Conundrum wrote:
No one has convinced why the block on the treadmill wouldn't continue to move if the belt was stopped abrutly when it has the same momentum.
Part of my problem in helping you is that I'm still not quite sure what your block is doing. Is it moving with the treadmill belt or being tethered from the treadmill so that it is stationary relative to the treadmill apparatus itself? If it's moving with the belt, it will keep moving in the direction the belt was moving when the belt abruptly stopped (no change in the momentum of the block). If it is tethered from the treadmill, it will remain in the treadmill's rest frame (no change in the momentum of the block). The only way to change the momentum of the block is for some outside agent to introduce a net force on the block to compel it to change its momentum. Note that the tether likely produces a force, but that force is only enough to balance whatever force might be trying to pulling the block in the direction that the treadmill belt is moving. If that force disappears, then the tether force also disappears.
Hope that helps.