To solve the problem, we need to calculate the acceleration of a body being pushed across a horizontal floor, given its weight, the coefficients of static and dynamic friction, and the acceleration due to gravity.
### Step-by-Step Solution:
1. **Identify the given values:**
- Weight of the body (W) = 64 N
- Coefficient of static friction (μs) = 0.6
- Coefficient of kinetic friction (μk) = 0.4
- Acceleration due to gravity (g) = 9.8 m/s² (or can be approximated as 10 m/s² for simplicity).
2. **Calculate the normal force (N):**
Since the body is on a horizontal surface, the normal force (N) is equal to the weight of the body.
\[
N = W = 64 \, \text{N}
\]
3. **Calculate the force of static friction (Fs):**
The maximum static friction force can be calculated using the formula:
\[
F_s = \mu_s \cdot N
\]
Substituting the values:
\[
F_s = 0.6 \cdot 64 = 38.4 \, \text{N}
\]
4. **Determine the force of kinetic friction (Fk):**
Once the body starts moving, the kinetic friction force acts on it. The kinetic friction can be calculated as:
\[
F_k = \mu_k \cdot N
\]
Substituting the values:
\[
F_k = 0.4 \cdot 64 = 25.6 \, \text{N}
\]
5. **Calculate the net force (F_net) acting on the body:**
The net force acting on the body when it is moving is the applied force minus the kinetic friction force. The applied force (F) is equal to the maximum static friction force since it just started moving:
\[
F = F_s = 38.4 \, \text{N}
\]
Therefore, the net force is:
\[
F_{\text{net}} = F - F_k = 38.4 - 25.6 = 12.8 \, \text{N}
\]
6. **Calculate the mass (m) of the body:**
Using the weight and the acceleration due to gravity, we can find the mass:
\[
m = \frac{W}{g} = \frac{64}{9.8} \approx 6.53 \, \text{kg} \quad \text{(or use } g \approx 10 \text{ for simplicity, } m \approx 6.4 \, \text{kg)}
\]
7. **Calculate the acceleration (a) of the body:**
Using Newton's second law, \( F = m \cdot a \), we can find the acceleration:
\[
a = \frac{F_{\text{net}}}{m} = \frac{12.8}{m}
\]
Substituting \( m = \frac{64}{g} \):
\[
a = \frac{12.8}{\frac{64}{g}} = \frac{12.8g}{64} = 0.2g
\]
### Final Answer:
The acceleration of the body is:
\[
a = 0.2g \, \text{m/s}^2
\]
