You are a team of Imagineers at Disneyland Paris, designing a new attraction. This ride involves a roller-coaster-like car: Physics Report, UCD, Ireland

Question

You are a team of Imagineers at Disneyland Paris, designing a new attraction. This ride involves a roller-coaster-like car that can hold 8 passengers, with a mass of 700 kg, starting 66 m up in the air. This car starts by effectively free-falling 60 m.

The track curves at the bottom so that the car can slide up an 8-m-high hill before hitting a horizontal straightaway 50 m 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 10 m 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, and stopping neatly at the end of the braking area.

The car should stop at the end of the braking section, on the way back toward the launch pad.

Below is a crude cartoon of the ride:

Tasks

• To decide on an appropriate braking force and length of the braking the region needed on the straightaway to stop the car at the right location, and
• The effective spring is 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.