Question

The image below illustrates the application of two forces on a box placed on a frictionless surface.
The image is of a box in the middle and on the left side of the box, 16 N is pushing on the box, and on the right side of the box, 12 N is pushing on the box.
What is the mass of the box if it experiences an acceleration of 2 m/s²?

Answer 1

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**.