Modern roller coasters have vertical loops. 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.

(a) what is the speed of the roller coaster in m/s at the top of the loop if the radius of curvature there is 14 m and the downward acceleration of the car is 1.4 g?
(b) how high above the top of the loop must the roller coaster start from rest, assuming negligible friction?
(c) if it actually starts 5 m higher than your answer to the previous part, how much energy did it lose to friction? its mass is 1400 kg.