A roller coaster car (mass= 988 kg including passengers) isabout to roll down a

Question

A roller coaster car (mass= 988 kg including passengers) isabout to roll down a track. The diameter of the circular loop is20.0 m and the car starts out from rest 40.0 m above the lowestpoint of the track. Ignore friction and air resistance. (a) At whatspeed does the car reach the top of the loop? (b) What is the forceexerted on the car by the track at the top of the loop? (c) Fromwhat minimum height above the bottom of the loop can the car bereleased so that it does not lose contact with the track at the topof the loop? The answers are: (a)19.8 m/s (b)29.0 kN (c) 25.0 m. I amhaving trouble working this problem out. Help? A roller coaster car (mass= 988 kg including passengers) isabout to roll down a track. The diameter of the circular loop is20.0 m and the car starts out from rest 40.0 m above the lowestpoint of the track. Ignore friction and air resistance. (a) At whatspeed does the car reach the top of the loop? (b) What is the forceexerted on the car by the track at the top of the loop? (c) Fromwhat minimum height above the bottom of the loop can the car bereleased so that it does not lose contact with the track at the topof the loop? The answers are: (a)19.8 m/s (b)29.0 kN (c) 25.0 m. I amhaving trouble working this problem out. Help?

Explanation / Answer

a) At the top of the loop            v =[2g (H - 2R)]              = [2 * 9.8 ( 40 - 20)]              =19.8 m/s b) F = m v2 / R - mg          = 988 * 392 / 10 - 988 * 9.8    = 29047.2 N c) h = 5R / 2 = 5 * 10 / 2 = 25 m

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