A horizontal force of `1.2kg` is applied on a `1.5kg` block, which rests on a horizontal surface If the coefficient of friction is `0.3` find the acceleration produced in the block.

Explanation

To solve the problem step by step, we need to follow these calculations:

### 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:
- \( m = 1.5 \, \text{kg} \) (mass of the block)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 1.5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 14.7 \, \text{N} \]

### Step 2: Calculate the normal force (N)
Since the block is resting on a horizontal surface, the normal force (N) is equal to the weight of the block:
\[ N = W = 14.7 \, \text{N} \]

### Step 3: Calculate the frictional force (F_friction)
The frictional force can be calculated using the formula:
\[ F_{\text{friction}} = \mu \cdot N \]
Where:
- \( \mu = 0.3 \) (coefficient of friction)

Calculating the frictional force:
\[ F_{\text{friction}} = 0.3 \cdot 14.7 \, \text{N} = 4.41 \, \text{N} \]

### Step 4: Calculate the applied force (F_applied)
The applied force is given as \( 1.2 \, \text{kg} \) equivalent force. To convert this to Newtons:
\[ F_{\text{applied}} = 1.2 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 11.76 \, \text{N} \]

### Step 5: Calculate the net force (F_net)
The net force acting on the block can be calculated as:
\[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \]
Calculating the net force:
\[ F_{\text{net}} = 11.76 \, \text{N} - 4.41 \, \text{N} = 7.35 \, \text{N} \]

### Step 6: Calculate the acceleration (a)
Using Newton's second law, we can find the acceleration:
\[ F_{\text{net}} = m \cdot a \]
Rearranging for acceleration:
\[ a = \frac{F_{\text{net}}}{m} \]
Calculating the acceleration:
\[ a = \frac{7.35 \, \text{N}}{1.5 \, \text{kg}} = 4.9 \, \text{m/s}^2 \]

### Final Answer
The acceleration produced in the block is:
\[ a = 4.9 \, \text{m/s}^2 \]

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