State laws of dry friction.

Short Answer:

The laws of dry friction describe the relationship between frictional force and the normal reaction between two dry surfaces in contact. These laws were first proposed by Coulomb and apply to both static and kinetic (sliding) friction. They state that friction always acts in the opposite direction of motion, is proportional to the normal reaction, and is independent of the area of contact. Also, the limiting friction (maximum static friction) is greater than kinetic friction. These laws are fundamental in analyzing equilibrium and motion in mechanical systems.

Detailed Explanation :

Laws of Dry Friction

In Engineering Mechanics, when two solid surfaces come into contact, a resisting force develops that opposes motion or the tendency of motion between them. This resisting force is called dry friction, as it occurs between unlubricated surfaces. The laws of dry friction define how this frictional force behaves under different conditions of motion and contact.

These laws were first established through experiments conducted by Charles-Augustin de Coulomb in the 18th century. They form the foundation for studying the mechanics of rigid bodies, machines, and structures where friction plays an essential role.

Dry friction can be divided into two main types:

  1. Static friction – friction when the body is at rest.
  2. Kinetic (or dynamic) friction – friction when the body is in motion.

The laws apply to both types but are most commonly used to describe limiting friction (the maximum value of static friction) and kinetic friction (the constant frictional force during motion).

Definition of Dry Friction

Dry friction is defined as the resisting force that acts between two solid surfaces when there is no lubrication and one surface tends to move or slides over the other.
It always acts tangentially to the contact surface and opposite to the direction of motion or applied force.

Coulomb’s Laws of Dry Friction

The following are the main laws of dry friction:

  1. The Frictional Force Always Acts Opposite to the Direction of Motion

The first law states that friction always resists motion or the tendency of motion between two surfaces.
If a force tries to move one surface over another, friction develops in the opposite direction to prevent or resist the motion.

Explanation:
When a body rests on a surface and an external force is applied, the surface reacts by generating a frictional force in the opposite direction. This opposing force balances the applied force up to a certain limit, ensuring the body remains stationary or moves with uniform motion.

Example:
When you push a book lying on a table, the frictional force acts in the opposite direction of your push to resist motion.

  1. The Magnitude of Frictional Force is Equal to the Force Required to Maintain Equilibrium

As long as a body remains stationary, the frictional force increases with the applied force to maintain equilibrium. The moment the applied force exceeds a certain limit, the body starts moving.

Explanation:
At first, small applied forces are balanced by an equal amount of static friction. As the applied force increases, the frictional force also increases up to its maximum value, called limiting friction.
Beyond this limit, motion begins, and friction becomes constant (kinetic friction).

Mathematically,

where,

  • = static frictional force
  • = limiting friction
  • = coefficient of static friction
  • = normal reaction
  1. The Limiting Friction is Proportional to the Normal Reaction

The maximum value of frictional force, known as limiting friction, is directly proportional to the normal reaction between the two surfaces.

Mathematically,

where,

  • = limiting friction,
  • = coefficient of friction,
  • = normal reaction.

Explanation:
If the normal reaction increases (by pressing the surfaces together more firmly), the frictional resistance also increases proportionally. This is why it is harder to push a heavier object than a lighter one on the same surface — the heavier object exerts a greater normal reaction.

  1. Friction is Independent of the Area of Contact

The total area of contact between two surfaces does not affect the magnitude of friction, provided that the normal reaction remains the same.

Explanation:
Friction depends on the microscopic irregularities and interlocking of the surfaces, not on the total visible area. Increasing the area reduces the pressure per unit area but increases the total contact points; thus, the overall effect remains the same.

Example:
Whether a brick rests on its large or small face, the frictional resistance to sliding remains the same if the normal reaction is unchanged.

  1. Kinetic Friction is Less than Limiting Friction

Once motion starts, the frictional force slightly decreases and becomes constant. This constant value is known as kinetic or dynamic friction, and it is always less than the limiting friction.

Explanation:
When motion begins, surface irregularities do not have enough time to interlock completely, reducing resistance. Therefore, the kinetic frictional force remains almost constant and slightly lower than static friction.

Mathematically:

where,

  • = kinetic frictional force
  • = coefficient of kinetic friction (μₖ < μₛ)
  • = normal reaction

Example:
It is easier to keep a box moving once it has started sliding than to start it from rest.

Graphical Representation

If we plot a graph between the applied force and the frictional force acting on a body:

  • Initially, friction increases proportionally with applied force (static region).
  • At the point of limiting friction, the body is about to move.
  • Beyond this point, friction drops slightly and remains constant (kinetic region).

This graph visually demonstrates that limiting friction > kinetic friction.

Importance of Laws of Dry Friction

The laws of dry friction are fundamental in mechanical engineering and practical applications such as:

  1. Design of Brakes and Clutches: Ensuring sufficient friction to stop or transmit motion.
  2. Analysis of Machines: Used to calculate power losses due to friction in moving parts.
  3. Stability of Structures: Friction prevents slipping in inclined planes and retaining walls.
  4. Traction Control: Determines tire grip on road surfaces.
  5. Material Handling: Helps in designing conveyors and sliding mechanisms.

Limitations of Coulomb’s Laws

While these laws are highly useful, they have some limitations:

  1. They apply only to dry, unlubricated surfaces.
  2. They assume surfaces are rigid, though in practice, deformation occurs.
  3. They neglect effects of velocity, temperature, and wear on friction.
  4. They are not valid for very smooth or very rough surfaces.

Despite these limitations, Coulomb’s laws provide a strong theoretical foundation for most engineering analyses involving friction.

Conclusion

In conclusion, the laws of dry friction describe how friction behaves between solid surfaces without lubrication. They state that friction acts opposite to motion, is proportional to the normal reaction, and is independent of the contact area. The limiting friction represents the maximum resistance before motion begins, while kinetic friction is slightly less. These laws are vital for understanding mechanical systems, designing friction-based devices, and ensuring stability in engineering applications.