A roller-coaster car of mass is released from rest at a point P that is a vertical…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A roller-coaster car of mass m is released from rest at a point P that is a vertical distance h above the station level. The track is frictionless until the car has cleared a vertical loop of radius R whose top is 20m above the station level. Immediately after the loop, the car enters a straight 30m-long brake run in which kinetic friction with coefficient μk acts until the car comes to rest.
(a) Derive an expression for the minimum value of h that allows the car to just maintain contact with the track at the top of the loop.
(b) Using your result from part (a), determine the distance the car travels along the brake run before coming to rest, expressed in terms of the given quantities and fundamental constants.
(c) Suppose the initial release height is 1.10 times the minimum found in part (a). Determine the speed of the car at the end of the brake run, showing all reasoning.
(d) Discuss qualitatively how increasing μk would affect the required initial height for the car to come to rest exactly at the end of the brake run, keeping all other parameters fixed.