### Summary

Students design, build and test model roller coasters using foam tubing. The design process integrates energy concepts as they test and evaluate designs that address the task as an engineer would. The goal is for students to understand the basics of engineering design associated with kinetic and potential energy to build an optimal roller coaster. The marble 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.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### 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 a successful roller coaster. They must understand how to make it fast and fun, without compromising structural integrity, which is critical for ride safety.

### Learning Objectives

After this activity, students should be able to:

- Model, test, evaluate and modify a design.
- Invent a product to meet a need.
- Use science, math and engineering principles to design and optimize a product.

### More Curriculum Like This

**Physics of Roller Coasters**

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).

**A Tale of Friction**

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 work-energy theorem for non-conservative forces to quantify the friction along a curve...

**Mathematically Designing a Frictional Roller Coaster**

Students apply high school differential calculus and physics to design 2D roller coasters in which the friction force is taken into consideration. Student teams first mathematically design the coaster path (using what they learned in the associated lesson) and then use foam pipe wrap insulation mate...

**Building Roller Coasters**

Students build their own small-scale 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...

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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 K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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

- 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) Details... View more aligned curriculum... Do you agree with this alignment?
- 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) Details... View more aligned curriculum... Do you agree with this alignment?
- 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) Details... View more aligned curriculum... Do you agree with this alignment?
- 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) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Solve quadratic equations with real coefficients that have complex solutions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve quadratic equations in one variable. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Modeling, testing, evaluating, and modifying are used to transform ideas into practical solutions. (Grades 6 - 8) Details... View more aligned curriculum... 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) Details... View more aligned curriculum... 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) Details... View more aligned curriculum... Do you agree with this alignment?
- Describe and explain the purpose of a given prototype. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

- 5-7 6-foot 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 different-colored stickers: one marked "P," the other "K"

### 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 (inches of loop diameter/material costs) 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.

### 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.

### Procedure

Background

Roller coasters at amusement parks utilize potential energy and kinetic energy. Typically, a roller coaster car is pulled up by a motor, gaining 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 transfer the potential energy into kinetic energy while making it a thrilling ride.

If the car is going through a loop-de-loop, 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. This never holds true, as 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: Design and Preliminary Testing**

- Show Worksheet 1: Reference Diagram as an overhead transparency or make copies and pass ithem out as a handout to all students. Discuss the worksheet.
- Pass out Worksheet 2: Building Guidelines to all students. Review the task and design criteria.
- Divide the class into groups of three students each.
- Give each group one marble, a container to catch the marble, one foam piece, one toothpick, and a one-foot piece of masking tape.
- Have each team design and test a preliminary prototype.
- As they test, each group should be planning their final design and the amount of materials that will be needed. 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 listed in Worksheet 3 from the "store." If this is done at two separate times, the materials can be ready for students when they arrive for the second meeting.

**Part II: 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.
- Allow 10 minutes to finalize designs. Give each group one "P" sticker and one "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 go through it. Remember, each roller coaster must be able to stand alone and the marble must travel completely from start to finish. Permit 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 coasters and come up with an aesthetic ratting (such as 1-6 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 the groups have completed the tests, come to a consensus as a class about the results. Lead a discussion on observations about effective and non-effective 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?

### Attachments

### 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 loop-de-loops? (Answer: It takes a lot of kinetic energy to make it all the way around a loop-de-loop. 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.)

### Assessment

Pre-Activity Assessment

Observe student participation in class discussion on potential and kinetic energy.

Activity Embedded Assessment

Observe student participation within groups.

Post-Activity Assessment

*Estimating Velocity:* Have students estimate the velocity at the point where the Kinetic Energy is the highest (the lowest point of their 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 = m v^{2}/ 2 for the velocity. Note: if you set the two equal (m g h = m v^{2} / 2) you do not need to measure the mass of the ball!

Have students write-up their roller coaster designs, describing what worked and did not work.

### Activity Extensions

Have students research either the history or safety of roller coasters. When was the first loop-de-loop used?

Have students calculate the potential energy of the marble at several locations along their tracks.

### Activity Scaling

For upper level students, have them conduct the suggested activity extensions. Have them also compete for the fastest ride compared to its 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/

### Contributors

Marthy Cyr; C. Shade### Copyright

© 2013 by Regents of the University of Colorado; original © 2001 WEPAN/Worcester Polytechnic Institute### Supporting Program

Making the Connection, Women in Engineering Programs and Advocates Network (WEPAN)### Acknowledgements

Project funded by Lucent Technologies Foundation.

Last modified: October 10, 2017

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