**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Angle of static friction

** Angle of static friction: **Consider the block on the following surface.

The free body diagram is shown. The direction of resultant R measured from the direction of N is specified by tan a=F/N. When the friction force reaches its limiting static value F

_{max}, the angle a reaches a maximum.

Value of f_{s}. Thus

tan f_{s} = m_{s}

The angle fs is called the angle of static friction.

Angle of kinetic friction:

When slippage is occurring, the angle a has a value fR corresponding to the kinetic friction force.

tan f_{R} = m_{R}

__ Cone of friction:__ When a body is having impending motion in the direction of P the frictional force will be the limiting friction and the resultant reaction R will make limiting friction angle a with the normal as shown in the following figure. If the body is having impending motion in some other direction, again the resultant reaction makes limiting frictional angle a with the normal in that direction.

**Angle of Repose:**

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

Now consider the equilibrium of the block shown above. Since the surface of contact is not smooth, not only normal reaction, but frictional force also develops. Since the body tends to slide downward, the frictional resistance will be up the plane.

**Σforces normal to the plane =0, gives
N=Wcos θ …………1**

**Σforces normal to the plane =0, gives**

F=Wsin θ ……………2

F=Wsin θ ……………2

Dividing equ (2) by equ (1), we get

If N is the value of normal force when motion is impending, frictional force will be μN and hence

Hence, to avoid free sliding, the inclination angle should be less than the friction angle.