$18.$ A $9$ kg block is connected to an empty $0\mathrm{.}5$ kg bucket by a mass$-$

less rope running over a pulley as shown below in Fig. $1.$ The static

friction coefficient between the table and the block is $0\mathrm{.}4$ and the

kinetic friction coefficient $0\mathrm{.}3.$ Rockes are gradually added to the

bucket until the system just begins to move.

$3$

$($a$)$ Calculate the mass of rocks added to the bucket.

$($b$)$ Calculate the acceleration of the system.

Figure $1$: Problem #$8$ DiagramFigure $1$: Problem #$8$ Diagram