The Flip-Flap Railway in Coney Island, one of the first loop-the-loop roller coasters, had a loop of diameter 7.62 meters. It also purportedly had the nasty tendancy to snap the passengers' necks because of its exactly circular loop. . . Roller coasters today have loops that are more elliptical.
a. Calculate the minimum height above the bottom of the loop required to achieve enough speed so that the coaster does not loose contact with the track.
b. How many g's do the passengers experience at the loop bottom upon entering the loop?
c. Engineers are bringing back a modified version of the ride! In this version the passenger car (total mass of people plus car, m) collides with an empty car (mass, me = (sqrt(2) ? 1)m) at the location indicated in the figure to the right. The cars stick together and ride the rest of the way along the track. Write down the equations needed to find the minimum height above the bottom of the loop required in this case.
d. Solve for the minimum height required, carefully indicating any assumptions you made during your solution.