Answer
The magnitude of the applied force is 135 N
Work Step by Step
We can find the normal force $F_N$ between the box and the elevator floor.
$\sum F = ma$
$F_N - mg = ma$
$F_N = m(a+g) = (36.0~kg)(1.90~m/s^2+9.80~m/s^2)$
$F_N = 421.2~N$
Since the box is sliding at a constant speed, the applied force $F$ is equal in magnitude to the force of kinetic friction $F_f$.
$F = F_f$
$F = F_N~\mu_k$
$F = (421.2~N)(0.32)$
$F = 135~N$
The magnitude of the applied force is 135 N
