Two bodies with masses m and M are attached to each other through a frictionless pulley. What are the forces acting on the bodies and what are the motion equations of the bodies?

By Newton's second law, for every body with mass m moving with acceleration a the product ma equals the resultant of all the forces acting on it. For the two bodies we get, accordingly:      Ma1 = Mg - T      ma2 = mg - T Since the two bodies are tied together, but move in opposite directions, we can write a third equation:      a1 = - a2 Denote: a1 = a , and substitute into the first two equations:      Ma = Mg - T      ma = T - mg Add the two equations and get:      a (m + M) = g (M - m) Solve for a :      a = g( M - m)/(M + m) Solve the first equation for T :      T = M (g - a) Substitute the a we found, and get:      T = 2mM/(M + m)

Initial Values of Parameters Mass of left body (k) 4 kg Mass of right body (k) 7 kg Gravitational constant (g) 10 m/sec2