Two small beads of equal mass slide without friction on separate circular rails…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Two small beads of equal mass slide without friction on separate circular rails mounted horizontally. Rail 1 has a radius of 0.20 m, and Rail 2 has a radius of 0.35 m. Motors drive the beads so that each bead takes exactly 1.8 s to complete one revolution around its rail.
(a) Show algebraically that the ratio of the linear speeds of the beads is equal to the ratio of their rail radii.
(b) Calculate the linear speed of each bead.
(c) Determine the magnitude of the centripetal acceleration for each bead.
(d) Compute the ratio of the centripetal accelerations ac,1:ac,2 and explain how this result follows logically from your work in part (a).
(e) Suppose both rails were redesigned so that the beads instead complete each revolution in the same amount of time T′ that is one-third as long as before. Without explicit numeric calculation, state how the centripetal acceleration of each bead would change. Provide a clear justification based on proportional reasoning.