# Friction

We often simplify a problem by assuming that the motion of bodies takes place on "frictionless" surfaces. But in real world, all motions happening around us are affected by the force of friction. Therefore, a realistic approach to any mechanical problem requires that we identify the frictional forces acting on the system and include them in the respective equations of motion. Suppose a block 1 is placed on top of another block 2.

As long as the blocks are at rest and there is no attempt to produce a relative motion between them, the contact forces acting in a pair between the blocks are purely normal forces and directed perpendicular to the surface separating the blocks. But if a driving force F is applied to block 1 in an attempt to drag it to the right along the surface of block 2, the contact forces between the blocks act at an oblique angle to the surface of separation.

The components of contact forces perpendicular to the surface are the normal forces N and - N. The components of contact forces parallel to the surface are the frictional forces f and - f . By Newton's third law, these frictional forces always act in an action-reaction pair. Their directions are such that they resist any real or impending relative motion between the two blocks. In our case, since the driving force F is applied to the right, the frictional force on block 1 acts to the left and the frictional force on block 2 acts to the right.

The resistance to the relative motion between two solid bodies is known as solid friction, or simply friction. The resistance to the relative motion between a solid body and a fluid is known as fluid friction, or more commonly as drag force. The relative motion between two solid bodies can be produced in two different ways.

They can either slide over one another or they can roll over one another. Accordingly, solid friction can be classified into two types: sliding friction and rolling friction. And again, the friction that exists when the bodies are about to slide over one another is not the same as the friction that exists when the bodies are actually sliding over one another. The first type is called static friction, and the second type is called kinetic friction.

Consider a block of mass m resting on a rough, horizontal surface. A driving force F is applied rightwards to the block. As the magnitude of F is increased slowly, the force of static friction fs acting leftwards on the block also increases equally in magnitude to keep the block at rest. When the block is just about to move to the right, the force of static friction attains its maximum value which is called the force of limiting friction.

According to the laws of static friction, force of limiting friction is directly proportional to the magnitude of the normal force between the two surfaces. In other words, the ratio of force of limiting friction and normal force is a constant known as coefficient of static friction. Once the block begins to move, the force of kinetic friction fk comes into play, which is usually smaller than the force of limiting friction. By the laws of kinetic friction, force of kinetic friction is also directly proportional to the magnitude of normal force. The corresponding ratio of force of kinetic friction to normal force is a constant called coefficient of kinetic friction. Generally, the first coefficient is greater than the second for a given pair of surfaces.

It will be useful to introduce few more terms. Suppose a block rests on a rough plane inclined at a small angle to the horizontal. The angle of inclination is gradually increased until, at a certain point, the block is just about to slide down the incline. The corresponding angle of inclination of the plane is known as angle of repose.

The angle of friction between a given pair of surfaces is the angle between the total contact force and the normal force at the instant when one surface is just about to slide over another.

If the driving force acting on a block is slowly rotated through 360° keeping it parallel to the surface of the floor, the total contact force acting on the block remains within an imaginary inverted right circular cone, as long as the block is at rest. This cone is known as cone of friction.

#### Basic level videos

Static And Kinetic Friction 1:02:11 Basic
350 7.5
Angle Of Repose And Angle Of Friction 1:06:42 Basic
350 7.5
Examples Of Motion On Rough Surfaces I & II 49:14 Basic
250 4
Examples Of Motion On Rough Surfaces III 1:01:19 Basic
350 5
Examples Of Motion On Rough Surfaces IV 1:11:34 Basic
350 7.5
Problems On Motion On Rough Surfaces I 52:27 Basic
300 5
Problems On Motion On Rough Surfaces II 1:09:32 Basic
350 7.5
Problems On Motion On Rough Surfaces III 45:08 Basic
250 4
Rolling Friction 1:01:54 Basic
350 7.5
Drag Force 50:02 Basic
300 5
Problems On Drag Force 31:27 Basic
250 4

#### Advanced level Videos Note: (CE) Stands for Problems from Competitive Examination Papers

Advanced-Level Problems On Friction I 54:56
300
5
Advanced-Level Problems On Friction II 1:15:46
350
7.5