For those of you who don't know about it-- this tunnel between the Bay Area and New Jersey was built around 1933 to deliver mail. The link below takes you through its various stages to its current role, delivering burritos coast to coast at a speed of a mile a sec.
http://idlewords.com/2007/04/the_alameda-weehawken_burrito_tunnel.htm
Wednesday, April 11, 2007
The Alameda-Weehawken Burrito Tunnel
Posted by Manohar at 4:36 PM
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11 comments:
Very interesting indeed...Did you notice that the 42 coincides with the Hitch-hiker's guide to galaxy's magic number 42?
I didnt get the idea of the chord tunnel at first... For those of you who had the same question, here is my explanation... If you take 2 points in earth (sphere), the shortest path connecting the 2 points is a chord. If you imagine correctly, the chord then lies at different distance below the surface of the earth with the greatest depth at the center of the chord. In other words, it is like a steep decline for half-way. Apparently, the inertia of the decline takes you back to the other side with the body reaching a velocity of 0 when it arrives on the other end... The time taken to do this constant irrespective of the points you choose and it is 42 minutes...Isnt that amazing?
@mindframes: that is correct, the two ends of the chords are at surface radius and every point in between the distance to center starts to decrease until the middle and then starts to increase again till u hit surface radius. Which is also what the depth graph and temperature graph shows.
So although there is acceleration, the burrito will always slide on the bottom of the tunnel... hence the need to reduce friction.
Very very interesting...And to think that they came up with an idea of chord tunnel...Wow..its really too good..
One question....I am not sure if this theory will hold true if the chord runs across the center of the sphere (diameter). At zero gravity in the center of the earth, wouldnt it stop?
@mindframes: actually thats a classic example of simple harmonic motion.
Ignoring friction, the object accelerates till the center of the earth and the momentum will keep it going till it reaches the surface on the other end at which point its velocity will be exactly zero. It will fall back and keep oscillating.
With friction, It will be like any simple harmonic motion in real life, the distance will keep dwindling until it settles in the center.
@mano: I think the simple harmonic motion funda is only true for every line between 2 points in the sphere "except" the center of the earth.... When the line is through the center of the earth, when an object reaches the center core of earth, the gravity acting on it will be zero and hence the force acting on it should be zero...In this case, I am not sure if the inertia can still carry it to the other side or not...Not sure if I am missing something...
@mano: I read up on web and the SHM seems to be true for any 2 points... The weight of the object will be zero when it passes through the center of the earth. Apparently, force will still act on the body as if it were a point mass... I still dont understand it fully...May need some more reading I guess...:)
@mindframes: I remember this case as an example in 12th class physics. The hypothetical question was to calculate some crap assuming different radius of the hypothetical planet with different 'g' values. I ofcourse got the answer wrong at that time- and will probably get it wrong if I were to attempt it now.
I'm not sure what your question is about the point mass. I do realise that all computations in these examples are made assuming they are point masses. Lets talk over beer :)
Just found that this whole burrito thing is a hoax posted by someone smart who took all the pains to make it look genuine... The physics involved overrode all the fundamental questions that one would ask...:)... Why would anyone build a tunnel all the way from california to new york to send burritos...;)
@mindframes: True. This guy is a supersmart dude.. read his analysis of why the space shuttle is all crap..
All along I had the suspision that this was a hoax. (esp. before I read this article)
This proves that we are smarter than we think we are :)
But today I was thinking of commenting that this is awesome thing nobody even cared to recogonize.
That proves, we believe anything which is packaged right..*Sigh*
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