You always make baseless claims, but you never simply provide a post number. This is because your claims are simply lies.
It was in #1980
"Yes, when JB and I go to great pains to get the cart to exactly balance on an inclined treadmill, it is in fact in balance on an inclined treadmill. That seems obvious enough to me." There was a later post about selecting wheels and so forth.
Yes, that is why the cart stays where it is. It balances on the belt.
A ground based view is just fine. What you fail to recognize is that ANY inertial frame is just fine. What you also fail to recognize is that the cart DOES exactly what is claimed. Your 70 pages of faulty nonsense incomprehensible theories can't change physical reality.
A roadside observer sees a windspeed car moving from left to right. The cart has KE and velocity relative to that observer. I now move to the cart using a car. From this vantage, I see the cart as stationary and a relative KE of 0.
I now want to 'hold' the cart so that is appears stationary before the roadside observer, so I simultaneously slow the wind and cart, until both are stationary. All observers agree that the cart, wind and car are stationary, and have zero KE wrt to ground. This is the correct interpretation of transference between frames in this case.
The next move, is to take the cart and put it on a moving belt that moves right to left. It is now simply
asserted that the cart is at windspeed. The argument is supported by the 'equivalent' view of the belt, but this has no meaning, because it has no physical counterpart in the model that is used to derive the stationary result, (other than a random treadmill) nor does it have any connection with real wind performance. It has no connection with windspeed travel at all, but added after the fact.
Also, this is an artificial reference, producing an image to the 'left' of stationary wrt ground. This means that all objects on that belt, accelerate from -beltspeed to zero, finally resulting in zero KE wrt ground. A possible physical counterpart is an artificial road, moving right to left wrt to a roadside (ground) observer, in still air, but
not in wind I have previously shown this graphically in #1846.
However, the cart is never seen to move back with the belt, because manual manipulation places it as what is simply called 'windspeed'. The cart remains not at windspeed, but near zero wrt to ground. As I claim, and you confirm, the cart remains on the belt due to the balance mechanism inherent to the cart. Any object capable of overcoming what force it has to the belt, can act in a similar manner. I have mentioned that I have seen oranges remain stationary while spinning on a moving belt. The means are different, but the result is the same.
The model has many flaws, but I will stick to the KE. If as before I travel with the cart, but the cart moves sideways towards the car, the relative KE is no longer zero. That force should be the same at the treadmill, but the videos show that this force to be unrealistically low. Also, the cart does not display the dynamic response that would be expected of a 6oz cart traveling at perhaps 10mph.
It seems to me that this view creates a lot of problems regarding velocity and KE, whereas my interpretation does not. As you say, any inertial frame is fine, so mine is as valid as yours, but it is easy to demonstrate that your model is inconsistent in many ways and breaks Newtonian law, which is said to hold across all frames. This must mean that is is your frame of reference that is false.
We have built and demonstrated this cart. We have provided plans, parts lists, build instructions, and even built a number of carts for people that requested them. Rather than spend $40 to see for yourself, you'd rather attempt to debate it with a whole lot of people that have seen it for themselves and understand it completely.
The treadmill is not the cart.