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Let's break down the given problem step by step.

### Given:
- Mass of the cargo box, \( m = 90 \, \text{kg} \)
- Applied force, \( F_{\text{applied}} = 500 \, \text{N} \)
- Coefficient of friction, \( \mu = 0.52 \)
- Gravitational acceleration, \( g = 9.8 \, \text{m/s}^2 \)

### Step 1: Calculate the normal force
The normal force \( F_{\text{normal}} \) is equal to the weight of the box since there is no vertical acceleration. So, we can find it as:
\[
F_{\text{normal}} = m \cdot g = 90 \cdot 9.8 = 882 \, \text{N}
\]

### Step 2: Calculate the force of friction
The force of friction \( F_{\text{friction}} \) can be calculated using the coefficient of friction:
\[
F_{\text{friction}} = \mu \cdot F_{\text{normal}} = 0.52 \cdot 882 = 458.64 \, \text{N}
\]

### Step 3: Calculate the net force
The net force \( F_{\text{net}} \) acting on the box is the difference between the applied force and the force of friction:
\[
F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 500 - 458.64 = 41.36 \, \text{N}
\]

### Step 4: Calculate the acceleration
Now, using Newton's second law \( F = m \cdot a \), we can find the acceleration \( a \) as:
\[
a = \frac{F_{\text{net}}}{m} = \frac{41.36}{90} \approx 0.459 \, \text{m/s}^2
\]

### Final Answer:
The acceleration of the cargo box is approximately \( 0.459 \, \text{m/s}^2 \).

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Would you like further details or have any questions on the process?

### Related Questions:
1. How would the acceleration change if the mass of the box were increased?
2. What happens to the acceleration if the coefficient of friction is reduced to 0.3?
3. How can you calculate the stopping distance of the box given an initial velocity?
4. What if the box is being pulled at an angle? How would that affect the normal force and friction?
5. How would the solution differ if the surface were inclined?

### Tip:
Always check whether the force you're applying is sufficient to overcome friction before calculating acceleration!

A 90-kg cargo box is slid along the floor by a 500-N force. The coefficient of friction between the box and the floor is 0.52. Find the acceleration of the cargo box.

Find out how to calculate the acceleration of a 90-kg cargo box being pushed by a 500-N force with a coefficient of friction of 0.52. This physics problem applies Newton's Second Law of Motion to determine acceleration in the presence of friction. Suitable for high school students (Grades 9-12).

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