FRICTION:

you have learnt laws of friction and problems involving dry friction. The relative sliding motion of one body on another body is resisted by forces called as friction forces. The sense of these friction forces is such as to oppose the impending or real sliding motion. While there is no impending motion, the friction forces should be found by using the equations of static equilibrium. The limiting static friction is attained when relative sliding motion of the surface is impending and is given by following :

                                                            F_max = μ N

Where μ is the coefficient of static motion and N is the normal reaction.

While sliding motion actually occurs, the retarding friction force has the magnitude μ_k N, where μ_k is the coefficient of kinetic friction.

The angle among the normal reaction N and the resultant reaction R is called the angle of friction while sliding motion of the surfaces is impending. This angle φ is associated to the coefficient of friction by :

                                                      tan φ = μ

The maximum angle of inclination of the inclined plane, whereas the body kept on it is just on the point of moving down the plane, is called as the angle of repose.

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

You have also learned in this section, the engineering applications where dry friction plays vital role, e.g. wedges utilized to lift heavy loads and screw jacks frequently used in presses and other mechanisms. By drawing free body diagrams mentioning correct sense of friction forces and applying equations of equilibrium, you may analyse the engineering applications where dry friction is involved. In case of belt and rope drivers, onto a curved surface, whereas sliding motion is impending the ratio of tensions is given by following:

                                           T₁ / T₂ = e^{μ α}

Where   T₁ = tension of the tight side,

              T₂ = tension on the slack side,

              μ = coefficient of friction, and

              α = angle of lap in radians.

In case of V belt the above formula is changed by multiplying α by cosec the angle among two surfaces of contact forming V.