To find the mass of the box, we can use Newton's second law of motion, which states:
\[ F = m \cdot a \]
where:
- \( F \) is the net force acting on the object,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.
In this scenario, there are two forces acting on the box: 16 N to the left and 12 N to the right. Since the box is on a frictionless surface, we can calculate the net force acting on the box.
The net force \( F_{\text{net}} \) can be calculated as:
\[ F_{\text{net}} = F_{\text{left}} - F_{\text{right}} = 16 , \text{N} - 12 , \text{N} = 4 , \text{N} \]
The box experiences an acceleration \( a = 2 , \text{m/s}^2 \). Now, we can rearrange the equation \( F = m \cdot a \) to solve for mass \( m \):
\[ m = \frac{F_{\text{net}}}{a} \]
Substituting the values we have:
\[ m = \frac{4 , \text{N}}{2 , \text{m/s}^2} = 2 , \text{kg} \]
Thus, the mass of the box is 2 kg.