Re: [Phys-L] quickest route

[Bill Nettles <bnettles@uu.edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
> Sent: Saturday, July 27, 2013 12:19 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] quickest route

[snip]

> Guessing i.e. hypothesizing is fine, but then we need to /check/ the
> hypothesis.  When I do the check, I find that the times are equal for a 3:4:5
> triangle, i.e. θ = 36.87° ...  and also equal for θ = 90° ... but not otherwise!
> Generalizing from these two examples doesn't work.  For details, see below.


[snip]

>   I assume no friction, including no air friction and no sliding
>   friction.  Therefore the spherical cow does not roll; it merely
>   slides along the path without rolling.  I did not use the word
>   "roll" in the original problem statement.  As David Bowman points
>   out, analyzing a realistic rolling motion would be messier.

Not really that messy if one rolls on plane surfaces.  Because the actual value of g falls out of the problem, any object which accelerates down the plane like K*g* sin(theta), where K is some constant depending on the details, and K*g for the straight down part will have equal times at tan(theta) = 0.75 or theta = 36.87...  Spheres  or disks which roll without slipping have such an acceleration.