When you say that the ball has moved to the left, how is this so? isn't the ball going to the back of the carriage, and so from our perspective going to the 'right'?
Sorry for all these posts, i still don't really understand how we can deduce the train to be turning left/right. I understand the pendulum analogy you used but other than that i can't really see how the train is moving to the right.
Let me have a go at explaining, this is definitely tough
Consider the train moving forward and us looking down on it, as per the question.
Now an important concept to understand here is
inertia, the tendency for objects to remain in their set path. It's the reason why the tissue box at the back of your car flies forward when you brake suddenly: Because the tissue box wants to keep moving forward, and there is nothing forcing it to stop with the car.
In this example, the train makes a movement halfway through the balls path (when it starts to curve). Now, moving forward or backward would never cause the ball to curve, like braking a car on a straight road would never cause the tissue box to hit the side window. Doesn't make sense. But why is the train turning right not left?
Consider the ball as a separate object, because it is. When the train turns, the ball is going to want to continue to go straight on the initial path. Consider the train turning left, that is, moving down the page if we are looking at the diagram, and the ball staying where it is. Except this isn't the right way to think of it. We want to stick with the train. For this to make sense, as we move
down the page with the train, the ball stays where it is, and so moves
upwards on the diagram. Not quite what we need.
Consider the train turning right. The train would move up the page, and so as we go up the page with the train, the ball must stay where it is and so move down the page in our reference frame. This corresponds to the turn in the diagram.
I tried to take out all the jargon, does this help at all? I feel like an animation would be the best way to explain this, hopefully this helps a little