Question

a box with a mass of \m\ sits on the ground at rest. a student presses down on the box with an applied force $f_a$. the box remains at rest. write an equilibrium equation for the box and then solve it for the box’s mass. which of the following equations is correct for the box’s mass \m\?
$\square$ $m = f_n + f_a$
$\square$ $m = f_n - f_a$
$\square$ $m= \frac{f_n - f_a}{g}$
$\square$ $m = \frac{f_n + f_a}{g}$
$\square$ $m = (f_n + f_a) * g$

Explanation:

Step1: Analyze Forces in Vertical Direction

The box is in equilibrium (at rest), so vertical forces sum to zero. The normal force \( F_N \) acts upward, the applied force \( F_A \) and weight \( mg \) act downward. So, \( F_N = F_A + mg \).

Step2: Solve for Mass \( m \)

Rearrange the equilibrium equation:
\( F_N - F_A = mg \)
Divide both sides by \( g \):
\( m = \frac{F_N - F_A}{g} \)

Answer:

\( \boldsymbol{m = \frac{F_N - F_A}{g}} \) (the third option)