Toffo wrote:Let's say a train powered by an overhead electric wire moves frictionlessly along an infinitely long linear track, and some light is shining out of the train's side windows. That's what the train needs the electricity for, for lights.
The aforementioned light carries linear momentum in track frame, like light emitted from moving things tends to do. During a very long time a very large amount of momentum would be carried away by the light.
Where does all that momentum come from?
SDK wrote:... The electricity?
Where else? It is a closed system with a conspicuous energy input, and a stated lack of energy outputs, except for the one in question. In fact, why is it even a train? It boils down to representing an electric light! No infinite frictionless track required.
Its impressive to know all the tons of complicated maths and right-hand rules and mass-energy equivalency and reference frames etc etc but even if all you knew of was the conservation of energy, you'd get the answer.
The momentum must
be coming from the electricity, the question is set up so that there is no other plausible answer.
Toffo wrote:I see. Now let's say a train is moving on two rails frictionlessly, then the train arrives to a segment of tracks where the rails are hot. The train happens to be a good heat conductor, and it happens to have a large heat capacity, that's why the train sucks energy from the hot rails, which causes the train to lose velocity, as so well explained by you. Where does the kinetic energy of the train go ?
More complicated, yes.
I'll eat my hat if that kinetic energy doesn't become heat.
The only question is, is the [extra] heat [from that kinetic energy] now in the rails or in the train?
The train definitely slows down? I'm not clear on that
If it definitely slows down, then the train is going to experience drag over the hot part of the track. Drag force is going to have to go through the wheels, since we are ignoring all other sources of friction/drag.
I'd wager (with my no-maths approach) that its in the wheels (or related track-contacting gear) now as heat.
This is at odds with a "frictionless" track however, it may not be compatible with the question?
Can you have a frictionless track that conducts heat? Seems incompatible.