Problem $1$

A block with a mass of $0\mathrm{.}045$ kg is attached to a low mass spring, hanging vertically from the ceiling. The spring has a stiffness of $15\mathrm{.}0\frac{N}{m}.$ At time $t=0s,$ the spring is stretched from its relaxed length by $s_i=0\mathrm{.}08m.$ At this point, the block is $2\mathrm{.}0$ m above the floor $($measured from the top of the block$)$ and moving downward at a speed of $v_i=2\mathrm{.}0\frac{m}{s}.$

$($a$)$ What is the speed of the block when the spring has a stretch $s_f=0\mathrm{.}14m?$ Start from a fundamental principle and show all work. Be explicit about your choice of system.

$($b$)$ At the point where the stretch of the spring is $0\mathrm{.}14$ m $,$ what is the net force on the block? Express your answer as a three$-$component vector, using the coordinate system in the diagram $(+x$ is right, $+y$ is up$,+z$ is out of the page$).$