Not if you can avoid describing the cart's behaviour as if it was one.
The point is that I can. "Frames of Reference" are not magic, and neither are they necessary, and certainly not the only means of analyzing motion.
The motor and generator are oblivious to the cart's motion, and see only the force applied to the shaft. A refrigerator motor is no different from any Spork motor in any other application.
The "stick" propeller reference shows that the motor power is proportional to the cube of the angular velocity. It is not an
effective propeller, but a mimic of the load a propeller presents.
Drag = 1/2.Cd.A.V^2.
Power = f*v
So, drag power is proportional to V^3 and that applies to angular velocity w^3. Real props show the same characteristic. A generator's power output is related to w, that too applies to real motors.
That is a big problem, because simply expressed, Thrust = P/v where v is the airspeed, but that is martinet fixed to the cart's speed by the gearing.
It's wrong in principle and hampered mechanically. There is good reason why it is so slow.
You may say that the cart is not electrical, but the same argument applies mechanically, and Spork's submission is offered as proof of concept, yet is fatally flawed. If that's wrong, then what else is wrong? The TM? Indeed.
Nice. Maybe we're getting somewhere. Can you justify any of that, or are you just going to stick with declaring it's true because you say so?
By what other means would you like? It's not I who says it's true, but Newton. If you disagree, then surely you will find that formula contradicted in text books. It's not a random wiki. I checked it by working it against first principles. There are other means of determining thrust based on pressure models for example and they can be found at NASA's web site. Cross check that, and the common factor is Newton's impact theorem. Solid.
Despite the position you may still hold on cotton reels, I bet there is more to them than you thought. There is less to the TM than you think.
I perhaps ought to point out that if it were quite so simple as declaring that the wheel can supply (T*w) power and the prop consumes (T*w3) power, then it would be impossible to push or tow the cart as the power needed to move it would always exceed the power used to move it.
Well, I'm saying it
can't.
But the power to tow, comes from the towing vehicle. Not the cart itself.
The towing vehicle will have an engine and fuel. Apples and pears.