A block of mass 3kg is placed on a rough horizontal surface `(mu_(s)=0.4)` . A force of `8.7N` is applied on the block. The force of friction between the block and floor is .

Options

A. `8.7N`
B. 12N
C. 10N
D. zero

Explanation

To solve the problem, we need to determine the force of friction acting on the block when a force of 8.7 N is applied. Here’s a step-by-step solution:

### Step 1: Calculate the weight of the block
The weight (W) of the block can be calculated using the formula:
\[ W = m \cdot g \]
where:
- \( m = 3 \, \text{kg} \) (mass of the block)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 3 \, \text{kg} \times 10 \, \text{m/s}^2 = 30 \, \text{N} \]

### Step 2: Determine the normal force (N)
On a horizontal surface, the normal force (N) is equal to the weight of the block:
\[ N = W = 30 \, \text{N} \]

### Step 3: Calculate the maximum static friction force
The maximum static friction force (f_s) can be calculated using the coefficient of static friction (μ_s):
\[ f_s = \mu_s \cdot N \]
where:
- \( \mu_s = 0.4 \)

Calculating the maximum static friction:
\[ f_s = 0.4 \times 30 \, \text{N} = 12 \, \text{N} \]

### Step 4: Compare the applied force with the maximum static friction
The applied force (F) is given as:
\[ F = 8.7 \, \text{N} \]

Now, we compare the applied force with the maximum static friction:
- Maximum static friction = 12 N
- Applied force = 8.7 N

Since \( 8.7 \, \text{N} < 12 \, \text{N} \), the block will not move.

### Step 5: Determine the actual force of friction
Since the applied force is less than the maximum static friction, the actual force of friction (f) will be equal to the applied force:
\[ f = F = 8.7 \, \text{N} \]

### Conclusion
The force of friction between the block and the floor is **8.7 N**.

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