Question

A roller-coaster car has a mass of 498 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and- down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and Bare parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively. (a) If the vehicle has a speed of 20.5 m/s at point , what is the force exerted by the track on the car at this point? V (b) What is the maximum speed the vehicle can have at B and still remain on the track? m/s

Answer 1

Fc is centripetal acceleration.

F, a) tatal force exerted, F= mg + Fc R Mv2 a 498x20.52 < = 20.9 KN 10 4988 9.8 4.8 kN mgz F= 20.9+4.8 [F= 25.7 kN 7 by Fez mg -> Mov? = mg maximum kelouty, v=Jg R2 . = 19.8x15. = - R2 maximum V = 12.12 m/s

a) Fc and mg is acting downward

for staying in the track the roller coaster centripetal force should be <= Mg ( here Fc is acting upward)