In S.-Petersburg there was a brochure with a strange title: "powered wheelchairs and scooters underground railroad between S.-Petersburg and Moscow. Fiction novel while in three chapters, and unfinished". The author of this booklet, A. A. Family, offers an ingenious project that interesting to learn about Amateur physical paradoxes.
The project consists in carrying out a 600-kilometer tunnel that would connect both of our capital on a completely direct underground line. Thus, for the first time would be a chance for humanity to make the path straight, and do not walk in crooked paths, as it was still". (The author wants to say that all our roads, obeying the curvature of the earth, followed by the arcs, while the proposed tunnel will be held in a straight line along the chord.)
This tunnel, if you can dig would be amazing property, which possesses neither one road in the world. It is that any crew in such a tunnel should move itself. Remember our underground well, prosurvival globe. Leningrad-Moscow tunnel - same well, only not drilled to the diameter and along the chord. However, when looking at the picture it may seem that the tunnel dug horizontally and that the train, therefore, there is no reason to roll it into force of gravity. But this is only an illusion: spend mentally radii to the end of the tunnel (the direction of the radius is the direction of the plumb line); you will understand then that the tunnel is dug at an angle to the plumb, i.e., not horizontal, but inclined.
If to dig a tunnel between Leningrad and Moscow, the train raced it back and forth under its own weight, without locomotives.
In this oblique well every body should swing, being captivated by the power of gravity, forward and backward, all the while clinging to the bottom. If in the tunnel to hold the rails, rail car will roll over them: the weight will replace the thrust of the engine. Initially, the train will move very slowly. With each second the speed of powered wheelchairs and scooters trains will increase; soon it will reach unimaginable magnitude, so that the air in the tunnel is already significantly interfere with his movement. But forget for a moment about this annoying impediment to the implementation of many tempting projects, and follow the train further. Comcases until the middle of the tunnel, the train will have such a huge rate that is many times faster than a cannon projectile! that run will come almost to the opposite end of the tunnel. If not for friction, there would not be this "almost": the train without a locomotive itself would have reached from Leningrad to Moscow. The duration of the flight in one end, as shown by calculation, is the same as for falling through a tunnel dug by diameter: 42 minutes 12 seconds. Strangely it does not depend on the length of the tunnel; travel in the tunnel Moscow - Leningrad, Moscow - Vladivostok and Moscow - Melbourne continued to be the same time *.
The same was repeated with any other crew: trolley, carriage, automobile, etc. Really fantastic road that, she remained motionless, rushes on all the crews from one end to the other, and then with incredible speed!
* You can prove another, no less interesting position related to the bottomless well: the duration of the swing does not depend on the size of the planet, but only on its density.