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.

Stress-strain curve for Metal Alloy https://chart-studio.plotly.com/~PERLatMSU/17.embed

You are working for a Nascar team and an engineer on the team called Cole Trickle believes that he has come up with an ingenious plan. He thinks that he can drastically reduce the ability of tires to create side friction and still stay on the track (side friction is friction occurring either up or down the track to keep you at a constant vertical position on the road when it is inclined - see diagram). The team boss says this is a ridiculous idea and asks how will the car stay on the road, he turns to you and asks you to develop a computational model that proves whether the car will stay on the track or not. You have started some code and it needs finishing.

Here is the starter code:

https://www.glowscript.org/#/user/paul.w.irving/folder/Public/program/Nascar

After the success of your model, the team boss has decided to employ your modeling skills to check whether it is safe to go on his winter vacation. He wants to know what speed he would need to be traveling to go in uniform circular motion around a mountain road if he has tires that have a coefficient of friction of .36 and is going around a mountain road of a radius 125 meters and the road is inclined at 22.2 degrees.