Quote:
Originally Posted by sjastro
One that you are familiar with Craig.
Excluding a vertical straight wire, what should the shape of a wire be such that a bead released from one end of the wire will slide to the opposite end under gravity in the shortest period of time.
Common sense says the wire should be straight but the answer is in fact a cycloid.
http://en.wikipedia.org/wiki/Cycloid
Regards
Steven |
Ok .. so this one's got me stumped, also.
(I'm sure what Steven says is correct, but my brain needs more !!
)
If a vertical wire is fastest of all, then why wouldn't a wire, slightly off the vertical, also be faster than a Brachistochrone Curve (cycloid) ?
If such a wire did result in a faster descent, then there must be an angle at which it wouldn't be a faster descent .. what is that angle if friction is excluded ?
(The second question may be irrelevant if the inference in the first question is proven invalid. I suspect the issue here is in the wording. There is something about the bead having to be 'constrained'. It would appear that there must also be constraints applying to the end-points, as well. (??). I'm not sure of the significance of these constraints, however .. ).
Cheers