A small bead can slide without friction on a fixed circular wire hoop of radius…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A small bead can slide without friction on a fixed circular wire hoop of radius 0.40m placed in a vertical plane. The bead is given a speed v at the lowest point so that it moves in a complete vertical circle.
(i) Identify which real force(s) contribute to the required centripetal force at (a) the lowest point, (b) a point where the bead is horizontal, and (c) the highest point of the circle.
(ii) Derive the minimum speed vmin that must be imparted at the lowest point so that the bead just maintains contact with the hoop at the highest point.
(iii) For the speed equal to vmin, determine the normal reaction between the bead and the hoop at the lowest point and at the highest point.