Kinetics

# Friction

Friction is a self adjusting and opposing force. Lets dive into more detailed explanation.

When we throw a ball with certain velocity on the floor, it rolls, covers some distance and then comes to rest. $\text{We have, } v^2=u^2+2as$

According to this relation, there must be retardation on the motion of the ball. So, a retarding force must be acting on the ball.

When we give a gentle push to an object, it may not move. But on giving it harder push, it starts moving. It shows that some force must be opposing the applied force.
From these observations, we can conclude that an opposing force always acts between the two objects whenever one object moves or slides or tends to move or slide over another object. This opposing force is friction.

Thus, friction is defined as an opposing force which is set up between the surfaces of the body in contact, when one body slides or rolls or tends to do on the surface of another body.

Friction is a self adjusting force. It always adjusts itself equal to the applied force. If we push a block lying on a horizontal surface, it may not move. It means that the applied force is equal to the frictional force. If we increase the applied force, the block may still remain at rest. It means that the frictional force has also been increased and has become equal and opposite to the applied force. However, there is a limit upto which the frictional force increases with the applied force. If we apply force beyond this limit, the block starts to move. This value of the frictional force is known as limiting friction.

Hence, the maximum value of the frictional force which comes into play before a body just begins to slide or roll over the surface of another body is called limiting friction. Friction is the force directed opposite to the direction of motion or attempted motion. The frictional force is always parallel to the surfaces in contact.

## Cause of Friction

### Classical Approach

It is the projection based approach which says that the friction is caused due to the roughness in the surfaces of the two bodies in contact. The surfaces of bodies contain irregularities in the form of projections. Even the smooth surface possess some irregularities which we can see when observed with a microscope.

When one of the bodies is placed over another body, the projections in the surfaces of the bodies get interlocked. When one of the bodies is pushed, the projections of the body exert some sideways force on the projections of another body. According to Newton’s third law of motion, the projections of another body also give equal and opposite reaction. This opposite reaction is friction which is equal to the applied force.

If the body is pushed with more and more force, the interlocking of projections break and the body starts to move.

### Modern Approach

It is the modern concept of friction that says that the friction is caused due to the intermolecular force of attraction between the two bodies in contact. If two highly smooth surfaces are in contact, then there is more friction. This is because large number of molecules come in contact which increases the intermolecular force of attraction.

## Static Friction and Dynamic Friction

​When we apply force to move a block, it does not move but when the applied force becomes greater than the the limiting frictional force, the body starts to move.
The frictional force that comes into play before the body starts to move is known as static friction.
and,
The frictional force that acts when the body is in steady motion is known as dynamic friction. Dynamic friction is also known as kinetic friction.
On moving the block, static friction increases and becomes equal to limiting friction, then, the limiting friction slightly decreases and becomes dynamic friction. Dynamic friction is always less than the limiting friction.
​Graphically,

## Laws of Limiting Friction

There are some laws that limiting friction obeys. They are;

• Limiting friction depends upon the nature and the state of roughness of then two surfaces in contact.
• It is parallel to the two surfaces in contact and acts opposite to the motion of the body.
• ​Limiting friction is directly proportional to the normal reaction between the two surfaces.
• ​If normal reaction is constant, limiting friction does not depend upon the shape or area of the surfaces of the two bodies in contact. It is explained by the modern theory of cause of friction. When two surfaces are put together the actual area of contact is very less than the apparent area of contact. The pressures at the contact points are very high and the molecules are pushed very close so that attractive forces between them weld the surfaces together at contact points. In other words, the points become “cold-welded” together. To move one surface over other these welds have to be broken.

When the apparent area of contact of the body is decreased the number of contact points is decreased. As the weight of the body is not changed, pressure at the contact points is increased. As a result, contact points flatten so that total area and pressure return to their original values. It explains why the friction is independent of the area of contact of the surfaces.

## Magnitude of Limiting Friction and Dynamic Friction

Experiments show that the magnitude of limiting friction is directly proportional to the normal reaction between the surfaces in contact. Consider a block of mass $m$ lying on a horizontal surface.

The normal reaction $R$ is the perpendicular force exerted by the surface on the block. $\therefore R=mg$ If $(F_s)_{\text{max}}$ be the limiting friction between the surfaces in contact then according to the law of friction $(F_s)_{\text{max}}∝R$ $(F_s)_{\text{max}}=\mu_sR$ Where $\mu_s$ is the proportionality constant and is called coefficient of static friction. $mu_s=\frac{(F_s)_{\text{max}}}{R}=\frac{\text{Limiting Friction}}{\text{Normal Reaction}}$

Hence, the coefficient of static friction between two surfaces in contact is defined as the ratio of limiting friction to the normal reaction. Its value depends upon the nature of the two surfaces in contact. Usually, its value is less than one unless an adhesive is applied or surfaces contain projections and cavities. $\text{As }F_s≤(F_s)_{\text{max}}$ $\therefore F_s≤\mu_sR$

Now, let us consider that the block of mass is moving with velocity $v$. If $F_k$ be the kinetic friction between the surfaces in contact, then according to the law of friction, $F_k∝R$ $F_k=\mu_kR$ Where $\mu_k$ is the proportionality constant and is called coefficient of dynamic or kinetic friction. $\mu_k=\frac{F_k}{R}=\frac{\text{Dynamic Friction}}{\text{Normal Reaction}}$ Hence, coefficient of dynamic friction between two surfaces in contact is defined as the ratio of the dynamic friction to the normal reaction.