Problem $2(25$ Marks$)$

Two blocks with masses $(m_1$ and $m_2)$ on a table are moved by a hanging mass $(\{$:$m_3)$ attached to a

pulley $($see figure below$).$ Assume the masses of the cables and pulleys can be ignored, all the

cables are rigid, and all surfaces including bench and pulley are frictionless.

A$.$ Draw separate free body diagrams for the three blocks $(m_1,m_2,$ and $\{$:$m_3).(6$ marks$)$

B$.$ When $m_3$ hits the ground, what is the displacement of $m_2$ on the bench? $(3$ marks$)$

C$.$ If $m_1,m_2$ and $m_3$ are $1\mathrm{.}00kg,2\mathrm{.}00kg$ and $3\mathrm{.}00kg,$ respectively, what is the tensions for

each cable, i$.$e$.,T_{12},T_{23}$ and $T_3?(6$ marks$)$

D$.$ What is the acceleration of $m_3?(4$ marks$)$

E$.$ If all the blocks start from rest, how long will $m_3$ take before it hits the ground? $(6$ marks$)$