A 4 kg mass is resting on a horizontal surface. For this surface `mu_s = 0.6` & `mu_(k) = 0.2`. Force required to move the body with `5ms^(-2)` acceleration is (g = `10ms^(-2)`)

Options

A. 20 N
B. 24 N
C. 28 N
D. 32 N

Answer

To solve the problem of determining the force required to move a 4 kg mass with an acceleration of 5 m/s² on a horizontal surface, we will follow these steps:

### Step 1: Calculate the Normal Force (N)
The normal force (N) acting on the mass can be calculated using the formula:
\[ N = m \cdot g \]
where:
- \( m = 4 \, \text{kg} \) (mass of the object)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ N = 4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 40 \, \text{N} \]

### Step 2: Calculate the Frictional Force (F_k)
The frictional force (F_k) opposing the motion can be calculated using the kinetic friction coefficient (\( \mu_k \)):
\[ F_k = \mu_k \cdot N \]
where:
- \( \mu_k = 0.2 \)

Substituting the values:
\[ F_k = 0.2 \cdot 40 \, \text{N} = 8 \, \text{N} \]

### Step 3: Apply Newton's Second Law
According to Newton's second law, the net force (F_net) acting on the mass is given by:
\[ F_{\text{net}} = m \cdot a \]
where:
- \( a = 5 \, \text{m/s}^2 \)

Substituting the values:
\[ F_{\text{net}} = 4 \, \text{kg} \cdot 5 \, \text{m/s}^2 = 20 \, \text{N} \]

### Step 4: Calculate the Total Force (F)
The total force (F) required to move the mass must overcome both the frictional force and provide the net force for acceleration:
\[ F = F_{\text{net}} + F_k \]
Substituting the values:
\[ F = 20 \, \text{N} + 8 \, \text{N} = 28 \, \text{N} \]

### Conclusion
The force required to move the body with an acceleration of \( 5 \, \text{m/s}^2 \) is **28 N**.