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11-07-2007, 05:13 PM | #1 |
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Lev Okun gave this problem to Andrei Sakharov to pass the time while they were being
Lev Okun gave this problem to Andrei Sakharov to pass the time while they were being driven from Moscow to JINR in Dubna. However, it didn't work (to pass the time) because immediately after being told the problem, Sakharov pulled out a pen, took Lev's magazine and wrote down the solution, without any hesitation whatsoever.
how long does the problem take you? problem is in following post |
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11-07-2007, 05:13 PM | #2 |
Banned
Posts: 497
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An infinitely stretchable rubber band has one end nailed to a wall, while the other end is pulled away from the wall at the rate of 1 m/s; initially the band is 1 meter long. A bug on the rubber band, initially near the wall end, is crawling toward the other end at the rate of 0.001 cm/s. Will the bug ever reach the other end? If so, when? |
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11-07-2007, 05:15 PM | #3 |
Just Hook it to My Veins!
Location: all over the Internet
Posts: 44,548
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uhm no?
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11-07-2007, 05:20 PM | #4 |
Socialphobic
Location: The Filthy South
Posts: 11,300
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What is circumference of the earth again?
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11-07-2007, 05:21 PM | #5 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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I just did this little experiment and the object on the rubber band was only moved half of the distance I pulled the rubber band
so like I move rubber band 4 inches and the thing on the rubber band is only moved 2 inches so the bug will never reach the end of the rubber band, right? I mean the bug will always be moving at a slower velocity than the band is increasing, he would be like 0.500000000000000000000000000001 (exaggreated) m/s and the thing is increasing at 1 m/s he should be given a 27.77777777777777 hour head start Last edited by bardy : 11-07-2007 at 05:26 PM. |
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11-07-2007, 05:24 PM | #6 |
Banned
Posts: 497
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youve solved the wrong problem, bardy. thats a good start, though, eh?
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11-07-2007, 05:25 PM | #7 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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I modified?
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11-07-2007, 05:27 PM | #8 |
Minion of Satan
Location: You don't play guitar hero if you are a guitar hero.
Posts: 6,008
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yes if the rubberband is stretched evenly. some huge number in time though.
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11-07-2007, 05:27 PM | #9 |
Minion of Satan
Location: ¯\(º_o)/¯
Posts: 8,658
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um theoretically i guess the band would always be pulling the bug to the halfway point, which would mean the bug was always proportionately getting closer to the end of the band. i don't think this would hold up to scientific scrutiny though, would it?
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11-07-2007, 05:28 PM | #10 |
Banned
Posts: 497
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at the wall, the bug is moving bug crawl speed. at the halfway point, the bug is moving half of the band stretching speed plus its crawl speed. if it ever makes it to the end, it will be moving as fast as the band expands plus its crawl speed
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11-07-2007, 05:29 PM | #11 |
Banned
Posts: 497
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well andrei sakharov has clearly put me to shame so far, but i will not giv eup hope
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11-07-2007, 05:30 PM | #12 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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yeah the further you pull the rubber band the less the bug is going to be pulled by it, upon futher inspection... so I dunno????????????????????????????????????????????? ?? I am bored at work and playing with rubber bands I need to go home
edit: nm |
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11-07-2007, 05:31 PM | #13 |
Just Hook it to My Veins!
Location: all over the Internet
Posts: 44,548
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walking on sunshine
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11-07-2007, 05:32 PM | #14 |
Banned
Posts: 497
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edit - nvm read that wrong
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11-07-2007, 05:35 PM | #15 |
Immortal
Location: helllllloooooo!!
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it would probably pull the nail out after a while
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11-07-2007, 05:35 PM | #16 |
Registered User
Location: Sherwood Forest
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Not if it's infinitely stretchable...
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11-07-2007, 05:38 PM | #17 |
Immortal
Location: helllllloooooo!!
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nm
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11-07-2007, 05:43 PM | #18 |
Master of Karate and Friendship
Location: in your butt
Posts: 72,975
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eventually the bug will get tired and fall off the rubber band
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11-07-2007, 05:44 PM | #19 |
Banned
Posts: 497
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i wonder if i should just give up and look at the answer... who knew this problem would be so hard!
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11-07-2007, 05:46 PM | #20 |
Banned
Posts: 497
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i guess i might as well have something to do during analytical chemistry
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11-07-2007, 05:47 PM | #21 |
Just Hook it to My Veins!
Location: all over the Internet
Posts: 44,548
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something to pass the time.
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11-07-2007, 05:58 PM | #22 |
Immortal
Location: helllllloooooo!!
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someone fix my errors
I gave the band an original length of 1m which is probably the wrong way to look at this, but whatever Length of Band = L Bug Velocity B(t) Pull Velocity P(t) distance bug travled Db L = 1m + 1m/s * t del for a second |
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11-07-2007, 06:00 PM | #23 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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someone figure out the acceleration of the bug I dont want to
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11-07-2007, 06:05 PM | #24 |
The Man of Tomorrow
Posts: 26,965
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Assume that the bug's distance from the wall when the band is not stretched is f(t) and the length of the rubber band (when it is stretched) is r(t). Let the distance from the wall to the bug (crawling along the band as it is stretched) be b(t). Then for an infinitesimal period dt, we have
b(t+dt) = b(t)r(t+dt)/r(t) + df(t). Setting r(t+dt) = r(t) + r'(t)dt and df(t) = f'(t)dt, rearranging, (b(t+dt)-b(t))/dt = b(t)r'(t)/r(t) + f'(t). Taking the limit as dt approaches 0, b'(t) = b(t)r'(t)/r(t) + f'(t). The solution to this differential equation with boundary condition b(0)=0, is b(T) = r(T)(Integral t=0->t=T f'(t)/r(t) dt), If the bug reaches the end of the band at time T, so that b(T)=r(T), then we have Integral t=0->t=T f'(t)/r(t) dt = 1. The solution in T of this equation (when one exists) gives the answer for the general case. Let f(t) = 0.00001t, and r(t) = t***. Then we have Integral t=0->t=T 0.00001/(t***) dt = 1, or, carrying out the integral, 0.00001 ln(T***) = 1. So, T = e100000 - 1 seconds. |
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11-07-2007, 06:10 PM | #25 |
Immortal
Location: helllllloooooo!!
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I will let everyone know that future boy obtained his solution from this page:
http://www.feynmanlectures.info/solu...and_sol_3.html |
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11-07-2007, 06:11 PM | #26 |
The Man of Tomorrow
Posts: 26,965
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no way, i did that just now between gears of war matches.
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11-07-2007, 06:12 PM | #27 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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just giving credit where credit is due
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11-07-2007, 06:13 PM | #28 | |
Apocalyptic Poster
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Quote:
No, sorry, what? Is it basically one of those mathematical pieces of reasoning that takes advantage of the adhoc nature of physics? like these things? Given that a and b are integers such that a = b + 1, Prove: 1 = 0 1. a = b + 1 1. Given 2. (a-b)a = (a-b)(b***) 2. Multiplication Prop. of = 3. a2 - ab = ab + a - b2 - b 3. Distributive Propoerty 4. a2 - ab -a = ab + a -a - b2 - b 4. Subtraction Prop. of = 5. a(a - b - 1) = b(a - b - 1) 5. Distributive Propoerty 6. a = b 6. Division Property of = 7. b + 1 = b 7. Transitive Property of = (Steps 1, 7) 8. Therefore, 1 = 0 8. Subtraction Prop. of = |
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11-07-2007, 06:15 PM | #29 |
Immortal
Location: helllllloooooo!!
Posts: 20,823
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uh no that is the solution
there are a few ways to get to it but that is the right answer |
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11-07-2007, 06:16 PM | #30 |
Banned
Location: i'm from japan also hollywood
Posts: 57,805
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lev okun and andrei sakharov sound like some shitty dudes to hang out with
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