, have them compete for the fastest ride compared to the coaster length.
References
Marden, Duane. Roller Coaster Database. A comprehensive, searchable database with information and statistics on 5,000+ roller coasters throughout the world. http://www.rcdb.com/
Copyright
© 2013 by Regents of the University of Colorado; original © 2001 WEPAN/Worcester Polytechnic InstituteContributors
Marthy Cyr; C. ShadeSupporting Program
Making the Connection, Women in Engineering Programs and Advocates Network (WEPAN)Acknowledgements
Project funded by Lucent Technologies Foundation.
Last modified: August 5, 2021
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