That is completely wrong. KE is a relative measurement. Again, please read an intro physics text.
Yes, but not physically. Momentum is not scalar, but a vector.
What do you think momentum
is? It goes with the mass. Like the momentum of of the particles that make it. Masses warp space time. Why? Good question, no real answers yet, but it goes with the mass.
If you instantly stop a mass in an elastic collision, it will move move in the opposite direction, but with the same absolute KE. The cart is said to be "moving", but not wrt to the treadmill observer. However, when the cart travels back with the belt, all is in order. The cart's velocity is that of windspeed, but in the other direction. Then the KE is correct. It agrees (as it should) with both the belt and treadmill observer. Just like the elastic collision it represents.
When actually at windspeed, the cart should have KE, it has none. It is simple to demonstrate (from the belt) that this is the case.
If I simply assume that there are no frames involved, and what I am seeing is what it as appears to be, then I have no problem at all. All frames, or perspectives as the really are, are in complete accord. You will not be able contradict my stance. That is flat out. Any test, any time, it will pass, whereas the treadmill is a frame produces contradictions.
That is completely wrong. In the frame of the moving belt surface, the KE of the cart is the same before and after it is placed on the belt. You can not mix reference frames when comparing KE, just as you can not mix reference frames when comparing velocity.
Yes, I can, otherwise you are suggesting non-locality. Newton's laws hold for all relative velocities likely to be experienced by the cart.
Also, it supports my claim. No KE from any view, when the cart is said to be windspeed. I need not mix frames, it fails from the belt.
What if I use the treadmill for its intended purpose? Standing on the static belt, I record all relative KE's and velocities. If I then start the belt, so to run in place, apart from the local changes in limb motion, nothing changes. Indeed, I have no KE becuase I am not moving.
If I raise myself by the side rails, then I am also much the same. No KE, no change to my previous readings. From this position, I can lower my feet to the belt, and do much as I please. 'Run', let my feet slide and so forth. No change. The only way there is a change is if use the belt as a reference, but even then, its influence seems to be by how well I am attached to it.
This is implausible. I can't see how a reliable relationship between so-called frames can be based upon this. It also forces me to accept the belt as an "absolute reference", before I can even begin measure it.