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Hi everybody, I've really been struggling with this basic idea, I have drawn it out about half a dozen times, watched numerous videos, read descriptions, played with applets but I still can't see it.

Lets just start with a simple atwood machine with a massless rope and frictionless pulley. There are two masses A and B at heights y1 and y2 from the 0 point at the center of the pulley. You pull the rope through a distance d. because the rope does not stretch, the distance between points on the rope does not change(this is why the acceleration is the same for both sides of the atwood machine). I have marked points P, Q, and R in the attached diagram. As I said before, the relative distance between these points are constant. Therefore, when P moves distance d, so should Q and R since this is just equivalent to sliding the rope along a numberline (also drawn). The final y coordinates of the masses are Ya = y1 + d and Yb = y2 - d. The correct answer is stated as Ya = y1+d/2 and Yb = y2 - d/2.

What am I missing?

Lets just start with a simple atwood machine with a massless rope and frictionless pulley. There are two masses A and B at heights y1 and y2 from the 0 point at the center of the pulley. You pull the rope through a distance d. because the rope does not stretch, the distance between points on the rope does not change(this is why the acceleration is the same for both sides of the atwood machine). I have marked points P, Q, and R in the attached diagram. As I said before, the relative distance between these points are constant. Therefore, when P moves distance d, so should Q and R since this is just equivalent to sliding the rope along a numberline (also drawn). The final y coordinates of the masses are Ya = y1 + d and Yb = y2 - d. The correct answer is stated as Ya = y1+d/2 and Yb = y2 - d/2.

What am I missing?

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