Feb 12, 2013 · A student has a weight of 650 N. While riding on a roller-coaster this same student has an apparent weight of 1.97 x 103 N at the bottom of a loop that has a radius of 17.0 m. The speed of the roller-coaster is I just need the forumla, doesn't even have to be manipulated. Modern roller coaster loops are not circles: clothoids (Cornu spirals) and other mathematical curves have been introduced to obtain a smaller radius of curvature at the top and to avoid the sudden onset of large forces on the rider [1–4]. In this paper, the word ‘loop’ will be used as a shorthand for a vertical roller coaster loop. where A is the acceleration, V is the velocity, and r is the radius. However, if an entire loop were a circle with constant radius, there would be two big problems: 1. The roller coaster slows down as it climbs the loop, so centripetal acceleration would drop near the top. 2. Modern roller coasters have vertical loops like the one shown in the figure below. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats.