I don't know. It seems from the video that the profile above the belt is OK, but going the wrong way. It's a headwind. This seems to fall almost to zero at prop height, but then at that point, there should be a tailwind.
When you add connections to the ground for the cart on the treadmill as you did in your bar example, you must add the same connections to an immense object moving at wind speed for the cart on the road, otherwise you are not treating the two frames equivalently.
No, I think that immense object would be the ground. I think that the treadmill is the ground. Difficult to argue that it is then going at windspeed.
I can measure no change at all in wind or motion when I turn off the belt.
This seems to conform to my expectations.
OK, then, you have specified the frame of reference as the inertial frame in which the objects were initially (momentarily and approximately) stationary. That is arbitrary. KE of the first object is non-zero in that frame after acceleration, but not in all frames. KE is relative.
Not arbitrary. I have merely set the datum. I have confirmed that to be stable. I am indeed looking for a difference. It would seem to me that from both the 'frame' of the cart and that of the buffer, I should see the same result. No matter how relative, I should see at the work done returned to me.