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Thursday, April 26, 2007

isi lurking + an unrelated problem

here is a sum that held me in due to oversight on my part.it has got only one twist- thats all!
here goes-

imagine a rubber string, fixed at one end, is streched linearly in a horizontal plane so that the free end always has a velocity 'v0'.if an insect at the free end starts moving towards the fixed end with velocity v1 , at T=0, and initial length of string is L, find the time at which the insect reaches the fixed end.
my question is that wat shud b the min value for v1/v0.

sorry for for the accccute wording though- cudnt help it.

u know i already feel like reading for college- i feel exhausted with this standard syllabus already.
if u ppl hav applied for isi-bstat admission,discuss in this thread.


Arun Chaganty said...
This comment has been removed by the author.
Arun Chaganty said...

Let's see, if its given that the string is always elongating at a constant rate (v0), and if we were to put this string on the ground (can ignore gravity, hence bend), and ignore the weight of the insect (for any extra pull it may give to the string, hence elongating it), we can ignore that it is elastic, and just ignore the fact that the tip moves at all. So it'll be:

Time == L/(v1) (by considering relative motion)

and we have v1/v0 -> 0+ (v0 can -> inf, and v1 can -> 0+)

But, possible stupidities here:

-> the string most definitely will break after a while. Therefore, the time would have to be that value. Can't be found unless you give me the curve and blah blah

-> as I said before, if the insect is of considerable mass that it can change the elongation of the string, then this wouldn't be vaild if it is interpreted that the constant motion of the end of the string is before and when the insect is crawling is after.

I hope that I haven't made the same mistake.

What do you mean by 'exhausted with this standard syllabus). And if you mean with what we're learning, well, join the group! ;)

(NOTE: I get which mistake you may have made: I initially just considered the wire to be a moving particle, and forgot that the bug was moving on it. Stupid me. )

obiwankenoby said...

well its not a puzzle.
sorry tht i cud not make myself clear though-the elastic limit is not attained.
the answer is,to my knowledge,t=L(exp(vo/v1))/v0.
i did not take into account the dist of insect from fixed end 'x'-is varying wrt time.and when i did
the velocity of insect due to elongation of the string=xv0/[L+vot].
i know its tough to express here.
but u hav worked it out.

Arun Chaganty said...

Oh, I get what your saying. Oh course, I should shoot myself. Twice.

Arun Chaganty said...

Well, I've worked it out, to get the differential equation:

dx/dt = V_i + x*V_o/(L_o + V_o*t)

BUT note here:
x = to the actual distance of the insect from the fixed point, *after* elongation (so final limit would be L_o + V_ot)

V_i = V of insect
V_o = V of tip of string.

I do believe that the solution comes out to be the same.

Man, I feel so bad that I didn't get this Q right on. I mean, during mechanics I used to swallow these pills whole. Then, I just slacked around I guess.

obiwankenoby said...

hey dont get worked up
tell me abt ur summer prog dreams though.i will have to wait for mine till 15th may
i just went off today there bag and baggage to IISER and was told that somehow i missed a circular about hostel facilities not being available till 15th.
wat hits hard is that today there was somekind of a traffic jam due to opposition ruminating on the nandigram issue.so we were stranded on the way the whole time-and we didnt use our car today-we went by bus.
net result- stuffy heat endure it from 930am to 300pm and get nothing.
actually I am getting worked up but i guess theres nothing i could do rlly.

Arun Chaganty said...

Well, you stay in Kolkata right? So, I guess it'd be much better than say travelling by train and getting stranded ;)

Either way, I'm stuck in a puddle right now. I can't say where I'm going. I'm panicky right now. I think the only solution is for me to go personally to meet the profs. BUT that means I have to travel an insane distance to get anywhere. OUCH!

My current idea is to make something, and send it to the professors. I've been working on the specifications right now, to see if I can go to code. Have a few kinks though. Will post when ready.

obiwankenoby said...

i will be posting on raman and his body of work possibly in parts-plagiarised from a popular science work by g.venkataraman.nice book.
i hav got another one on bose and his statistics but it flies well over me.