The Mudcat Café TM
Thread #104378   Message #2353399
Posted By: JohnInKansas
30-May-08 - 07:09 PM
Thread Name: BS: Random Traces From All Over
Subject: RE: BS: Random Traces From All Over
A professor I knew many years ago sort of "had a dream" about a much shorter tunnel to connect Boston and Washington DC for a communter train. He presented the problem of calculating the "resonant frequency" for a "train" dropped into one end of the hole and arriving at the other on a number of freshman physics exams. (it's a non-linear pendulum problem)

In the absence of friction and windage (standard quiz conditions for freshmen) it turns out that the trip from one end to the other would be expected to take about a minute or two. For extra credit you could calculate the "peak velocity" at the center of the tube, which - recollection is - was about 2,300 mph, but it might have been a little less.

His "after test" critique always discussed the "make up energy" required for friction and windage, improvements possible by using a "constant slope" instead of straight-line hole for the tunnel, and a few other "practical bits."

We never did figure out for sure whether he really believed the tunnel might someday be "bored" to his specifications, although many students were, especially by the crigique.

John