I. (25 points)
T3
θ
m1 T1 m2 T2 m3
This is the same situation as problem I on Exam 1, except now there's friction!!! Three boxes (with masses $m_1$, $m_2$, and $m_3$, as shown in the diagram) are on a flat surface with coefficient of kinetic friction $\mu_k$, and are connected with two massless ropes. You pull on a third rope, giving it a force $T_3$ at an angle $\theta$ above the horizontal, and the three boxes move to the right (all with the same acceleration). The tensions in the two ropes connecting the boxes are $T_1$ and $T_2$.
1.1 (9 pts) Draw three separate free-body diagrams, one for each box. Label all forces.
1.2 (8 pts) Find the magnitude of the total frictional force that the floor exerts on all three boxes. For parts 1.2 express your answers in terms of the variables $m_1$, $m_2$, $m_3$, $T_3$, $\theta$, $g$, and $\mu_k$. (You don't have to use all these variables in each answer, but your answer should include only these variables and no others.)
1.3 (8 pts) Find the acceleration of the boxes (just one answer). (And see above.)
