Ring moves on curved path faster

[apr]

A ring on curved path (say on bent rod) will move longer distance than the one moves on straight line in same interval of time (the two rings are released simultaneously - one moves on curved path and other one moves horizontally) - How to explain? by which principle one can explain?

 

[Doc Al]

A ring on curved path (say on bent rod) will move longer distance than the one moves on straight line in same interval of time (the two rings are released simultaneously - one moves on curved path and other one moves horizontally) - How to explain? by which principle one can explain?

Do you have a diagram to illustrate what you mean? Assuming I understand you correctly, why do you think the two rings taking different paths will travel from A to B in the same time?

 

[rcgldr]

My guess is that the original poster question is similar to which path is best for gravity to pull a ring on a frictionless wire to get from point A to point B in the shortest time. If the goal is to get the same time as a straight line from A to B, then the path of shortest time could be modified in numerous ways to get the time to be the same.

 

[WannabeNewton]

This is the so called Brachistochrone problem: http://en.wikipedia.org/wiki/Brachistochrone_curve and is usually solved using the calculus of variations but the resulting curve depends crucially on the setup hence Doc Al's request for a diagram.

 

[apr]

Sorry I don't have the diagram. The question asked me over the phone by a teenager - I replied as said by rcgldr in previous post here. But not satisfied really.