Question

The masses of blocks A and B are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on the floor and are connected by a massless string passing over a massless and frictionless pulley. An upward force F is applied to the pulley. Find the acceleration aA of a block A and aB of block B when the value of F is: (a) 124 N, (b) 294 N, (c) 424 N

Answer 1

Also need Tension in the rope

Answer 2

It is better to work in the pulley's frame of reference. The acceleration of pulley can be found out by

a = F/(ma+mb)
This acceleration is in upward direction. Therefore a pseudo force will act on both the masses in the downward direction. We can now draw their free body diagram

Be extremely careful to note that a' is the acceleration of ma and mb in the pulley frame of system and NOT the inertial frame which is the ground. We can write equation of motion for both masses and solve for a' and T.

Now we have to find aA and aB which are their acceleration in the ground frame of reference.
Now the entire system is going upwards with "a".

Mass a is moving upward with "a" and downwards with "a' "
So its total downward acceleration will be = aA = a' - a

Mass b is moving upwards with "a" and upwards with "a' "
So its total upwards acceleration will be = aB = a' + a