A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is

Options

A. `1 ms^(-2)`
B. `3.9 ms^(-2)`
C. `4.9 ms^(-2)`
D. `6 ms^(-2)`

Explanation

To solve the problem step by step, we will first identify the forces acting on the body and then calculate the acceleration.

### Step 1: Identify the forces acting on the body
When the body is pushed, two types of friction are involved: static friction (when the body is at rest) and kinetic friction (when the body is in motion). The static friction coefficient is given as 0.5, and the kinetic friction coefficient is given as 0.4.

### Step 2: Calculate the weight of the body
The weight (W) of the body can be calculated using the formula:
\[ W = mg \]
Where:
- \( m = 60 \, \text{kg} \) (mass of the body)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:
\[ W = 60 \, \text{kg} \times 10 \, \text{m/s}^2 = 600 \, \text{N} \]

### Step 3: Calculate the maximum static friction force
The maximum static friction force (F_s) can be calculated using the formula:
\[ F_s = \mu_s \times R \]
Where:
- \( \mu_s = 0.5 \) (coefficient of static friction)
- \( R = W = 600 \, \text{N} \)

Calculating the maximum static friction force:
\[ F_s = 0.5 \times 600 \, \text{N} = 300 \, \text{N} \]

### Step 4: Calculate the kinetic friction force
Once the body starts moving, the kinetic friction force (F_k) acts on it. This can be calculated using the formula:
\[ F_k = \mu_k \times R \]
Where:
- \( \mu_k = 0.4 \) (coefficient of kinetic friction)

Calculating the kinetic friction force:
\[ F_k = 0.4 \times 600 \, \text{N} = 240 \, \text{N} \]

### Step 5: Determine the net force acting on the body
The applied force (F_applied) is equal to the maximum static friction force since that is the force required to start moving the body. Therefore:
\[ F_{\text{applied}} = 300 \, \text{N} \]

Now, the net force (F_net) acting on the body when it is moving can be calculated as:
\[ F_{\text{net}} = F_{\text{applied}} - F_k \]
Calculating the net force:
\[ F_{\text{net}} = 300 \, \text{N} - 240 \, \text{N} = 60 \, \text{N} \]

### Step 6: Calculate the acceleration of the body
Using Newton's second law of motion, we can find the acceleration (a) of the body:
\[ F_{\text{net}} = ma \]
Where:
- \( F_{\text{net}} = 60 \, \text{N} \)
- \( m = 60 \, \text{kg} \)

Rearranging the formula to find acceleration:
\[ a = \frac{F_{\text{net}}}{m} \]
Calculating the acceleration:
\[ a = \frac{60 \, \text{N}}{60 \, \text{kg}} = 1 \, \text{m/s}^2 \]

### Final Answer:
The acceleration of the body is \( 1 \, \text{m/s}^2 \).

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