A force of `98N` is just able to move a body of weight `45kg` on a rough horizontal surface What are the coefficient of friction and angle of friction ? .

Explanation

To solve the problem, we need to find the coefficient of friction (μ) and the angle of friction (θ) for a body of weight 45 kg that is being moved by a force of 98 N on a rough horizontal surface.

### Step 1: Calculate the Normal Force (N)
The normal force (N) acting on the body is equal to its weight when the surface is horizontal. The weight (W) can be calculated using the formula:

\[ W = m \cdot g \]

where:
- \( m = 45 \, \text{kg} \) (mass of the body)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating the weight:

\[ W = 45 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 441 \, \text{N} \]

Thus, the normal force \( N = 441 \, \text{N} \).

### Step 2: Determine the Coefficient of Friction (μ)
The coefficient of friction (μ) is defined as the ratio of the frictional force (F_f) to the normal force (N). Since the force of 98 N is just able to move the body, this force is equal to the maximum frictional force:

\[ F_f = 98 \, \text{N} \]

Using the formula for the coefficient of friction:

\[ \mu = \frac{F_f}{N} \]

Substituting the values:

\[ \mu = \frac{98 \, \text{N}}{441 \, \text{N}} \]

Calculating μ:

\[ \mu \approx 0.222 \]

### Step 3: Calculate the Angle of Friction (θ)
The angle of friction (θ) can be found using the formula:

\[ \theta = \tan^{-1}(\mu) \]

Substituting the value of μ:

\[ \theta = \tan^{-1}(0.222) \]

Calculating θ:

\[ \theta \approx 12.4^\circ \]

### Final Results
- Coefficient of friction (μ) ≈ 0.22
- Angle of friction (θ) ≈ 12.4°