Hypercoaster

What makes a safe roller coaster?
What makes a roller coaster fun?

Valerie Chang
and
Alice Lin

Materials (for each group):

• 2 or more lengths of pipe insulation
• tape
• marbles (be sure each team has one the same size and weight)
• stopwatch
• steel ball
• scissors

Directions:
Cut pipe insulation in half to make two long chutes. Each group should make a coaster using tape to stick it together and using furniture as supports. Build as crazy a ride as you can that still delivers the marble to the finish.

• What limits the height of your loops?
• What limits the length of your coaster?
• How sharp can you make your turns?

Questions:

• Why can't you make your loops as high as you want?
• Why can't you make your coaster as long as you want?
• Why did the steel ball roll down faster than the marble?

Explanation:
All three questions can be answered by an understanding of energy. Without energy, the ball cannot move. At the beginning of the coaster, the ball has someamount of potential energy, that is, some amount of energy proportional to the height off the floor that the ball is. Immediately after you let the ball go, if you don’t push it, it has zero kinetic energy, that is, energy of motion. The relationship between potential energy and kinetic energy is that their total, the total amount of energy, is always the same. At the top of a hill, when the ball is barely moving, almost all of the energy is potential energy. As the ball rolls down the hill, it speeds up as some of that potential energy is transformed into kinetic energy. At the very base of the coaster, the ball is rolling it’s fastest, when all the potential energy has been turned into kinetic energy.

Hence, this means that the ball can never climb a hill, or go through a loop that is higher than its beginning hill (that would mean that it spontaneously gained energy!).

So then with this knowledge in energy, lets turn to the marble vs steel ball problem. Why did the marble roll down the coaster slower than the steel ball? The answer to this question lies in the potential energy. It turns out that the potential energy is not only proportional to height off the floor, it is proportional to mass as well! The more massive the ball is, the more potential energy it starts with. So if both the marble and steel ball start out with all other things equal, the steel ball has the advantage of more potential energy. At the bottom of a hill, this greater potential energy translates into greater kinetic energy (ie more speed!).

So then, if truly, at all points, the energy is always the same, why can’t the roller coaster extend forever, and why does it sometimes fail to climb a hill or roll through a loop that was not as high as it’s initial hill? That is because the energy really is not the same at all points in the coaster. As the ball speeds through the insulation, it encounters friction. Friction is what causes the track to heat up right after the ball has rolled through. Well, guess what, this heat is a form of energy too! And since energy is never spontaneously created, this energy has come from the energy of the ball. This means that as the ball rolls, it continuously loses some of its energy, and eventually will run out of energy and stop.

Resources:
Roller Coaster Physics: http://141.104.22.210/Anthology/Pav/Science/Physics/book/home.html

Hypercoaster: http://www.ktca.org/newtons/14/hypercoaster04.html

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