Introduction, Types And Friction Of Horizontal Surfaces

TYPES  OF FRICTION

There are three types of friction.
Static friction
Dynamic or Kinetic friction
Rolling friction

Static friction:
The opposing force that comes Types of friction into play when one body tends to move over the surface of another, but the actual motion has yet not started is called static friction. 
If applied force is P and the body remains at rest then static friction F = P.
If a body is at rest and no pulling force is acting on it, force of friction on it is zero.
                

Static friction is a self-adjusting force because it changes itself in accordance with the applied force and is always equal to net external force.
Consider a block ‘B’ which is resting on a horizontal table. Let a small pan be attached to the block by means of a horizontal thread passing over a smooth frictionless pulley.
When the weight in the pan is less, the block does not move because the pulling force or applied force ‘P’ is balanced by the frictional force ‘f’ which is called static friction. Frictional force is a self adjusting force. As the weight in the pan increases the pulling force ‘P’ increases and accordingly the frictional force ‘f’ also increases. If the weight in the pan is increased further then the block tends to slide over the surface. At this stage the force of friction also reaches a maximum value called limiting friction (fs). This maximum force equals the magnitude of the force to pull, when the body just begins to move.

Introduction, Types And Frictions On Horizontal Surfaces

Limiting friction:

‘The maximum value of static friction that develops on a body when the body just tends to slide over the surface of another body is called the ‘limiting friction’.
If the applied force is increased, the force of static friction also increases. If the applied force exceeds a certain (maximum) value, the body starts moving. 

This maximum value of static friction upto which body does not move is called limiting friction.
The magnitude of limiting friction between any two bodies in contact is directly proportional to the normal reaction between them. 

            F_lR  or F_l = µ_sR
Direction of the force of limiting friction is always opposite to the direction in which one body is at the verge of moving over the other

Coefficient of static friction : 
(a) µs is called coefficient of static friction and is defined as the ratio of force of limiting friction and normal reaction µs = F/R
(b) Dimension : [M⁰L⁰T⁰]
(c) Unit : It has no unit.
(d) Value of µ depends on material and nature of surfaces in contact that means whether dry or wet, rough or smooth polished or non-polished. 
(e) Value of µ does not depend upon apparent area of contact.

Introduction, Types And Friction On Horizontal Surfaces

Dynamic Friction or Kinetic Friction:

If the applied force is increased further and sets the body in motion, the friction opposing the motion is called kinetic friction.
When the applied force increases just beyond the value of limiting friction, the body is set into motion. But even after the body begins to move over the surface of another body, by overcoming the limiting friction, certain force is required to keep the body in uniform motion.
The frictional force which comes into play after the motion has started is called the kinetic friction (fk) or dynamic friction, which will be numerically equal to the force required to keep the body to slide over another body with uniform motion.

(i) Kinetic friction depends upon the normal reaction. F_k R or F_k = µ_k R where µk is called the coefficient of kinetic friction 
(ii) Value of µ_kdepends upon the nature of surface in contact.
(iii) Kinetic friction is always lesser than limiting friction Fk < Fl  µ_k < µs

i.e. coefficient of kinetic friction is always less than coefficient of static friction. Thus we require more force to start a motion than to maintain it against friction. This is because once the motion starts actually ; inertia of rest has been overcome. Also when motion has actually started, irregularities of one surface have little time to get locked again into the irregularities of the other surface.

(iv) Kinetic friction does not depend upon the velocity of the body.

Types of Kinetic Friction:
Sliding friction: The opposing force that comes into play when one body is actually sliding over the surface of the other body is called sliding friction. 
e.g. A flat block is moving over a horizontal table. 

Introduction, Types And Frictions On Horizontal Surface

Rolling friction: When objects such as a wheel (disc or ring), sphere or a cylinder rolls over a surface, the force of friction that comes into play is called rolling friction. 
Rolling friction is directly proportional to the normal reaction (R) and inversely proportional to the radius (r) of the rolling cylinder or wheel. 
    F_r R or
    F_r = µ_r R  where µr is called coefficient of rolling friction. It would have the dimensions of length and would be measured in metre

Rolling friction is often quite small as compared to the sliding friction. That is why heavy loads are transported by placing them on carts with wheels. In rolling the surfaces at contact do not rub each other. 
The velocity of point of contact with respect to the surface remains zero all the times although the centre of the wheel moves forward. 

Rolling friction is another type of dynamic friction. It comes into play when one body rolls on the surface of the other body. When a body like a ball, a drum, a wheel or a cylinder, rolls over the surface of another body it experiences the rolling friction (fr). The rolling friction in very much less than the sliding friction. It is inversely proportional to the radius of the rolling body. Its value decreases if the area of contact is small and if the surface is hard. 
The rolling friction is due to two reasons
The surface of the rolling body deforms a little bit when the portion of the rolling body is in contact with the surface. 
The rolling body deforms the surface on which it is rolling. In general, rolling friction <kinetic friction < limiting friction.

Variation of frictional force with pulling force
Then the frictional force remains constant which is represented by the line ‘CP’, and which is independent of the velocity. In this figure PQ is the measure of kinetic friction or kinetic frictional force and which will not increase even if the pulling force is increased. It is clear that PQ < BE, i.e; kinetic friction is less than static friction    (fk< fs).

Introduction, Types And Frictions On Horizontal Surfaces

Distinction between static and kinetic friction
When the body is at rest over the surface of another body the frictional force increases from zero to maximum value with the pulling force. The variation of frictional force with the increase of pulling force is shown graphically in Figure. The frictional force increases with the pulling force from A to B, when the body is at rest over the surface of another body. The frictional force is maximum at B. The dotted line BE represents the limiting frictional force. When the applied force or pulling force is increased beyond ‘E’ the frictional force decreases by small amount which is shown in Figure as BC.
        

Static friction > sliding friction > Rolling friction.
For a given pair of surfaces \( \mu _s > \mu _K > \mu _r \)
The above graph between friction and force applied shows the concept of static, sliding and limting friction. It can be easily seen that static >kinetic)    The force of static friction between two surface attains a maximum value when, the two surfaces just begin to slide or slip relative to each another.