Answer
The mass of the box is 1.9 kg.
Work Step by Step
Let's consider the force equation for the three vertical forces acting on the box. Let's assume that the applied force $F$ of 23 N keeps the box at rest. Then the acceleration is zero.
$\sum ~F_y = ma$
$F ~sin(\theta) + F ~cos(\theta)\cdot \mu_s - mg = 0$
$m = \frac{F ~sin(\theta) + F ~cos(\theta)\cdot \mu_s}{g}$
$m = \frac{23 ~N ~sin(28^{\circ}) + 23 ~N ~cos(28^{\circ})\cdot 0.40}{9.80 ~m/s^2}$
$m = 1.9 ~kg$
The mass of the box is 1.9 kg.
