A force of 3kg wt is sufficient to pull a block of 4kgwt over a flat surface. What is the angle of friction ?

Explanation

To solve the problem, we need to find the angle of friction given that a force of 3 kg weight is sufficient to pull a block of 4 kg weight over a flat surface.

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
- The weight of the block (W) is given as 4 kg wt. This is equivalent to \( W = 4g \) where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
- The pulling force (F) is given as 3 kg wt, which is \( F = 3g \).

2. **Identify the Normal Force (N)**:
- On a flat surface, the normal force (N) acting on the block is equal to its weight:
\[ N = W = 4 \, \text{kg wt} \]

3. **Set Up the Equation for Friction**:
- The frictional force (F_f) opposing the motion can be represented as:
\[ F_f = \mu N \]
- Here, \( \mu \) is the coefficient of friction.

4. **Relate the Forces**:
- Since the block is just about to move, the pulling force (F) is equal to the frictional force (F_f):
\[ F = F_f \]
- Thus, we can write:
\[ 3g = \mu (4g) \]

5. **Cancel Out g**:
- Since \( g \) appears on both sides, we can cancel it out:
\[ 3 = 4\mu \]

6. **Solve for the Coefficient of Friction (μ)**:
- Rearranging gives:
\[ \mu = \frac{3}{4} = 0.75 \]

7. **Calculate the Angle of Friction (θ)**:
- The angle of friction (θ) is related to the coefficient of friction by the equation:
\[ \tan \theta = \mu \]
- Therefore:
\[ \tan \theta = 0.75 \]

8. **Find θ using the Inverse Tangent Function**:
- To find the angle θ, we take the arctangent (inverse tangent):
\[ \theta = \tan^{-1}(0.75) \]
- Using a calculator, we find:
\[ \theta \approx 36.86^\circ \]

### Final Answer:
The angle of friction is approximately \( 36.86^\circ \).

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