NOTE: The system is released from rest in a vertical plane.
DISCUSSION
Recall the four-step plan for solving kinetics problems.
Step 1: FBDs
Here it is recommended (as for all problems using the Newton/Euler approach) to draw individual FBDs for the system: one each for block A and block B, and for the pulley.
Step 2: Kinetics (Newton/Euler)
Write down the Euler equation for the pulley, along with the Newton equations for A and B in the vertical direction. With that, you have three equations and five unknowns (TA, TB, aA, aB and αpulley). Please note that the tensions TA and TB are NOT equal to the weights of blocks A and B.
Recall from ME 270 that friction opposes (impending) motion. For this problem, you need to decide in which direction (CW or CCW) the pulley will be rotating. To do this, consider first the friction-free case. Once the direction of rotation is determined from that, draw the pulley FBD with the friction torque opposing that motion.
Step 3: Kinematics
It is recommended that you write down the acceleration of points C and E on the pulley (see figure above) in terms of the acceleration of the pulley center O. Then, relate the accelerations of A and B to the accelerations of C and E, respectively.
Step 4: Solve
At this point, you have five equations and five unknowns. Solve!
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