1. Engineering Mechanics: Statics
Chapter 6: Friction

2. Introduction
Ideal assumption – forces between contacting surfaces act normal to the surfaces
Real surfaces – there are tangential forces between contacting surfaces = “Friction forces”
Friction force occurs when one contacting surface tends to slide along another.
Minimize the effects: bearings, screws, gears, flow of fluids in pipe
Maximize the effects: brakes, clutches, belt drives, wedges

3. Types of Friction Dry friction
- unlubricated surfaces in contact under a tendency to slide
- friction occurs in the direction opposite to the impending motion
- called Coulomb friction  
Fluid friction
- adjacent layers in a fluid are moving at different velocity
Internal friction –solid material under cyclical loading 

4. Dry Friction Mechanism of Dry Friction Static friction: Fmax = msN
limiting value for impending motion!!!
Kinetic friction: Fk = mkN

5. Dry Friction The direction of R is specified by tan a = F/N
When the friction force reaches Fmax, the angle a reaches a maximum value fs . Thus,
tan fs = ms
When slippage is occurring, tan fk = mk
The angles fs and fk are called angle of static friction and angle of kinetic friction which define the limiting direction of the total reaction R for each case.

6. Cone of Friction
If motion is impending, R must be one element of the cone of static friction
If motion is not impending, R is within the cone. The cone vertex angle is 2fs
If motion occurs, the angle of kinetic friction is applied. The reaction R must lie on the surface of cone of vertex angle 2fk

7. Types of Friction problems
1. Motion is impending (body about to slip)
Fmax = msN
2. Condition of motion is not known –find friction force F from equilibrium equation
If F < Fmax (= msN) – body is in equilibrium and friction force = F
If F = Fmax (= msN) – body is in equilibrium  motion is impending
If F > Fmax (= msN) – impossible  not in equilibrium
3. Relative motion exist
Fk = mkN

8. Sample Problem 6/2
Determine the range of values which the mass m0 may have so that the 100-kg block will neither start moving up the plane nor slip down the plane
The coefficient of static friction for the contact surfaces is 0.30

9. Sample Problem 6/5
The three flat blocks are positioned on the 30 degree incline as shown, and a force P parallel to the incline is applied to the middle block. The upper block is prevented from moving by a wire which attaches it to the fixed support. The coefficient of static friction for each of the three pairs of mating surfaces is shown. Determine the maximum value which P may have before any slipping takes place.

10. Problem 6/9
The 30-kg homogeneous cylinder of 400-mm diameter rests against the vertical and inclined surfaces as shown. If the coefficient of static friction between the cylinder and the surfaces is 0.30, calculate the applied clockwise couple M which would cause the cylinder to slip.