I answered (a) then saw that you had already done that! Very good.
For (c), a "range" of values for
must have both an upper and lower bound. The upper bound is easy:
cannot be so large as to have no motion at all. The total force on the system is
(you must have calculated that when you did (a)) and the masses will not move if that is negative
leads to
. Now you are told that the mass A, which, as you calculated for (b) has speed
when B stops falling and so the only force on mass A is the friction force
. The acceleration due to that is
and that must stop A before it reaches the pulley.
A is initially distance 2h from the pulley. After B has fallen a distance h, A will have moved distance h also and so will be distance h from the pulley. Using decceleration
to determine the time required for A to stop. Calculate the distance A will have traveled. Find the value of
so that distance would be exactly h. That is the lower bound for
.