A wooden block of mass 100 Kg is kept on a horizontal platform. A force of 60 N is required to just slide the block. But a force of 49N is just sufficient to keep the block.moving with uniform velocity. What is the coefficient of kinetic friction?

Options

A. 0.5
B. 0.25
C. 0.05
D. 0.005

Explanation

To find the coefficient of kinetic friction for the wooden block, we can follow these steps:

### Step 1: Identify the known values
- Mass of the block (m) = 100 kg
- Force required to just slide the block (static friction force, F_s) = 60 N
- Force required to keep the block moving with uniform velocity (kinetic friction force, F_k) = 49 N

### Step 2: Calculate the weight of the block
The weight (W) of the block can be calculated using the formula:
\[ W = m \times g \]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \).

Calculating the weight:
\[ W = 100 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 981 \, \text{N} \]

### Step 3: Calculate the coefficient of kinetic friction
The coefficient of kinetic friction (μ_k) can be calculated using the formula:
\[ \mu_k = \frac{F_k}{W} \]

Substituting the known values:
\[ \mu_k = \frac{49 \, \text{N}}{981 \, \text{N}} \]

Calculating the coefficient:
\[ \mu_k \approx 0.0499 \]

### Step 4: Final answer
The coefficient of kinetic friction is approximately \( \mu_k \approx 0.05 \).

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