Over Thanksgiving break I had a conversation with my family about amusement parks and rollercoasters. One night I decided to do some research on some recently constructed rides. Cedar Point amusement park in Ohio recently unveiled their newest ride, Valravn. This is the tallest dive coaster ever constructed. The train is towed up to the top of the coaster, 68 m high and drops freely. In total the drop is 65 m long. Using the conservation of energy equation, I was able to calculate exactly how fast the train is going at the bottom of the drop. I used an initial height of 65 m and set the base of the drop at 0 m in order to find the final velocity. I chose to neglect air resistance at first in order to find what the final velocity would be with no non-conservative forces acting on the system.
The Valravn has a top speed of 75 mph. That means air resistance and possibly some friction between the train and the track it is on have slowed the train down. But, the major non-conservative force acting on the system should be air resistance, which is a drag force.
Unfortunately, I was not able to find the specs for the train, and was therefore unable to determine the cross-sectional area and I did not have the drag force constant. But, the amount of kinetic energy lost was equal to
But, because I was not able to find the mass of the train and the passengers, I was not able to determine the amount of energy lost to air resistance and friction.
This rollercoaster is a great example of the conservation of energy, because this is a free fall coaster. All of the energy used to carry the riders throughout most of the 1 minute 58 second ride is all in the form of potential energy at the top of the ride, and is converted to kinetic energy as the train falls towards the earth.