schroder said:
Here is a little thought experiment:
Haha, he's back
Turn the tread until it is Vertical, while keeping the cart Horizontal. You will need to place a Horizontal support table under the cart and maybe add an extra set of wheels for support but the basic operating parameters are unchanged from the Horizontal tread situation.
Now when the tread runs, it will deliver exactly the same turning force to the drive wheels as before. Yes ( ) or No ( )
Yes, if we ignore that the aerodynamical situation has changed a bit. Acceptable.
The cart will move in the Horizontal Direction as before with the same velocity as before. YES ( ) or NO ( )
Yes.
(I realize that when the cart does move it will disconnect from the tread, but its initial velocity away from the tread will be exactly the same as before. Alternatively, you can consider the tread as tracking along with the cart if you find that easier)
Are not all the forces and velocities exactly the same in both the Horizontal and Vertical tread situations? YES ( ) or NO ( )
No, but almost. I'll tell you what has changed. What has changed is that this is not a setup that transforms into a DWFTTW situation. There's an extra force in the game, which is the force of gravity (which compensates the force of the upward drive of the treadmill if the cart is heavy enough).
Does the relative velocity between the Vertical tread and the Horizontal cart provide a true indication of the cart’s velocity in the Horizontal plane in which the cart is moving? YES ( ) or NO ( )
As long as you stick to "true indication of velocity" you are terribly in error. There is no more true velocity than any other. There is no "correct" and "erroneous" velocity. There are only velocities which correspond to each other in different situations but which can be linked with a Galilean transformation. Clearly the setup you describe is not equivalent with the DWFTTW "outdoor" setup (there is no Galilean transformation which can transform your setup in the "outdoor" situation), so there is no corresponding velocity to that case. As we now have genuinely different situations, you can talk about any velocity you like. It isn't related to a velocity of the DWFTTW cart.
Would it not make a LOT more sense, and lead to the CORRECT velocity of the cart, to take the relative velocity of the cart with respect to a point on the table on which it is running and NOT wrt the tread? YES ( ) or NO ( )
No. You can consider any velocity you like, but none will correspond to the velocities in the "true DWFTTW outdoor situation", as no Galilean transformation links to it.
Multiple Choice:
If the Vertical tread is running at 10 m/s and the cart moves Horizontally at 2 m/ sec , what is the cart’s true velocity on the surface of the table?
a) 10 m/sec (Idiot)
b) 12 m/sec (Vanesch)
c) 2 m/sec (Schroder)
d) Impossible to determine by the present laws of physics need to calculate the prop pitch wrt the inexplicable air ground interface and then pray to God. (Jeff)
The velocity wrt to the table is of course 2 m/sec. But as I said, this velocity has nothing to do with the DWFTTW setup. You actually constructed a cart with a motor and a propeller.
If you picked 2 m/sec you get a door prize for the CORRECT answer and this would also be the correct answer on the Horizontal treadmill running at 10 m/sec.
No, because 1) the two situations are NOT linked by a Galilean transformation and 2) there is no "correct" velocity or "wrong velocity" in the absolute sense.
Schroder,
Member of New York Academy of Science
Bwahaha ! You bought that ticket on a fancy fair ?