A rope with mass density σ kg/m lies in a heap at the edge of a table. One end of the rope initially sticks out an infinitesimal distance from the heap. You grab this end and accelerate it downward with acceleration a. Assume that there is no friction of the rope with itself as it unravels. As a function of time, what force does your hand apply to the rope? Find the value of a that makes your force always equal to zero.
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