The pulley of mass M_p has a radius of gyration about O of k_O. If a motor M supplies a force to the cable of P = a (b − ce^−dx), where x is the amount of cable wound up, determine the speed of the crate of mass Mc when it has been hoisted a distance h starting from rest. Neglect the mass of the cable and assume the cable does not slip on the pulley.

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Given: Mp = 10 kg Mc = 50 kg ko = 0.21 m r = 0.3 m h = 2 m a = 800 N b = 3 c = 2 d = m