Suppose that initially the system of masses shown below is held motionless. All surfaces are frictionless, and the pulley is fixed to mass M. The string is completely inextensible: its length is constant. We are interested in the acceleration of each mass at the instant right after they are released. Note that at this instant the string holding m2 is still vertical.
[Figure: System showing mass M on horizontal surface connected via pulley to hanging masses m1 and m2]
(a) Draw free-body diagrams showing and labelling all forces that act on the three masses at the instant right after they are released.
(b) Write Newton's second law as it applies to each mass. Explain briefly why M accelerates.
(c) Let A be the acceleration of mass M, a1 that of m1, and a2 that of m2. Find a relation between the accelerations of the three masses.
(d) Determine the tension T in the string and the three accelerations in terms of the masses and of the gravitational acceleration, g.
(e) Take the limits of your results in part (d) as M → ∞. What do they become if instead you take m1 → 0, or if you take m2 → 0 (not both at the same time)? Do your results make sense in all those limits?