Two masses are connected by a massless string and a frictionless, massless pulley.  One mass, m = 3.70 kg, hangs freely, and the other mass, M = 6.50 kg, slides along a horizontal surface with a coefficient of kinetic friction,μK, of 0.645.M moves to the right, and m drops with an initial velocity of 0.685 m/s.The system moves a distance, d, before coming to rest

.(a) (5 points) Determine the initial kinetic energy of the system.

 (b)(5 points)Write down the expression for the change in potential energy of the system in terms of m, M, and d.

 (c)(5 points)Write down the work that friction does on the system in terms of m, M, μK, and d. 

 (d)(10 points)Use the work-kinetic energy theorem to calculate d.