Sorry, I had homework…what I have is below, but I welcome all other input.
I think I fixed the ramp / rail / cart thing in my previous post (I should really proofread more carefully).
I calculated the torque produced by gravity around point G, and the torque from tension around point E. I then subtracted the two values to find the overall torque. For example, for point A:
torque_gravity = (mg)(distance_AG)(angle_AG to vertical)
torque_tension = (T)(distance_AE)(angle AE to ET)
So the overall torque around point A is 442 Nm in the counterclockwise direction.
With this method, I got that all four rollers have torque in the counterclockwise direction, of magnitudes 442, 402, 24082, and 24092 Nm (A, B, C, D).
This is where I get stuck again, because I don’t know how this correlates to figuring out which rollers make contact–is it the magnitude of the torque? The difference in the respective pairs?