Let `F,F_N and f` denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero,

Options

A. `FgtF_N`
B. `Fgt1`
C. F_Ngtf`
D. `F_N-fltFltF_N+f`.

Answer

To solve the problem regarding the relationship between the magnitudes of the contact force \( F \), the normal force \( F_N \), and the frictional force \( f \) when none of these forces is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Forces**:
- The contact force \( F \) is the total force exerted by one surface on another when they are in contact. It can be applied in any direction.
- The normal force \( F_N \) acts perpendicular to the surfaces in contact.
- The frictional force \( f \) acts parallel to the surfaces in contact and opposes the relative motion.

2. **Components of the Contact Force**:
- The contact force \( F \) can be broken down into two components:
- A vertical component (which corresponds to the normal force \( F_N \)).
- A horizontal component (which corresponds to the frictional force \( f \)).

3. **Using the Pythagorean Theorem**:
- Since \( F_N \) and \( f \) are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the contact force \( F \):
\[ F = \sqrt{F_N^2 + f^2} \]

4. **Analyzing the Relationships**:
- From the equation \( F = \sqrt{F_N^2 + f^2} \), we can deduce that:
- \( F \) will always be greater than both \( F_N \) and \( f \) because it is the resultant of these two perpendicular forces.
- This means \( F > F_N \) and \( F > f \).

5. **Considering the Magnitudes**:
- We can also analyze the difference between the normal force and the frictional force:
\[ F_N - f \]
- This difference can be either positive, negative, or zero, depending on the specific values of \( F_N \) and \( f \). However, we cannot definitively say whether \( F_N \) is greater than \( f \) or vice versa without additional information.

6. **Conclusion**:
- The relationships established show that the contact force \( F \) is the vector sum of the normal force \( F_N \) and the frictional force \( f \). The exact relationship between \( F_N \) and \( f \) cannot be determined without specific values.