The Shortest way there is the Longest way round

[agor95]

This saying is very old and I hope we can use this to assist in two active threads.

The question we have 'Where does the energy come from?'

https://en.wikipedia.org/wiki/File:Brachistochrone.gif

So a ball starts at the same height, mass and zero momentum.

Then end with same height mass & different momentum?

All this happens due to it's path.

Does that mean they have the same input energy and finish with
different output energy?

[AB Hammer]

I would like to see the same test on a rotating platform.

[jim_mich]

Then end with same height mass & different momentum?

Wrong.
This has been discussed a number of times here on the forum.

Two equal objects following different paths but which end up moving at a same horizontal height will have a same horizontal velocity.
The object simply arrive at different times. They take different amounts of time to fall because of their different path angles.

[agor95]

@Jim_Mich

I remember the post around 8 years ago on this topic.
Hopefully we have some new members & guests.

So it is good to keep members on the right track.

If you had not stated there was no difference in momentum then I would have done so.

So with hard geometry in a static frame of reference this is true.

Note. A question is never wrong.

Regards

[agor95]

@AB Good point.

Also the Rotating Frame needs to vary.