2020/10/29 by Zafar Ahmed, Ahmed, Zafar, Amal Nathan Joseph +1
Physics and Astronomy · #Classical Physics (physics.class-ph) #Experimental and Theoretical Physics Studies #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.2010.15514
openalex publication_date 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a particle has to fall first vertically 1 m from A and then move horizontally 1 m to B, it takes a time t(=τ1+τ2=τ3=3/√(2g))=0.67 s. Under gravity and without friction, if it sides down on a linear track inclined at 450 between two points A and B of 1 m height, it takes time t(=τ4=2/√(g))=0.63 s. Between these two extremes, historically, Bernoulli (1718) proved that the fastest track between these points A and B is cycloid with the least time of descent t=τB=0.58 s. Apart from other interesting cases, here we study the frictionless motion of a particle/bead on an interesting track/wire between A and B given by y(x)=(1-xν)1/ν. For ν> 1 the track becomes convex and t>>τ4, and when ν>1.22, the motion with zero initial speed is not possible. We find that when ν∈ (0.09653, 0.31749), τ4