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The Ultimate Roller Coaster ContestThe-Ultimate-Roller-Coaster-Contest

  • Subject: Physical Science
  • |
  • Grade(s): 6-8
  • |
  • Duration: Three class periods

Lesson Plan Sections


Students will:
1. Understand the principle of conservation of energy.
2. Know that mechanical energy forms gravitational potential energy and kinetic energy.
3. Explain the losses of mechanical energy to heat due to friction.
4. Predict the conditions under which a person will feel lighter or heavier in a moving vehicle.


Each group should have the following:
Tennis ball (or similar-sized ball)
Two pieces of 70 cm ? 200 cm corrugated cardboard or foam board
Heavy-duty scissors
Box knife
Hot glue and glue gun


1. Tell students they will be designing and constructing cardboard "tennis ball" roller coasters with three hills. The tennis ball in each design must start from the top of the first hill, roll up and down the other two hills, and exit the end of the track. Each roller coaster will be judged in a class competition. The track with the greatest total of vertical heights for all three hills—if the tennis ball completes the course—will be named the winning design.
2. Have students consider the following when designing their roller coasters:
  • Can all the hills be the same height? If not, why? Can they get bigger or must they get smaller? How will you determine how big or how small the hills can be and still win this contest?
  • Does the steepness of the hill count? Is it better to make the hills steep or not so steep? Why?
  • How curvy should the tops of the hills and the valleys be? Should you design sharp turns or smooth turns? Why?
  • What provides resistance on the roller coaster causing the tennis ball to slow down? How can this resistance be reduced?
Note: Leave students with enough time to make revisions to their original design—an important factor in the world of design and engineering.
3. Divide students into small groups and give each group the materials listed earlier. The left and right roller coaster tracks will be made from the two pieces of corrugated cardboard that must be cut out as identical shapes. Each valley in the roller coaster must dip to a height of 20 centimeters from the bottom of the cardboard. Have students use heavy-duty scissors or a box knife to cut out both tracks. They will probably have their own ideas on how the roller coaster should be shaped, but here is an idea on how to lay out the roller coaster on the cardboard.
4. From the excess cardboard, students should cut out twenty-five 4 cm ? 12 cm rectangles. These rectangles will serve as spacers between the two cutout tracks. Put glue along both of the 12-centimeter edges and fasten them to various places between the two tracks so that the tracks are rigid and separated by a distance of 4 centimeters.
5. Here is an example of how the score for a roller coaster should be calculated for the contest. Measure the heights of each of the three required hills and add them up. The roller coaster with the greatest total height of the three hills, whose tennis ball successfully completed its journey, is the winner.

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Adaptation for older students:
High school physics students will enjoy this contest and should be encouraged to analyze the energy transitions in greater depth. Challenge your physics students to make the following calculations. Then display student answers next to the appropriate areas on their roller coasters.
  • What is the gravitational potential energy (GPE) of the tennis ball at the top of each hill?
  • Calculate the amount of GPE lost between each hill and the total energy lost to heat due to frictional interactions.
  • Determine the kinetic energy at the bottom of each hill and calculate the velocity at those locations.

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Discussion Questions

1. Consider your favorite roller coaster ride and imagine that it could be transported to the planet Mercury or the planet Jupiter. On which planet would the ride be more thrilling or less thrilling than it is here on Earth. Explain your choices.
2. Relate the principle of "conservation of energy" in an analysis of a roller coaster ride from start to finish. Include in your discussion the names of all relevant energy forms and where and when on the ride energy transformations are occurring.
3. Imagine that you are among the first group of passengers to test out a newly constructed roller coaster. The slide down the first hill is thrilling, but before you get to the top of the second hill, you start sliding backward and get trapped between the first two hills. Discuss what practicalities the designer forgot to include in transforming his creation from the idealized blueprint to the real world.
4. Some roller coasters feature an upside-down "loop." Explain why these features are always placed at the beginning of the ride and never near the end.
5. It's all fun and games until somebody gets hurt. Imagine that you are designing the world's ultimate roller coaster. Describe the features you would incorporate into your design and explain what limits you would put on those features to prevent fun from becoming dangerous.
6. Not everyone enjoys the thrilling experience of a roller coaster ride. Theorize and discuss the scientific, physiological, psychological, and sociological reasons for why some seek such thrills and others avoid them.

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The trip to school on the bus is not supposed to be as thrilling as a ride on a roller coaster, but in many ways you experience the same energy transitions at a slower rate. Starting from home, and in chronological order, describe what is happening to the bus as you experience an increase in gravitational potential energy (GPE), an increase in kinetic energy (KE), a transformation from GPE to KE or vice versa, and any transformations from the total mechanical energy (GPE + KE) into heat.

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Riding on the Gravity Express
Amusement park rides, water park rides, and rides in the local playground provide thrills while gravitational potential energy (GPE) and kinetic energy (KE) transform from one to the other. Make a list of such rides and explain where in the ride the GPE and the KE are the greatest. Where do the forces act in each ride providing the resistance that converts the total GPE and KE into heat?

The Thrill Factor
On rides such as roller coasters (and even swings), where the rider experiences fast changes in velocity due to increases or decreases in speed or simply changes in direction, the rider is subjected to unbalanced forces that give the rider an illusion of feeling heavier or lighter than normal. Through our sensing of these unbalanced forces, we judge the "thrill factor" of a ride to be high when they occur frequently in a ride. Some of the best rides give us the illusion of weightlessness for short periods of time. Where on the roller coaster would you expect to feel heavier, and where would you feel lighter? Use Newton's law of inertia to explain these illusions of heaviness and lightness, also known as positive and negative "g forces." Students can design and conduct experiments and demonstrations to back up their explanations.

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Suggested Readings

Roller Coasters, or, I Had So Much Fun I Almost Puked
Nick Cook. Carolrhoda Books, 1998.
It's all here -- the history of coasters, the physics that make them work, different types of roller coasters, and how they are designed and constructed. There are great pictures, easy-to-understand explanations, and even a section on tips for a scarier ride.

Roller Coasters
Mike Schafer and Scott Rutherford. MBI Publishing, 1998.
This book includes a history of roller coasters and sidebars explaining how they work, but primarily gives region-by-region information on the best coasters in the United States. Included are the location, length, age, and features of each. The authors also provide an unofficial top-twenty ranking of the best-of-the-best.

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Roller Coaster Physics - The Book
Tony Wayne tells us everything there is to know about the physics of energy transitions while experiencing the ups and downs on your favorite roller coaster ride.

Amusement Park Physics: Roller Coaster
Read about the principles for designing roller coasters and then immediately apply this knowledge by designing and testing your own online roller coaster.

Inventing the Scream Machine
When were they invented? How have they changed? Who are the heroes of the roller coaster industry? Starting in the 18th Century, follow the historical evolution of the modern roller coaster on this clickable and informative roller coaster history timeline

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Click on any of the vocabulary words below to hear them pronounced and used in a sentence.

speaker    principle of conservation of energy
Definition: The principle that within the universe, or any closed system, although energy may transform from one kind to another, the total energy remains constant.
Context: The principle of conservation of energy states that as potential energy transforms into kinetic energy (and vice versa), the total energy should remain constant at all times and in all places on the roller coaster.

speaker    friction
Definition: A resistance to relative motion of two surfaces that are in contact with each other as they roll or slide across one another.
Context: Due to frictional interactions between the roller coaster car and the track, the mechanical energy is lost and transformed into heat.

speaker    gravitational potential energy (GPE)
Definition: The energy that a mass has because of its vertical separation ("height") from the earth; calculated with GPE = mgh , where m is the mass, g is the acceleration due to gravity (-9.80 m / s 2 on Earth), and h is the height from some arbitrarily defined initial height.
Context: All the energy needed to run a roller coaster to the end of the track comes from the gravitational potential energy that it has when lifted to the top of the first and highest hill.

speaker    heat (thermal energy)
Definition: The atomic and molecular energy of matter due to the kinetic energy of the atoms and molecules vibrating and moving with random motions.
Context: As the mechanical energy of a system such as a roller coaster is transformed into heat, we can expect that the temperature of that system and the environment in which it exists will rise somewhat.

speaker    kinetic energy (KE)
Definition: The energy that a mass has because it is moving; calculated with KE = mv 2/2, where m is the mass and v is the velocity.
Context: As the roller coaster glides down each hill, the gravitational potential energy is converted into kinetic energy and you and the car go faster and faster.

speaker    mechanical energy
Definition: Energy generally associated with a moving mass or the action, or the potential action, of a force being applied through a distance.
Context: The two forms of mechanical energy that are relevant to the understanding of how a roller coaster works are gravitational potential energy and kinetic energy.

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This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of theMid-continent Research for Education and Learningin Aurora, Colorado.
Grade level: 6-8
Subject area: Physical science
Understands energy types, sources, and conversions, and their relationship to heat and temperature.
Knows that energy is a property of many substances (e.g., heat energy is in the disorderly motion of molecules and in radiation; chemical energy is in the arrangement of atoms; mechanical energy is in moving bodies or in elastically distorted shapes; electrical energy is in the attraction or repulsion between charges).

Grade level: 6-8
Subject area: Physical science
Understands energy types, sources, and conversions, and their relationship to heat and temperature.
Understands that energy cannot be created or destroyed but only changed from one form to another.

Grade level: 9-12
Subject area: Physical science
Understands energy types, sources, and conversions, and their relationship to heat and temperature.
Knows that all energy can be considered to be either kinetic energy (energy of motion), potential energy (depends on relative position), or energy contained by a field (electromagnetic waves).

Grade level: 6-8
Subject area: Technology
Understands the nature of technological design.
Designs a solution or product, taking into account needs and constraints (e.g., cost, time, trade-offs, properties of materials, safety, aesthetics).

Grade level: 9-12
Subject area: Technology
Understands the nature of technological design.
Evaluates a designed solution and its consequences based on the needs or criteria the solution was designed to meet.

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Ted Latham, physics and science/technology teacher, Watchung Hills Regional High School, Warren, New Jersey.

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