Key concepts
Physics
Gravity
Potential energy
Kinetic energy
Friction
Conservation of energy

Introduction
Have you ever ridden a roller coaster? Have you ever wanted to design your own? There are plenty of expensive toys and even video games that will let you build your own coasters—but in this project you’ll make one out of paper and tape and learn about roller coaster physics along the way!

Background
Roller coasters are all about physics! Unlike other vehicles, such as cars and trains, roller coaster cars do not have an engine that propels them. Instead they rely on gravitational potential energy, which they gain by initially being towed up a large hill. (There are other kinds of potential energy, such as elastic potential energy, which is the kind you get when you stretch a rubber band. In this project will be referring just to gravitational potential energy.)

Potential energy is “stored” because of an object’s elevation or height off the ground. When the coaster car starts going down the hill the potential energy is converted into kinetic energy, or the energy of motion. When the coaster car goes back up another hill it will lose kinetic energy (slow down) and gain some potential energy again. Some of that is also converted to heat due to air resistance and friction with the track, gradually causing the coaster to slow down. This process continues as the coaster car goes through loops, hills and turns until eventually it comes back to the beginning.

Due to conservation of energy (the total amount of energy in the system must be conserved), the total amount of kinetic energy and energy lost due to friction can never exceed the initial amount of potential energy the coaster car has. That means roller coaster designers have to make sure the coaster has enough initial potential energy to make it through the rest of the track. This places some limits on the design. For example, the coaster car can’t go through a loop or over a hill that is taller than the initial hill because going higher would require more energy than it has available. If the track is too long, friction might eventually cause the coaster car to come to a complete stop. In this project you will take these factors into consideration as you design your own coaster.

Materials

• Several pieces of paper (Construction paper works well.)
• Tape
• Scissors
• Ruler
• Pencil
• Piece of corrugated cardboard (as large as you would like your roller coaster footprint to be)
• Marble
• Helper (optional)

Preparation

• Create segments for your roller coaster track!
• To build a straight track piece: Cut a three-inch strip of paper. Use a ruler and pencil to draw lines that divide it into three one-inch-wide segments. Fold the outer two segments up 90 degrees along these lines.
• To build a loop or a hill track piece: Start with the same steps you used to make a straight piece. Then make marks every inch along the two long sides of the paper. Cut inward from these marks to the long lines you drew, forming one-inch square tabs on both sides of the strip. Fold these tabs up 90 degrees. Now you can bend the paper to make hills or loops. Tape the tabs together to make the paper hold its shape. This part can be easier with a helper—one person to hold the paper in place, and the other person to do the taping.
• To build a curved track piece: Start with the same steps you used to make a straight piece. Make marks every inch along one long edge of the paper. Then make two-inch cuts inward from these marks. Now fold the uncut side of the paper 90 degrees, and fold the one-inch tabs on the other side up 90 degrees. The bottom portion of this track piece is flexible because it has cuts in it so you can bend it horizontally to form a curve. Tape the tabs together to make the paper hold its shape.
• To build a support strut: Cut a 2.5-inch-wide strip of paper. Use a pencil and ruler to draw lines dividing it into five 0.5-inch segments. Crease along these segments and then fold them into a square shape (so two of the segments overlap) and use tape to hold them in place. Make one-inch cuts along the edges from one end, and then fold the resulting tabs outward. This will allow you to tape the tabs flat to a piece of cardboard, so your support strut can stand vertically.
• Make sure all curves, loops and hills are gradual. Avoid sharp corners or your “roller coaster car” (your marble) might crash and come to an abrupt stop.

Procedure

• Before you start building, plan out a design for your roller coaster. Draw your design on paper, and figure out how many supports and pieces of track you will need. Remember to consider the information in the “Background” section for your design. Make sure your marble starts at the top of a hill!
• Using a piece of corrugated cardboard as a base, assemble your track according to your plan. Tape the track segments together end to end to connect them.
• Place the marble at the top of your track and let it go. Watch carefully. What happens? Does it make it the whole way through the track?
• If the marble made it the whole way to the end, try making your track longer by adding more pieces. How long can you make your track before the marble comes to a stop?
• If your marble didn’t make it to the end, try to figure out why. Is there a spot in your track where the marble got stuck? Was the marble going too slowly to make it through a loop? If necessary, make changes to your design, such as making the curves more gradual or the initial hill taller to give the marble more potential energy. Try again. Can you get your marble to finish the track?
• Extra: You can also make roller coasters from foam pipe insulation (available at a hardware store) instead of from paper. This will allow you to make a much bigger coaster more quickly because it doesn’t involve as much cutting, folding and taping. See the “More to explore” section for examples.

Observations and results
If you followed the guidelines discussed in the “Background” section, you should have been able to design a working roller coaster. Because some energy is always lost to friction, your initial hill needs to be taller than any subsequent hills or loops so the marble has enough energy to make it through. The taller your initial hill, the longer your track can be. If your track had any turns that were too sharp, the marble might have collided with the walls and lost a bunch of energy in the collision. (This energy goes into bending the paper.) That would be painful or even dangerous for the riders if this was a real coaster! That’s why it’s important to make sure turns are smooth and gradual.

More to explore
Build a Paper Roller Coaster, from Science Buddies
Roller Coaster Marbles: How Much Height to Loop the Loop?, from Science Buddies
Energy Transformation on a Roller Coaster, from the Physics Classroom
Speedy Science: How Does Acceleration Affect Distance?, from Scientific American
Science Activities for All Ages!, from Science Buddies

This activity brought to you in partnership with Science Buddies