Answer
(a) The kinetic frictional force $f_k=21.17N$
(b) The kinetic frictional force $f_k=23.76N$
(c) The kinetic frictional force $f_k=18.58N$
Work Step by Step
The formula of the kinetic frictional force is $$f_k=\mu_kF_N=\mu_km(g\pm a)$$
with mass of the object in motion $m$, its acceleration $a$, coefficient $\mu_k$ and gravitational acceleration $g=9.8m/s^2$. The $\pm$ sign depends of the direction of $a$.
Here, we also have $\mu_k=0.36$ and $m=6kg$
(a) The elevator is stationary, meaning $a=0$
$$f_k=0.36\times6(9.8+0)=21.17N$$
(b) The elevator is moving upward with $a=1.2m/s^2$
This means, $F_N-mg=ma$. So $F_N=m(g+a)$
Therefore, $$f_k=0.36\times6(9.8+1.2)=23.76N$$
(c) The elevator is moving downward with $a=1.2m/s^2$
This means, $mg-F_N=ma$. So $F_N=m(g-a)$
Therefore, $$f_k=0.36\times6(9.8-1.2)=18.58N$$
