Here is an explanation from Science Buddies.org behind how a Roller Coaster works:
Slow and clanking, the string of cars is pulled up to the crest of the tallest point on the roller coaster. One by one, the cars start downhill on the other side, until gravity takes over and the full weight of the train is careening down into curves, twists, and turns. The roller coaster is a great example of conversions between potential energy (stored energy) and kinetic energy (the energy of motion). As the cars are being pulled up to the top of the first hill, they are acquiring potential energy. The chain that pulls them up the hill works against the force of gravity. At the top of the hill, the cars' potential energy is at it's maximum. When the cars start down the other side, this potential energy is converted to kinetic energy. The cars pick up speed as they go downhill. As the cars go through the next uphill section, they slow down. Some of the kinetic energy is now being converted to potential energy, which will be be released when the cars go down the other side.
You've probably noticed that the first hill on the roller coaster is always the highest (unless the coaster is given another "boost" of energy along the way). This is because not all of the potential energy is converted to kinetic energy. Some of the potential energy is "lost" in other energy conversion processes.
You can investigate the conversion of potential energy to kinetic energy with this project. There are as many possible variations to this project as there are twists and turns on a great roller coaster ride, but a good place to start is to see how much initial height you need in order to have your marble successfully navigate a loop in the track.
You'll use the same size loop for each of your tests, but you'll add (or subtract) track before the loop so that you can change the initial height where the marble starts. For each track configuration, you should try at least 10 separate tests with the marble to see whether it can loop the loop or not. You should also measure the slope of each track configuration. An easy way to think about the slope is the expression rise/run (see the illustration below). The rise is the height of the starting point, and the run is the horizontal distance from the starting point to the beginning of the loop.
The illustration above shows how to measure "rise" and "run" in order to calculate the average slope of the track leading in to the loop.
How much height (rise) will be required to successfully navigate a given loop size? A foam roller coaster for marbles is easy to build, so try it for yourself and find out!
Oh oh - I did it again Grade 5 ... my lesson turned in a Maths lesson ...
So you will need to measure the height (rise) and the run (length along the bottom) of your first hill run on your coaster.
I wonder how these numbers will compare? My challenge to you is to make a successful loop de loop.