A thrill-ride designer is comparing the forces experienced by a rider at three key…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A thrill-ride designer is comparing the forces experienced by a rider at three key locations on a perfectly circular vertical loop of radius r: (1) the very top, (2) the very bottom, and (3) a point on the side of the loop where the rider is horizontally level with the center. At each location, the rider maintains the minimum speed necessary to keep the cart in continuous contact with the track.
(a) For the top of the loop, identify the direction of each force acting on the rider and explain the relationship that must exist between those forces to ensure contact is maintained.
(b) At the bottom of the loop, describe how the forces on the rider combine to provide the required inward acceleration, and compare the magnitudes of these forces with those at the top.
(c) At the side location, analyze the directions of the relevant forces and explain why the minimum speed there is different from that at the top.
(d) Summarize how the minimum speed required for contact varies around the loop and connect this variation to the changing roles of gravitational and contact forces.