Chapter six: Friction Section A Frictional Phenomena 1

Friction Usual Assumption: Forces of action and reaction between contacting surfaces act normal to the surface  valid for interaction between smooth surfaces  often involves only a relatively small error in solution  in many cases ability of contacting surfaces to support tangential forces is very important (Ex: Figure beside)

Types of Friction Dry Friction (Coulomb Friction) occurs between unlubricated surfaces of two solids Effects of dry friction acting on exterior surfaces of rigid bodies Fluid Friction occurs when adjacent layers in a fluid (liquid or gas) move at a different velocities. Fluid friction also depends on viscosity of the fluid.  Fluid Mechanics Internal Friction occurs in all solid materials subjected to cyclic loading, especially in those materials, which have low limits of elasticity  Material Science

Mechanism of Dry Friction • Block of weight W placed on horizontal surface. Forces acting on block are its weight and reaction of surface N. • Small horizontal force P applied to block. For block to remain stationary, in equilibrium, a R horizontal component F of the surface reaction is required. F is a Static-Friction force. As P increases, static-friction force F increases as well until it reaches a maximum value Fmax . Fmax=µs*N 5/19/2018 4

Further increase in P causes the block to begin to move as F drops to a smaller Kinetic-Friction force Fk . Fk=µk*N μs is the Coefficient of Static Friction μk is the Coefficient of Kinetic Friction

Friction Angles Friction Angles: The direction of the resultant R measured from the direction of N. 5/19/2018 6

Types of friction problems 1. Impending motion is known to exist • F = F max = μs N (in the direction opposing to the impending motion). • Equations of equilibrium can be used as usual.

2. Relative motion is known to exist • F = μk*N (in the direction opposing to the motion).

3. Motion condition is unknown • Assume static equilibrium • Use equilibrium equation to solve the friction force F • Check the value of friction force F • No friction, (Px = 0) Equations of Equilibrium Valid • No motion, (Px < Fm ) Equations of Equilibrium Valid

(a) F < μ s N • Friction force necessary for equilibrium can be generated by the surface • The body is in static equilibrium as assumed (b) F = μ s N • Impending motion is deduced (c) F > μ s N • Impossible! Assumption of equilibrium is not valid • Motion occurs, F = μ k N