The correct answer is Fa $=$ approx $3\mathrm{.}0256$

$-$ I am looking for an explanation of how to solve it$.$

Particle A with mass $0\mathrm{.}2$ kg is guided by a horizontal slotted arm along a smooth slot in a vertical plate given

by the equation y$=($x$^(2))/(3),$ where x and y are in meters. The arm is constrained to move only vertically. When

x$=1\mathrm{.}2$m$,$ the arm is moving upward $(+$y$)$ with speed $2\mathrm{.}1($m$)/($s$),$ which is decreasing the rate $2\mathrm{.}1($m$)/($s$^(2)).$ The

coefficient of kinetic friction between the arm's slot and the particle is $0\mathrm{.}2.$ Assume the particle is in contact

with only one side of the plate's slot and with only one side of the arm's slot at any given instant.

Find the magnitude of the total force F$\_($A$)$ of the arm on the particle at this instant.