Kind of an extreme example here but if you were to build a train track tower on the west coast 10,000 ft high. It gradually sloped all the way to the east coast about 3,000 miles. Only dorps about 3 ft per mile. Would a train start rolling on its own with perfect wheels, if so how fast could it accelerate to? My first thought on this is that at this low grade wheel friction would be the dominating factor.
Friction would stop the train from rolling.
If you could, in fact, have “perfect” wheels – perfectly round, and frictionless – then, yeah, it would slowly accelerate and roll down the hill to the destination.
(Actually, I’m not at all sure what the breakeven grade is for modern RR equipment. Three feet per mile? Ten? Fifty? I don’t know.)
This site tells of the steepest US railroad grade. “The steepest adhesion railroad grade in the USA is found at the Cass Scenic Railroad in West Virginia. Shay geared steam locomotives haul tourist trains up a maximum grade of 11% on this former logging railroad.”
This site gives some physics background, and offers a value of the “rolling resistance coefficient” for a typical passenger railroad car as between 0.001 and 0.0024. Ordinary car tires on concrete score 0.01 to 0.015. I think this means that a railroad car will roll downhill on a grade approximately 1/10 as steep as a grade where a car will just stop rolling.
(More accurately, where the tangent of the grade is 1/10 the tangent of the grade where a car just stalls from rolling. But at very small angles, the tangent becomes linear with the grade itself, so “1/10th the grade” works well enough.)
As it happens, the height you chose is in the uncertainty zone. Most likely the grade isn’t quite steep enough, but it’s not way too low.
Best plan is to load the train’s cars to the maximum allowed – gravity pulls a 140-ton car twice as much as a 70-ton car, but the heavy car’s rolling resistance is less than twice as great. Once it’s rolling, a 140-ton car will keep rolling slowly on a grade of 5 feet per mile. Question is, is that enough to start a car that’s standing still.
Rolling resistance also scales with speed, doesn’t it? So if you’re just barely steep enough to keep the train rolling, it’ll come up to some steady low speed and stay there at equilibrium.
There’s a what-if article that discusses this, but for a bicycle rather than a train.
Although there’s a footnote that mentions trains and says that their coefficient of rolling resistance is similar to that of a bicycle, so maybe the analysis roughly applies to trains too.
You could build it so that the train starts on a grade that is a little bit steeper and then let it run the rest of the way on the slope that is just enough to keep it rolling.