From your reasoning, If there are 60N forces acting on the cart in the vertical direction, we should expect to see the following from F=MA:
60N=0.2A
A=300 m/s**2 or approximately 30gs +z direction-1g for earth's gravity acting on the cart in the -z direction or vertically over the belt since there is nothing to prohibit this acceleration other than the weight of the cart.
Since we do not see the carts rocketing off the belts vertically at 29 gs acceleration, I would think you might want to check the credibility of this claim.
If you want to use math to justify physics outcomes, first you must be able to understand what the equations are telling you!
ETA: I went back and look and you stated 80N in the vertical direction for force. This translates to approximately 39 vertical gs for acceleration!
Now you are trying to be funny? No one has claimed that the 60 N forces are acting directly on the cart. What has been established from this research is there are ground reaction forces of 60 N in all three spatial directions, measured in the force platform that is supporting the treadmill. These are essentially vibrations in specific frequency spectrums and they will most certainly be present on the treadmill belt, but exactly to what extent is unknown. It is also unknown to what exact extent they will have an effect on the cart, or in what manner that effect will be manifest.What
is known is that
these vibrations are present and since they are of a substantial magnitude, it would be disingenuous to discount their effect on a cart that weighs less than 200 grams and is very loosely coupled to the belt.
You
cannot claim that you have performed a valid, scientific Galilean transformation of the cart on a treadmill to the situation of a cart on a road in the wind, unless you have included a transform of these vibration forces. That is the entire point;
your transform is incomplete and inaccurate and invalid.
You cannot pick and choose what forces you would like to include and what you would like to exclude because you may be overlooking something that has an important effect on the cart. If you perform only a velocity transform of the cart on a treadmill, that can only result in a situation with a cart that is still on a running treadmill with the velocities transformed, and
nothing else, unless you can transform all of the forces that are acting, and you have no way of doing that.
This is not a matter of opinion. Your transform will not be accepted by any scientific body or get past any peer review. You may have some success peddling it on Internet talk forums, but that is as far as it will ever go.