A roller-coaster car of mass is released from rest at point P
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A roller-coaster car of mass m is released from rest at point P, a height H above the lowest point of the track. After descending, the car enters a vertical circular loop of radius R that lies in a vertical plane. Assume the track is perfectly smooth and the size of the car is negligible compared with R.
(a) Derive an expression for the speed vT of the car when it reaches the top of the loop in terms of H, R, and fundamental constants.
(b) Determine the minimum height Hmin (in terms of R) required for the car to maintain continuous contact with the track at the top of the loop.
(c) Let R=12m and H=2.8R. Calculate the magnitude of the normal force exerted on the car by the track (i) at the top of the loop and (ii) at the bottom just before entering the loop.
(d) Discuss qualitatively how increasing the loop radius while keeping the initial height fixed would affect the normal forces experienced at the top and bottom of the loop.