P. 4249. The two ends of a flexible rope of uniform density are fixed at the same height, as shown in the figure. Starting from the equilibrium position, we perform the following two experiments:
I. We pull down the midpoint of the rope till it reaches point A. (At this time the rope almost has a V-shape.)
II. From the equilibrium position we pull up the midpoint of the rope to the point B. (So now the shape of the rope is like an upside down V.)
The total work we did in the two processes is W. How much work is needed to lift the midpoint of the rope to the point C?
Deadline expired on 10 May 2010.