xkcd

I'd just like to point out that the reason Joe Biden's commute was so dull has less to do with the length of the trip then it does with the fact that Joe is pretty much the only person in the country who rides AmTrak. The North-east corridor (DC to Boston) is actually well used and earns enough to ...

I think this comic is wrong. Consider a circular loop with radius r, speed at bottom of loop v0, and speed at top of loop v1. Assume train of mass m is just coasting, i.e. no engines. By conservation of energy we have (1/2)m v0^2 = (1/2)m v1^2 + mg(2r). Multiply both sides by 2/(mr), yielding v0^2 /...