Consider the roller coaster shown above. The cars are launched with some initial
ID: 2217085 • Letter: C
Question
Consider the roller coaster shown above. The cars are launched with some initial velocity, vi, go down a hill of height h1 = 2.0 m, and over the first peak a height h2 = 6.0 m above the bottom of the track. This first peak has a radius of R = 8 m. If you want the passengers in the car to feel weightless (no force from the coaster seat) at the top of the hill, what is the smallest initial velocity vi that will allow this? (Neglect friction and air drag in this problem.) Give your answer in m/s to three significant figures.
Explanation / Answer
let force at top of hill be v' and vi = v to experience weightlessness, no force so mg = mv'^2 /r so v' = 8.86 m/s let speed = v initial energy = 0.5mv^2 final energy = 0.5mv'^2 + mg(h2-h1) both are equal so 0.5v^2 = 0.5*8.86^2 + 9.8(4) so v = 12.53 m/s vi = 12.53 m/s