Project 8: Breakneck -- The new roller-coaster at Michigan's Adventure

You are a team of engineers and scientists who are in the process of designing Michigan's Adventures exciting a new attraction “Breakneck”. This ride involves a roller-coaster like car that can hold 8 passengers, with a mass of 700 kg. This car starts by effectively free falling 60m. The track curves at the bottom so that the car can slide up an 8-m-high hill before hitting a horizontal straightaway 50m long. In the middle of the straightaway is a section of track that is used to slow the car down. You can have the car brake over any or all of the 10m length of that section.

Then at the end of the straightaway, a spring-like device hooks under the car. This device changes the car’s direction just in time to prevent it from apparently falling over the end of the track, sending it back over the braking section again, stopping neatly at the end of the braking area. The car should stop at the end of the braking section, on the way back towards the launch pad.

Your tasks are (a) to decide on an appropriate braking force and length of the braking region needed on the straightaway to stop the car at the right location, and (b) the effective spring constant of the turnaround device. The car has special accelerometers mounted which relay that information, and adjust the braking force to provide the acceleration you request. The most important piece of information for these devices is that a person can safely sustain accelerations of 3-4 “g’s” for a brief time, but not more than that.