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DISCUSSION and HINTS
There are two critical issues involved in solving this problem.
- One, is starting out with good free body diagrams. Recall from our lecture discussion that the Newton/Euler equations typically prefer INDIVIDUAL FBDs. Note this in the discussion of Step 1 below.
- Second, we need to be careful on signs in establishing our kinematics relating the acceleration of the two blocks to the angular acceleration of the pulley.
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw individual free body diagrams (FBDs) of the pulley and the two blocks. A single FBD of the entire system will not be useful here. Let’s say that we employ a “standard” xy-coordinate system (with x to the right and y up) for all FBDs.
Step 2: Kinetics (Newton/Euler)
You will need an Euler (moment) equation of the pulley about point C. In addition, write down the Newton equations for the y-motion for each of the two blocks. Write down all three equations using the sign convention discussed above.
Step 3: Kinematics
Here is where we need to be careful with signs. Write down the rigid body kinematics equations relating the accelerations of A and B back to the pulley center C:
aA = aC + α x rA/C – ω2rA/C
aB = aC + α x rB/C – ω2rB/C
This pair of equations will provide you with the relationships among aA, aB and α. Take note of the signs involved in these equations.
Step 4: Solve
From your equations in Steps 2 and 3, solve for the angular acceleration of the pulley and the accelerations of the two blocks.