If coefficient of static friction is `mu_(s)` and coefficient of kinetic friction is `mu_(k)` , which one is correct ?

Options

A. `mu_(s) = mu _(k)`
B. `mu_(s) gt mu_(k)`
C. `mu_(s) lt mu_(k)`
D. `mu_(s) le mu_(k)`

Answer

To solve the question regarding the relationship between the coefficient of static friction (µs) and the coefficient of kinetic friction (µk), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Static and Kinetic Friction**:
- **Static Friction (Fs)**: This is the frictional force that prevents an object from starting to move. It acts when the object is at rest and a force is applied to it. The maximum static friction force is given by \( F_{s, \text{max}} = \mu_s \cdot N \), where \( N \) is the normal force.
- **Kinetic Friction (Fk)**: This is the frictional force acting on an object that is already in motion. The kinetic friction force is given by \( F_k = \mu_k \cdot N \).

2. **Comparing the Two Coefficients**:
- It is generally observed that the coefficient of static friction (µs) is greater than the coefficient of kinetic friction (µk). This means that it takes more force to start moving an object than to keep it moving once it has started.

3. **Mathematical Representation**:
- From the definitions, we can write:
- For static friction: \( F_{s, \text{max}} = \mu_s \cdot N \)
- For kinetic friction: \( F_k = \mu_k \cdot N \)
- Since \( F_{s, \text{max}} \) is the maximum force before motion begins, and \( F_k \) is the force during motion, we conclude that:
\[ \mu_s > \mu_k \]

4. **Conclusion**:
- Therefore, the correct statement is that the coefficient of static friction (µs) is greater than the coefficient of kinetic friction (µk). Thus, we can conclude:
\[ \mu_s > \mu_k \]