The relationship between force and frictional force is governed by the principles of physics, particularly Newtonian mechanics and the laws of friction. Here’s a breakdown:

1. Frictional Force as a Reaction Force

• Frictional force opposes the relative motion (or attempted motion) between two surfaces in contact.
• When an external force is applied to an object, frictional force resists this applied force up to a certain limit.

2. Types of Friction

• Static Friction ($f_s$): The frictional force that prevents motion. It is equal and opposite to the applied force up to its maximum value ($f_s^{\text{max}}$), given by: $f_s \leq \mu_s N$ where:
  • $\mu_s$: Coefficient of static friction
  • $N$: Normal force
• Kinetic Friction ($f_k$): The frictional force acting when the object is in motion. It is constant and given by: $f_k = \mu_k N$ where:
  • $\mu_k$: Coefficient of kinetic friction

3. Dependence on the Applied Force

• Before Motion Begins: The static frictional force increases proportionally with the applied force, balancing it until the maximum static friction is reached.
• Once Motion Starts: Kinetic friction comes into play, and the frictional force becomes constant, regardless of changes in the applied force.

4. Direction of Frictional Force

• Frictional force always acts in the direction opposite to the relative motion (or attempted motion) of the object with respect to the surface.

5. Key Equations

• Net force considering friction is: $F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}}$
• For motion to occur, $F_{\text{applied}}$ must exceed $f_s^{\text{max}}$.

In summary, frictional force is dependent on the nature of the surfaces, the normal force, and whether the object is moving or stationary, while always acting to resist motion.

---

Would you like detailed examples or diagrams to clarify this? Here are some related questions to consider:

1. How does the coefficient of friction affect the frictional force?
2. What role does normal force play in determining frictional force?
3. How is frictional force modeled differently in fluid dynamics versus solid surfaces?
4. Can friction ever increase with velocity? If so, under what conditions?
5. How is energy lost due to frictional forces calculated?

Tip: Remember, reducing the coefficient of friction (e.g., by lubrication) or normal force (e.g., by lifting weight) decreases friction.