Consider the roller coaster shown above. The cars are launched with some initial

Question

Consider the roller coaster shown above. The cars are launched with some initial velocity, vi, go down a hill of height h1 = 2.5 m, and over the first peak a height h2 = 6.5 m above the bottom of the track. This first peak has a radius of R = 10 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

to feel weightless the gravitational force should provide the necessary centirpetal force

mg = mv22/R

v2---> velocity at the peak , R--> radius of the peak

v22= Rg

applying conservation of energy at point h1=1 and h2=7

mgh1+0.5m(vi)2= mgh2 + 0.5m(v2)2

vi=[2g(h2-h1)+gR]

=205.8=14.34 m/s

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