Question

A box weighing 347 N is sliding across a cement floor and the coefficient of sliding friction between the box and the floor is 0.2. If the force pushing the box is 500 N, what is the acceleration of the box?

A. 6 m/s2

B. 3 m/s2

C. 36 m/s2

D. 12 m/s2

Answer 1

To find the acceleration of the sliding box, we need to determine the net force acting on it. The steps to solve this problem are as follows:

1. **Calculate the force of friction (F_friction)**:
The force of friction can be calculated using the formula:
\[
F_{\text{friction}} = \mu \cdot F_{\text{normal}}
\]
Here, \( \mu \) is the coefficient of sliding friction (0.2) and \( F_{\text{normal}} \) is the weight of the box (347 N).

\[
F_{\text{friction}} = 0.2 \cdot 347 \, \text{N} = 69.4 \, \text{N}
\]

2. **Calculate the net force (F_net)**:
The net force is the applied force minus the force of friction.
\[
F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}}
\]
Given that the pushing force is 500 N, we can calculate \( F_{\text{net}} \):
\[
F_{\text{net}} = 500 \, \text{N} - 69.4 \, \text{N} = 430.6 \, \text{N}
\]

3. **Calculate the acceleration (a)**:
Now we can use Newton's second law to find the acceleration:
\[
F_{\text{net}} = m \cdot a
\]
We need to find the mass (m) of the box first using its weight:
\[
F_{\text{weight}} = m \cdot g \quad \text{(where } g \text{ is the acceleration due to gravity, approximately } 9.81 \, \text{m/s}^2\text{)}
\]
Rearranging gives:
\[
m = \frac{F_{\text{weight}}}{g} = \frac{347 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 35.36 \, \text{kg}
\]

Now using \( F_{\text{net}} \) to find acceleration:
\[
a = \frac{F_{\text{net}}}{m} = \frac{430.6 \, \text{N}}{35.36 \, \text{kg}} \approx 12.2 \, \text{m/s}^2
\]

Since the closest answer choice is D:

**Answer: D. 12 m/s²**