(Solved): Problem \#2 (25 Points) Given: A mechanical system is shown on the right. You may neglect the masse ...

Problem \#2 (25 Points) Given: A mechanical system is shown on the right. You may neglect the masses of the pulleys and cords, and you may assume that the block is initially at rest. Find: a) The kinematic (i.e., dependent motion) equations for the motor-pulley system. This includes the equations for position, velocity, acceleration, and displacement. b) The displacement of block $A$ if the motor pulls down the cord, which connects motor $M$ and pulley $B$, by a known distance of $?y_B$. c) The acceleration of block $A$ if a point on the cord connecting motor $M$ and pulley $B$ accelerates downward at $1\mathrm{m}/{\mathrm{s}}^2$. d) Assuming the mass of block $A$ is $m_A$ and is a known value, draw the free body diagrams (FBD) for the system (that is, one FBD for block $A$, one FBD for pulley $B$, and one FBD for pulley $D$ ). Label $F_c$ as the tension in the cord connecting motor $M$ and pulley $B$. e) The acceleration of block $A$ if $F_{\mathrm{c}}$ is the known constant tension in the cord connecting motor $M$ and pul