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experimentX
Group Title
Find a shape of inclined plane(not necessarily plane) that takes shortest time to reach from top to bottom. Assume the ball is sliding without any friction.
 2 years ago
 2 years ago
experimentX Group Title
Find a shape of inclined plane(not necessarily plane) that takes shortest time to reach from top to bottom. Assume the ball is sliding without any friction.
 2 years ago
 2 years ago

This Question is Closed

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1347894497129:dw
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
geowotsit?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
assume both h and w are not zero.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1347894819011:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
it's a pretty famous problem ...
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
http://en.wikipedia.org/wiki/Brachistochrone_curve
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep ... this is brachistochrome problem.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
I was thinking geodesic at first, shortest distance....
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i did this with calculus of variation. haven't done this with purely calculus.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
What about when h=w and h and approaches infinity
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
h and w*
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
take a circle with zero radius, you will get a straight line.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
* if w = 0 ...
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
http://www.cmsim.eu/papers_pdf/january_2012_papers/25_CMSIM_2012_Pokorny_1_281298.pdf (brachistochrone as special case of geodesic)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
dw:1347895370580:dw
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
I got that cycloid part........
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
What if h and w approaches infinity.....
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
It will never get to the bottom and you will never know..:)
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Then I think this should work:dw:1347895555863:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep ... this is a physics problem actually.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Oh ya @estudier ........ But what if h and w are very large.... but some finite number
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Will it still be that cycloid
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
yep .. it should be cycloid ... make by a huge circle.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
OMG! This math stuff is out my level
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Didnt get why cycloid........ I just know we need to maximise the accleration
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
Maybe at infinity, you have to go to some other mathematical model, maybe conformal, to analyze that (in conformal everything is a circle, point is circle with zero radius, line is infinite circle etc)
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
or sphere, perhaps..
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
I mean why cycloid is the answer to @experimentX question
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
It will only increase the length
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.
 2 years ago

estudier Group TitleBest ResponseYou've already chosen the best response.1
When you solve the problem, that's what comes out, a deeper meaning, you mean?
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
trust me ... things aren't that intuitive.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Ok..... I trust u. @experimentX
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
When did u learnt these stuff. @experimentX
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
At university
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
I will think on this problem.... see If I can get to the solution
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
told you i'm old guy
 2 years ago
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