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 6/4
The homogeneous rectangular block of mass m, width b, and height H is placed on the horizontal surface and subjected to a horizontal force P which moves the block along the surface with a constant velocity. The coefficient of kinetic friction between the block and the surface is mk. Determine (a) the greatest value which h may have so that the block will slide without tipping over and (b) the location of a point C on the bottom face of the clock through which the resultant of the friction and normal forces acts if h = H/2

10. 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.

11. 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.

12. Problem 6/12
600 mm
50 kg
12 kg
200 mm
75 mm
The 50-kg wheel rolls on its hub up the circular incline under the action of the 12-kg cylinder attached to a cord around the rim. Determine the angle q at which the wheel comes to rest, assuming that friction is sufficient to provent slippage. What is the minimum coefficient of friction which will permit this position to be reached with no slipping?