(Solved): 4. The given diagram describes a three-pulley system of M,P, and Q. These pulleys are connected to ...

4. The given diagram describes a three-pulley system of $$M,P$$, and $$Q$$. These pulleys are connected to two masses $$A$$ and $$B$$ as shown. Block $$A$$ is initially moving downward and attached to pulley $$P$$; therefore block A moves up and down with pulley $$P$$. The axle of this "block and tackle" pulley holds one end of the cable which runs over a pulley $$M$$ back around pulley $$P$$ and onwards to pulley $$Q$$ as illustrated on the diagram. Block $$A$$ is $$60\mathrm{kg}$$ and block $$B$$ is $$30\mathrm{kg}$$. The coefficient of static and kinetic frictions between block $$B$$ and the platform are $${?}_s=0.4$$ and $${?}_k=0.3$$ respectively. Assume that the pulleys are frictionless and have negligible masses. (a) Draw free body diagrams for the important objects. (b) Write the kinematic constraint that applies to blocks $$A$$ and $$B$$. (c) Determine the tension in the cable, and the acceleration of each block.