Angle of Friction and Resultant Reaction

Angle of Friction and Resultant Reaction

• The normal reaction N and the frictional force Fr can be confined to give a resultant R called the resultant reaction as shown in Fig. 8.5.1.

• The angle made by this resultant R with normal reaction N is called the angle of friction ϕ.

where ϕk is called angle of kinetic friction.

• If direction of applied force P is changed, keeping its angle with the surface of contact same throughout, the resultant R will take different positions in space but making the same angle ϕ with the normal reaction N.

• In such a case, R lies on the surface of a cone known as cone of friction as shown in Fig. 8.5.2. 

• If an object is kept on an inclined plane and the angle of inclination θ is increased, motion impends for a certain value of θ known as angle of repose.

• The angle of repose is equal to the angle of friction.

• This can be proved as follows:

• Consider F.B.D. of an object kept on an inclined plane of angle θ equal to the angle of fepose as shown in Fig. 8.5.3.

• Problems involving dry friction can be solved using either N and Fr or using R and ϕs.