Energy Loss Question

1. The problem statement, all variables and given/known data
A (smooth) rope of length L and mass m is placed above a hole in a table. One end of the rope falls through the hole, pulling steadily on the remainder of the rope. Find the velocity of the rope as a function of the distance to the end of the rope, x. Ignore friction of the rope as it unwinds. Then find the acceleration of the falling rope and the mechanical energy lost from the rope as the end of the rope leaves the table. Note that the rope length is less than the height of the table.

2. Relevant equations

3. The attempt at a solution
Well I already got the right equations for v and a….

v(x) = (2gx/3)^.5
a(x) = [(2g/3)^.5] / 2√x

But I don’t understand how to find the mechanical energy loss. It seems like mechanical energy shouldn’t be lost here, because the lost PE is just changing into KE…

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