A horizontal force of 20 N is applied to a block of 10 kg resting on a rough horizontal surface. How much additional force is required to just move the block, if the coefficient of static friction between the block and the surface is 0.4 ?

Options

A. 15.5 N
B. 10.3 N
C. 8.5 N
D. 19.2 N

Explanation

To solve the problem, we need to determine how much additional force is required to just move a block resting on a rough horizontal surface when a horizontal force of 20 N is already applied. The coefficient of static friction between the block and the surface is given as 0.4.

### 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:
- \( m = 10 \, \text{kg} \) (mass of the block)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 10 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 98 \, \text{N} \]

**Step 2: Calculate the normal force (N).**
On a horizontal surface, the normal force is equal to the weight of the block:
\[ N = W = 98 \, \text{N} \]

**Step 3: Calculate the maximum static friction force (Fs).**
The maximum static friction force can be calculated using the formula:
\[ F_s = \mu \cdot N \]
where:
- \( \mu = 0.4 \) (coefficient of static friction)

Calculating the static friction force:
\[ F_s = 0.4 \cdot 98 \, \text{N} = 39.2 \, \text{N} \]

**Step 4: Determine the total force required to overcome static friction.**
To just move the block, the total applied force must equal the static friction force. The total force (F_total) applied is the sum of the already applied force (F1) and the additional force (F2):
\[ F_{\text{total}} = F_1 + F_2 \]

Given that \( F_1 = 20 \, \text{N} \):
\[ F_{\text{total}} = 20 \, \text{N} + F_2 \]

Setting this equal to the static friction force:
\[ 20 \, \text{N} + F_2 = 39.2 \, \text{N} \]

**Step 5: Solve for the additional force (F2).**
Rearranging the equation to find \( F_2 \):
\[ F_2 = 39.2 \, \text{N} - 20 \, \text{N} = 19.2 \, \text{N} \]

### Final Answer:
The additional force required to just move the block is **19.2 N**.

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