To find the acceleration of the box, we can follow these steps:
1. **Calculate the force of friction (F_friction)**:
The force of friction can be calculated using the formula:
\[
F_{\text{friction}} = \mu \cdot F_{\text{normal}}
\]
where \(\mu\) is the coefficient of sliding friction and \(F_{\text{normal}}\) is the normal force. For a box on a horizontal surface, the normal force is equal to the weight of the box (the gravitational force acting on it).
Given:
\[
\mu = 0.15
\]
\[
F_{\text{normal}} = 660 \, \text{N}
\]
Now we can calculate the force of friction:
\[
F_{\text{friction}} = 0.15 \cdot 660 \, \text{N} = 99 \, \text{N}
\]
2. **Determine the net force (F_net)**:
The net force acting on the box can be found by subtracting the force of friction from the pushing force:
\[
F_{\text{net}} = F_{\text{push}} - F_{\text{friction}}
\]
Given:
\[
F_{\text{push}} = 500 \, \text{N}
\]
Substituting in the values:
\[
F_{\text{net}} = 500 \, \text{N} - 99 \, \text{N} = 401 \, \text{N}
\]
3. **Calculate the acceleration (a)**:
To find the acceleration, we use Newton's second law:
\[
F_{\text{net}} = m \cdot a
\]
where \(m\) is the mass of the box. First, we need to find the mass of the box using the weight (weight = mass Ć gravity):
\[
F_{\text{gravity}} = m \cdot g
\]
where \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)).
Thus, the mass \(m\) can be calculated as:
\[
m = \frac{F_{\text{gravity}}}{g} = \frac{660 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 67.14 \, \text{kg}
\]
Now we can find the acceleration:
\[
a = \frac{F_{\text{net}}}{m} = \frac{401 \, \text{N}}{67.14 \, \text{kg}} \approx 5.96 \, \text{m/s}^2
\]
4. **Round the acceleration**:
The calculated acceleration is approximately \(6 \, \text{m/s}^2\).
Thus, the answer is:
**D. 6 m/sĀ²**