Re: [Phys-l] time to bottom of ramp

[John Denker <jsd@av8n.com>]

On 10/26/2006 12:47 PM, fizix29@aol.com wrote:

> "Because the block sliding down the circular arc travels a greater distance (an arc length is
> greater than the length of the chord it defines) but arrives at the bottom of the ramp with the
> same speed that it had at the bottom of the inclined plane, it will require more time to arrive
> at the bottom of the arc. "
>
> I disagree.


This looks like a dumbed-down version of the brachistochrone problem.
  http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Brachistochrone.html

The J-shaped ramp looks to me like a much better approximation to the
brachistochrone, and therefore will win the race.

  (... unless there is another huge contribution to the problem that we haven't
  yet been told about ...)