A wooden block of 100 kg is about to be pushed on a floor of coefficient of friction 0.4. What is the magnitude of the force of friction on the wooden block when it is just pushed ?

Options

A. 392 N
B. 294N
C. 196N
D. 490N

Answer

To solve the problem, we need to find the magnitude of the force of friction acting on a wooden block when it is just about to be pushed. Here are the steps to arrive at the solution:

### Step 1: Identify the given values
- Mass of the wooden block (m) = 100 kg
- Coefficient of friction (μ) = 0.4

### 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 \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Substituting the values:
\[ W = 100 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 980 \, \text{N} \]

### Step 3: Determine the normal force
In this scenario, the normal force (N) acting on the block is equal to its weight when it is on a horizontal surface. Therefore:
\[ N = W = 980 \, \text{N} \]

### Step 4: Calculate the force of friction
The force of friction (F_friction) can be calculated using the formula:
\[ F_{\text{friction}} = \mu \times N \]

Substituting the values:
\[ F_{\text{friction}} = 0.4 \times 980 \, \text{N} \]
\[ F_{\text{friction}} = 392 \, \text{N} \]

### Conclusion
The magnitude of the force of friction on the wooden block when it is just pushed is **392 N**.

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