A force of 49 N just able to move a block of wood weighing 10 kg on a rough horizontal surface , then coefficient of friction is

Options

A. `1/2`
B. `1/4`
C. `1/6`
D. `1/8`

Answer

To solve the problem of finding the coefficient of friction (μ) for a block of wood weighing 10 kg that requires a force of 49 N to just start moving on a rough horizontal surface, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Weight of the Block:**
The weight (W) of the block can be calculated using the formula:
\[ W = m \cdot g \]
where \( m = 10 \, \text{kg} \) (mass of the block) and \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity).
\[ W = 10 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 100 \, \text{N} \]

2. **Understand the Forces Acting on the Block:**
- The applied force (F) to move the block is 49 N.
- The frictional force (f) opposing the motion is equal to the applied force when the block is just about to move. Therefore, \( f = 49 \, \text{N} \).

3. **Use the Formula for Friction:**
The frictional force can be expressed in terms of the coefficient of friction (μ) and the normal force (N):
\[ f = \mu \cdot N \]
Since the block is on a horizontal surface, the normal force (N) is equal to the weight of the block:
\[ N = W = 100 \, \text{N} \]

4. **Set Up the Equation:**
Substitute the known values into the friction formula:
\[ 49 \, \text{N} = \mu \cdot 100 \, \text{N} \]

5. **Solve for the Coefficient of Friction (μ):**
Rearranging the equation gives:
\[ \mu = \frac{49 \, \text{N}}{100 \, \text{N}} = 0.49 \]

6. **Conclusion:**
The coefficient of friction (μ) is approximately 0.49.

### Final Answer:
\[ \mu \approx 0.49 \]