Understanding Friction: Types and Properties

• Friction is the property of surfaces in contact that resists motion.
• Friction force acts opposite to the direction of motion or impending motion.
• Impending motion: state of a body on the verge of motion
• Limiting equilibrium: The condition in which the body is in impending motion.
• When relative motion exists, each surface exerts a friction force on the other, forming an action-reaction pair.

Types of Friction

• Dry friction: Friction between two dry surfaces, sometimes called Coulomb friction.
• Dry friction is due to surface irregularities.
• Fluid friction: Friction between particles or layers of fluids (liquids and gases)
• Fluid friction is mainly due to cohesive forces or intermolecular attraction.

Classification of Dry Friction

• Static friction: Experienced when the body is at rest or in equilibrium.
• Kinetic friction: Experienced when the body is in motion.
  • Sliding friction: When the body slides over the surface.
  • Rolling friction: When the body rolls over the surface.

Limiting Friction (FL)

• Maximum friction force that can develop between two surfaces before motion starts.
• Occurs when the body is in impending motion (limiting equilibrium).
• If a small horizontal force 'P' is applied to a block, friction force 'FL' develops in the opposite direction, preventing movement.
• As 'P' increases, 'FL' also increases until it reaches a limit.
• If 'P' exceeds this limit, the body moves and friction reduces.
• The force required to maintain uniform motion is less than the limiting static friction force.

Coulomb's Laws of Friction (For Static Friction)

• Applicable for sliding or rolling friction between dry surfaces.
• The direction of friction force is opposite to the direction of motion or intended motion.
• Friction force is independent of the area of contact.
• Friction force depends on the nature of the contact surface (irregularities) and is directly proportional to the normal reaction (NR).

Coefficient of Friction (μ)

• Static friction (µs): When the body is in impending motion, F₁ = µsNr.
• Kinetic friction (µk): When the body is in motion, F = µkNr.
• μk is less than µs.
• For moderate speeds, friction remains constant but decreases slightly with increased speed.
• Friction is less under dynamic conditions (motion) than in limiting equilibrium (at rest)
• When motion is about to start, F₃ = µsNR, at the start of motion, FK = µkNR.
• Fk is less than Fs because there is less interlocking between the surface irregularities in motion.

Graph Between F and P

• F = Friction force, P = Applied force
• F increases linearly with P until it reaches the limiting friction Fl, after which it remains constant at a lower value Fk.

Different Cases

• Case 1: Forces do not tend to move the body; friction force F = 0, NR = P + W.
• Case 2: Forces tend to move the body, but are not large enough; F = P < FL, NR = Py + W.
• Case 3: Forces are just sufficient to start motion; Fmax = FL = µsNr, NR = Py + W.
• Case 4: Forces cause motion and Fk = µk NR & NR = Py+W.

Angle of Friction (Φ)

• The maximum angle between the resulting reaction and the normal reaction when the body is in limiting equilibrium.
• Also called the limiting angle of friction.
• It is denoted by "$".
• tan Φ = µ.
• Tangent of angle of friction = coefficient of friction.

Cone of Friction

• In limiting equilibrium, if the line of action of the applied force 'P' is rotated in horizontal plane, the line of action of resultant will generate a cone.

Properties of the Cone of Friction

• Semi-vertical (vertex) angle = angle of friction (Φ)
• Altitude or height of cone = Normal reaction (NR)
• Base radius = Limiting friction force (FL)
• Generator of the cone = Resultant reaction (R)

Angle of Repose (θ)

• The angle at which blocks tend to slide down the plane under its own weight without external force.

Factors on which Friction Depends

• Nature of surfaces in contact.
• Normal reaction between the surfaces.

Applications of Friction

• Inclined planes / Horizontal planes (Block friction)
• Ladders (Ladder friction)
• Wedges (Wedge friction)
• Flat belts (Belt friction)

Inclined / Horizontal planes

• If 'P' is not sufficient to induce motion of the block is in static equillibrium.

Ladders

• Ladder is a structure used for climbing or scaling on the walls or roofs.
• In the absence of friction, ladder will slide down and fall on the floor.

Wedges

• Wedges are simple machines and are used to raise heavy loads by applying relatively small forces.

Belt Friction

• If there is a friction between the drum and belt, the tension will not be the same on both sides
• Tension is maximum on the side of impending motion as it has to overcome friction to start the motion
• Tension of two sides T₂ and T₁ are related by T₂/T₁ = e^(µβ)
• Simply it is the angle of contact of the belt

Band Brakes

• Band brakes are used to apply braking forces by operating lever.