The city of East Lansing is trying to attract more summer tourists. They've decided to replace much of the abandoned buildings on Grand River with an amusement park. They've hired the Tyrell Corporation to build it. You and your team recently graduated from MSU engineering program and have started working for Tyrell under their chief engineering officer Dr. Eldon Tyrell. Dr. Tyrell wants your team to design the amusement park's main attraction, the Nexus-6 roller coaster. The design of the Nexus-6 is such that a single occupant is strapped into a body suit that has a single connecter near the middle of the back of the suit, which connects to a metal alloy cable. This cable is attached to a well-oiled apparatus that slides along the track of the roller coaster.

The design calls for an initial hill that rises well above much of the EL skyline and easily the tallest coaster in the world while the rider is suspended underneath the track. The rider then drops down into the first of several loop-the-loops achieving a speed at the bottom of the first loop (pictured above) of 150 mph (the world's fastest coaster surpassing Dubai's Formula Rossa). All the while the rider is suspended on the outside of the loops. People are calling Dr. Tyrell a crazy man for conceiving of such an idea. Your team has been tasked with developing the detailed plans that demonstrate the ride will be safe, particularly with respect to the single metal alloy cable suspension system. Below is experimental data collected on the metal alloy. Don't let Eldon down.

Your team has decided to go on a retreat to the Overlook Hotel in the middle of the Colorado Mountains after the successful design of the Nexus-6 Rollercoaster. As you spiral up into the mountains the path becomes more and more treacherous with the road becoming very icy and banked. You stop at a gas station before you reach the most dangerous part of your trip a 125m radius curve banked at 22.2 degrees. You want to take the curve at a speed of 25 km/h. There are several different types of tires available for purchase at the gas station (frictional coefficient and width). You need to figure out information to help you decide on the type of tire that you should use.