A block of mass 4 kg is kept on a rough horizontal surface. The coefficient of static friction is 0.8. If a forace of 19 N is applied on the block parallel to the floor, then the force of friction between the block and floor is

Options

A. 32 N
B. 18 N
C. 19 N
D. 9.8 N

Answer

To solve the problem, we need to determine the force of friction acting on a block of mass 4 kg placed on a rough horizontal surface when a force of 19 N is applied parallel to the floor. The coefficient of static friction is given as 0.8.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the block (m) = 4 kg
- Coefficient of static friction (μ) = 0.8
- Applied force (F_applied) = 19 N

2. **Calculate the Normal Force (N):**
The normal force (N) on a horizontal surface is equal to the weight of the block, which can be calculated using the formula:
\[ N = m \cdot g \]
where \( g \) (acceleration due to gravity) is approximately \( 9.8 \, \text{m/s}^2 \).
\[ N = 4 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 39.2 \, \text{N} \]

3. **Calculate the Maximum Static Friction (F_s_max):**
The maximum static friction can be calculated using the formula:
\[ F_{s_{max}} = \mu \cdot N \]
Substituting the values:
\[ F_{s_{max}} = 0.8 \cdot 39.2 \, \text{N} = 31.36 \, \text{N} \]

4. **Compare the Applied Force with Maximum Static Friction:**
Now, we compare the applied force (19 N) with the maximum static friction (31.36 N):
- Since \( F_{applied} (19 \, \text{N}) < F_{s_{max}} (31.36 \, \text{N}) \), the block will not move.

5. **Determine the Force of Friction (F_friction):**
When the applied force is less than the maximum static friction, the force of friction will equal the applied force:
\[ F_{friction} = F_{applied} = 19 \, \text{N} \]

### Final Answer:
The force of friction between the block and the floor is **19 N**.