A rope of length L and mass M lies coiled on a table. Starting at t =

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A rope of length L and mass M lies coiled on a table. Starting at t = 0, one end of the rope is lifted from the table with a force F such that it moves with a constant velocity v,

(a) Find the height of the center of mass of the rope as a function of time.

(b) Differentiate your result in (a) twice to find the acceleration of the center of mass.

(c) Assuming that the force exerted by the table equals the weight of the rope still there, find the force F you exert on the top of the rope.

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