Siddhant Kolase - FOSD Unit-2

Unit-2: Friction

What is Friction?

- Friction is the resisting force that acts between two surfaces in contact and opposes the relative motion or tendency of relative motion between them.

Why Does Friction Occur?

- At a microscopic level, contacting surfaces are not perfectly smooth. They contain irregularities that interact with each other.
- Therefore, when one surface tends to move over another, resistance is produced.

Relevance of Friction in Engineering

- Friction can be both useful and undesirable.

Useful effects:

- Walking
- Braking of vehicles
- Power transmission by belts
- Clutches
- Brakes
- Screw and bolt connections
- Holding objects

Undesirable effects:

- Wear of machine components
- Heat generation
- Energy loss
- Reduction in efficiency
- Increased maintenance

Equilibrium

- In Engineering Mechanics, a body is said to be in equilibrium when the net (resultant) force and net moment acting on the body are zero.
- A parked car is in equilibrium because the forces acting on it are balanced.
- A car moving at constant velocity in a straight line can also be considered in equilibrium in the mechanics sense because its acceleration is zero and the resultant force is zero.

Limiting Equilibrium

- Limiting equilibrium is the condition of a body when it is just about to start moving under the action of an applied force.
- The body is still at rest, but even a very small increase in the applied force will make it move.

Limiting Friction

- Limiting friction is the maximum value of frictional force that acts between two surfaces when a body is just about to start moving.
- Limiting friction is the maximum friction that a surface can offer before the body starts moving.

Types of Friction

Static Friction

- Static friction is the frictional force that acts between two surfaces in contact when there is no relative motion between them and one surface has a tendency to move relative to the other.
- Static friction prevents a stationary body from starting to move.

Dynamic or Kinetic Friction

Dynamic friction is the frictional force that acts between two surfaces when there is relative motion between them.
Dynamic friction acts when one surface is actually sliding or moving relative to another surface.
It is also commonly called kinetic friction.

Sliding Friction

Sliding friction is the frictional force that acts between two surfaces when one surface slides over another surface.
It is a type of dynamic (kinetic) friction.
Sliding friction opposes the relative sliding motion between two contacting surfaces.

Rolling Friction

- Rolling friction is the frictional resistance that acts when a circular body rolls over a surface.
- Rolling friction opposes the rolling motion of a body such as a wheel, cylinder or ball.

Coefficient of Friction µ

- The coefficient of friction is a numerical value that represents the frictional characteristics between two surfaces in contact.
- The coefficient of friction tells us how much friction exists between two contacting surfaces compared with the normal reaction.

Angle of friction θ

- Angle of friction is the angle made by the resultant reaction with the normal reaction when a body is in limiting equilibrium.
- It is generally denoted by θ.

Angle of Limiting friction α

- the maximum value of the angle of friction, reached when friction becomes limiting friction (just before motion starts).
- It is denoted by α

Coulomb’s Laws of friction

1. The force of friction always acts in a direction opposite to that in which body tends to move.
2. Till the limiting value is reached, the magnitude of friction is exactly equal to the force which tends to move the body.
3. The magnitude of the limiting friction bears a constant ratio to the normal reaction between the two surfaces of contact and this ratio is called coefficient of friction.
4. The force of friction depends upon the roughness/smoothness of the surfaces.
5. The force of friction is independent of the area of contact between the two surfaces.
6. After the body starts moving, the dynamic friction comes into play, the magnitude of which is less than that of limiting friction and it bears a constant ratio with normal force. This ratio is called coefficient of dynamic friction.

Angle of repose ϕ

- Angle of repose is the maximum angle of an inclined plane with the horizontal at which a body placed on it is just about to start sliding down.

- The maximum inclination of the plane on which a body, free from external forces, can repose (sleep) is called Angle of Repose.

- At this angle, the body is in limiting equilibrium.

- It is also equal to the limiting angle of friction

Relationship between Angle of friction (θ) and Angle of repose (ϕ)

Cone of Friction

- Cone of friction is the imaginary right circular cone formed by the possible directions of the resultant reaction R when a body is on the point of slipping in any direction.

- The axis of the cone is along the normal reaction N.

- The semi-vertical angle of the cone is equal to the limiting angle of friction α.

- So, the cone of friction represents all possible directions of the resultant reaction at impending motion.

Equilibrium on Level Surface – Force Parallel to Plane

- Weight is the force with which the Earth attracts a body towards its centre.
- Weight is a vector quantity.
- SI unit of weight is Newton (N).
- Weight depends on the value of gravitational acceleration and therefore can vary with location.
- Unlike mass, weight is not constant everywhere.

Equilibrium on Level Surface – Force Inclined to Plane

- Force is an external agency that can change or tend to change the state of rest or uniform motion of a body, or change its shape or size.

Equilibrium on Inclined Plane

- A force system is a collection of two or more forces acting simultaneously on a body.

Classification of Force Systems
1. Collinear Force SystemA force system in which the lines of action of all forces lie along the same straight line.
2. Non-collinear Force SystemA force system in which the lines of action of the forces do not lie along the same straight line.
3. Concurrent Force SystemA force system in which the lines of action of all forces meet at a common point.
4. Non-concurrent Force SystemA force system in which the lines of action of the forces do not meet at a common point.
5. Parallel Force SystemA force system in which the lines of action of all forces are parallel to each other.
6. Non-parallel Force SystemA force system in which the lines of action of the forces are not parallel to each other.
7. Coplanar Force SystemA force system in which the lines of action of all forces lie in the same plane.
8. Non-coplanar Force SystemA force system in which the lines of action of the forces do not lie in the same plane.
Types of Coplanar Force Systems
1. Coplanar Collinear Force SystemA force system in which the lines of action of all forces lie along the same straight line and inthe same plane.
2. Coplanar Concurrent Force SystemA force system in which the lines of action of all forces lie in the same plane and meet at a common point.
3. Coplanar Parallel Force SystemA force system in which the lines of action of all forces are parallel to each other and lie in the same plane.
4. Coplanar Non-concurrent and Non-parallel Force SystemA force system in which the lines of action of all forces lie in the same plane but are neither concurrent nor parallel.

Principle of Equilibrium

- The principle of equilibrium states that a body is in equilibrium when the resultant force and the resultant moment acting on the body are zero.

Questions

1. State and explain the laws of friction.
2. Explain static friction and dynamic friction, differentiate between them.
3. Explain limiting friction and coefficient of friction.
4. Define angle of friction and derive its relation with coefficient of friction.
5. Define angle of repose and derive its relation with coefficient of friction.
6. Prove that angle of repose is equal to the limiting angle of friction.
7. Differentiate angle of friction and angle of repose

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