Paper Roller Coasters: Kinetic and Potential Energy

Background Information for Teachers

Roller coasters are an excellent way to teach your students about conservation of energy. Gravitational* potential energy is the amount of energy an object has due to its mass and its height off the ground. Kinetic energy is the amount of energy an object has due to its mass and its speed. When a roller coaster car reaches the top of its very first hill, it is very high off the ground but moving very slowly. That means it has a lot of potential energy but very little kinetic energy. When it goes over the top and starts going down the hill, its height rapidly decreases and its speed increases—the potential energy is converted to kinetic energy. When it goes back up the next hill or loop, its height increases and it slows down—some of the kinetic energy is converted back to potential energy. As the car goes on through the coaster track, energy is continually converted back and forth between kinetic and potential energy, but the total amount of energy is conserved. The "Roller Coaster Model Interactive" reference in the Additional Background section shows this with an interactive animation.

If you watch the roller coaster model animation, you will notice that the roller coaster car goes back and forth forever. In reality, you know that can't be true—eventually the car would slow down and come to a stop because of friction. While some energy is "lost" due to friction with the track and air resistance, this energy does not "disappear." It is converted to thermal energy. The total amount of energy is still conserved.

Why is this information useful? It puts practical limits on the length of the track and the height of loops/hills the roller coaster can go through. Conservation of energy means that, assuming the coaster cars are only towed up the first hill (and not any subsequent hills), a roller coaster can never make it through a loop/hill that is taller than the initial hill. Doing so would require more energy than the coaster had available to begin with, as shown in Figure 1. Because of friction, eventually a roller coaster will slow down and come to a stop, even if all the subsequent hills/loops are shorter than the first one (Figure 2).

Image Credit: Ben Finio, Science Buddies / Science Buddies
Figure 1. In this figure: the coaster starts out at the top of the first hill with maximum potential energy (PE) and almost no kinetic energy (KE) (1). As it goes down the hill, it gains KE and loses PE (2). At the bottom of the hill, it has maximum KE but almost no PE (3). As it goes back up the hill, it loses KE but gains PE again (4). It can never get to the top of the second hill because it does not have enough energy (5). Instead, it will roll back down and eventually settle at the bottom (3).

Image Credit: Ben Finio, Science Buddies / Science Buddies
Figure 2. In this figure, the second, third, and so on hills are all shorter than the first hill (1). However, because of friction, the roller coaster will still eventually come to a stop (4).

In this lesson your students will build their own roller coasters and experience these principles first-hand. You will challenge them to design a coaster that can make it through a large second hill/loop, and explain why their coaster can (or cannot) make it all the way to the finish.

*There are different types of potential (stored) energy, such as elastic potential energy (the energy you get from stretching a rubber band or a spring) or chemical potential energy (the energy stored in a battery). Usually the context makes the situation clear, so when talking about roller coasters we just say "potential energy" instead of "gravitational potential energy."

Additional Background Links

• Kinetic Energy, Ducksters
• Potential Energy, Ducksters
• Kinetic Energy, The Physics Classroom
• Potential Energy, The Physics Classroom
• Energy Transformation on a Roller Coaster, The Physics Classroom
• Roller Coaster Model Interactive, The Physics Classroom

Prep Work (15 minutes)

1. Search online for photos and/or videos of roller coasters that you can show your students. Try to find pictures that show the entire roller coaster, not close-ups of individual sections. Ideally, such pictures will show that the coaster's first hill is taller than all the subsequent hills and loops. This picture is a good example.
2. Optional: try building a simple roller coaster yourself, like the one shown in Figure 3. This will give you some experience building the coasters, along with a sense of how much time your students will need. If you are not working from a kit, print out a copy of the template (in English or Spanish). Printing on cardstock works best. To build the track pieces, cut them out along the solid lines, then fold along the dotted lines and tape the segments together to make the track hold its shape. Watch this video for assembly instructions. Note that the printable template includes optional funnel pieces (not pictured here).

Image Credit: Ben Finio, Science Buddies / Science Buddies
Figure 3. A basic paper roller coaster design.

Engage (5 minutes)

Ask your students if anyone has ever ridden a roller coaster. If you live near a popular amusement park, you could mention it as an example. Show them at least two pictures of a roller coaster, like this one. If you have internet access in your classroom, let them find some pictures on their own.

What differences do you notice between all the different roller coasters? Do they have any similarities?

All the roller coasters have some form of track and a car or train of cars that carries the riders. They generally consist of features like hills, loops, twists, and turns. However, there are also many differences between roller coasters. Some are metal, some are wood, in some the riders sit on top of the track, in others they hang below it, some go upside-down, some don't, etc. Students might notice that the first hill (the one the cars get towed up) is always taller than the other hills and loops, but don't give this away if they don't notice it.

Introduce the terms energy, kinetic energy, and potential energy. You can do so with a simple demonstration:

1. Explain that in general, "energy" is the ability to change something (lift an object, push an object, etc). Energy comes in many different forms. We will only talk about some of them in this lesson.
2. Make a simple ramp (e.g. a clipboard with one end propped up on a stack of books).
3. Hold a marble at the top of the ramp. Explain that right now, the marble has no kinetic energy, the energy of motion, because it is not moving. The marble does have gravitational potential energy, the energy an object has due to its height off the ground.
4. Release the marble and watch it roll down the ramp onto the floor/desk. Watch as the marble gains speed. Explain that as the marble rolled down the ramp, it lost gravitational potential energy (its height decreased) but gained kinetic energy (its speed increased). Its potential energy was converted into kinetic energy.
5. After leaving the ramp, the marble slows down and rolls to a stop because of friction. The energy did not "disappear," but was converted into thermal energy (which we commonly refer to as heat), another type of energy. If the marble crashed into anything, some of the energy may have been converted into acoustic energy (sound). The total amount of energy did not change.
6. Ask what students think would happen if the marble rolled back up another ramp. That's what they will investigate in this lesson by building roller coasters.

Explore (45 minutes)

1. Walk the entire class through building the initial hill using two "support" pieces and one "hill/loop" piece from the template (Figure 4). This will give the students practice with cutting, folding, and taping the pieces. This process can be easier if one person holds the track in place while another person applies tape.

Image Credit: Ben Finio, Science Buddies / Science Buddies
Figure 4. The roller coaster's initial hill.

2. Let each group experiment with rolling the marble down their hill to observe how it gains speed, and whether they need to add additional tape/supports to make their hill sturdier.
3. Now explain that their goal is to design and build the next section of their roller coaster, which should be either a hill or a loop. They want to make this an exciting roller coaster for the riders, so it should have a big loop or hill, not a boring little one. Ask each group to discuss how they could do this, based on what they know about kinetic and potential energy. They can use the student worksheet to make a drawing of their track design. Encourage students to make their drawings "to scale," meaning the relative heights of the different parts of the track should be accurate.
4. After they have agreed on a design, they should build their roller coaster.
5. Now, each group should test their track design without permanently taping the loop/hill segment into place. Instead, one person can operate the marble, while one or two other group members hold the track pieces in place. This will allow them to experiment and change the shape of their track before finalizing it.
6. Tell students to test their track by placing the marble at the top of the hill and releasing it. Watch carefully and observe whether the marble makes it through the loop/hill to the end of the track. They should record their observations on the student worksheet.
7. Now students should discuss what they observed with their group members. What happened to the marble? Did it make it all the way to the end? Did it get stuck anywhere or fall off the track? If so, can they figure out why that happened? What changes could they make to their track so the marble can get all the way through, or what modifications could make it more thrilling? This could be a good point to stop and have a brief discussion as a class.

   What did you observe when you tested your roller coasters? Can you explain the marble's motion in terms of energy? Does all the energy stay in the marble, or is it transferred to other forms?

   As you demonstrated with the ramp, the basic idea is that as the marble rolls down the hill, it loses potential energy but gains kinetic energy. In an ideal roller coaster with no friction, the sum of these two forms of energy would always remain the same. However, some of the marble's energy is converted to other forms. Some of it is converted to thermal energy (heat) because of friction. If the track is not sturdy enough, some of the energy could go into bending and flexing the track and supports (this energy is stored as elastic potential energy, the type of energy you get when you stretch a rubber band). If some of the turns in the track are too sharp, the marble's energy could be converted to acoustic energy (sound) when it crashes into the walls. Eventually, all the marble's kinetic and potential energy will be converted to other forms, and the marble will come to a stop.

8. Students should modify their track based on the discussion and test it again. What happens this time?
9. Students can keep trying to improve their coasters as time allows, continuing to document changes in their worksheet (use additional pages if necessary). If their first part is "working," they can also use extra paper to add more sections to their track. Keep them aware of the remaining time and let them know that they will need to permanently tape their coaster in place when time is up.

Reflect (10 minutes)

Discuss the results as a class, remembering to discuss the roller coaster's behavior in terms of energy. Prompt discussion with the following questions:

• What problems did groups encounter when testing their initial roller coaster designs? Did any groups encounter similar problems?
• What changes did you make to address these problems? Did groups find different solutions to these problems?
• Were any groups unable to get their roller coaster working in the allotted time? Can the class identify what went wrong and offer suggestions to fix it?

Allow each group to briefly show and demonstrate their roller coaster to the rest of the class.

Assess

• Ask each group to explain their roller coaster's operation to you in terms of energy and conservation of energy. At each point along the track, what type(s) of energy does the marble have? Qualitatively, how much of each type? Where else does energy go in the system?
• Ask each group to give the same explanation for a different group's roller coaster.

Make Career Connections

Discussing or reading about these careers can help students make important connections between the in-class lesson and STEM job opportunities in the real world.

Civil Engineers

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Career Profile

Did you notice your roller coaster track wobble, or even break, as the marble zipped around it? Civil engineers design huge structures like buildings, bridges—and yes, even roller coasters—and make sure those structures can safely withstand the forces they are subjected to. Roller coaster tracks are subjected to high forces (pushes or pulls) as the cars zoom through loops and around turns, and civil engineers must make sure the track is sturdy enough to keep the riders safe. Read more

Lesson Plan Variations

• Let the students expand their coasters by adding more segments. You can print additional templates or let them use rulers to draw and then cut out their own pieces.
• You can build larger roller coasters using foam pipe insulation, as shown in these Science Buddies projects:
  • Marble Roller Coaster: How Much Height to Loop the Loop?
  • Marble Roller Coaster: Converting Potential Energy to Kinetic Energy
• Have multiple groups work together to build a single, larger roller coaster. For example, a coaster could go between three levels (a desk, a chair, and the floor). Each of three groups could be responsible for building one section of the coaster, and their tracks must connect together to get the marble all the way from the desk to the floor.
• Compare heavier and lighter marbles and explore if the mass of the ball makes a difference (for example, a glass marble vs. a steel ball bearing of the same diameter).