A body of mass 60 kg is dragged with just enough force to start moving on a rough surface with coefficient of static and kinetic frictions `0.5` and `0.4` respectively . On applying the same force , what is the acceleration ?

Options

A. `0.98 m//s^(2)`
B. `9.8 m//s^(2)`
C. `0.54 m// s^(2)`
D. `5.292 m//s^(2)`

Explanation

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

### Step 1: Identify the given values
- Mass of the body, \( m = 60 \, \text{kg} \)
- Coefficient of static friction, \( \mu_s = 0.5 \)
- Coefficient of kinetic friction, \( \mu_k = 0.4 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

### Step 2: Calculate the normal force
The normal force \( N \) acting on the body is equal to the weight of the body since it is on a horizontal surface:
\[ N = m \cdot g = 60 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 588 \, \text{N} \]

### Step 3: Calculate the force of static friction
The force of static friction \( f_s \) that needs to be overcome to start moving the body is given by:
\[ f_s = \mu_s \cdot N = \mu_s \cdot (m \cdot g) = 0.5 \cdot 588 \, \text{N} = 294 \, \text{N} \]

### Step 4: Determine the applied force
Since the body is dragged with just enough force to start moving, the applied force \( F \) is equal to the force of static friction:
\[ F = f_s = 294 \, \text{N} \]

### Step 5: Calculate the force of kinetic friction
Once the body starts moving, the force of kinetic friction \( f_k \) acts on the body:
\[ f_k = \mu_k \cdot N = \mu_k \cdot (m \cdot g) = 0.4 \cdot 588 \, \text{N} = 235.2 \, \text{N} \]

### Step 6: Apply Newton's second law
The net force \( F_{\text{net}} \) acting on the body when it is moving is the applied force minus the force of kinetic friction:
\[ F_{\text{net}} = F - f_k = 294 \, \text{N} - 235.2 \, \text{N} = 58.8 \, \text{N} \]

### Step 7: Calculate the acceleration
Using Newton's second law, \( F = m \cdot a \), we can find the acceleration \( a \):
\[ F_{\text{net}} = m \cdot a \implies a = \frac{F_{\text{net}}}{m} = \frac{58.8 \, \text{N}}{60 \, \text{kg}} = 0.98 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the body is \( 0.98 \, \text{m/s}^2 \).

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