1. Friction

2. OBJECTIVES
To introduce the concept of dry friction and show how to analyze the equilibrium of rigid bodies subjected to this force.

3. Friction may be defined as a force of resistance acting on a body which prevents or retards slipping of the body relative to a second body or surface with which it is contact.

4. This force acts tangent to the surface at points of contact with other bodies and is directed so as to oppose the possible or existing motion of the body relative to these points.

5. Types of Friction Fluid friction Dry Friction (Coulomb Friction)
Contacting Surfaces Separated by a Film of Liquid or Gas.
This Type of Friction is Studied in Fluid Mechanics.
Dry Friction (Coulomb Friction)
Friction Between Contacting Bodies in the Absence of a Lubricating Fluid.

8. Frictional Force - F
Static-frictional force if equilibrium is maintained.
Limiting static-frictional force if it reaches its maximum value of Fs
Kinetic-frictional force when sliding occurs.

11. s - coefficient of static friction
s = tan-1(Fs/N) = tan-1(s N/N) = tan-1(s)

12. k - coefficient of kinetic friction
k = tan-1(Fk/N) = tan-1(k N/N) = tan-1(k)

13. Friction / Motion

14. Typical values of s Metal on Ice 0.03 – 0.05 Wood on Wood 0.30 – 0.70
Leather on Wood
0.20 – 0.50
Leather on Metal
0.30 – 0.60
Aluminum on Aluminum
1.10 – 1.70
Metal on Metal
0.15 – 0.20
Masonry on Masonry
0.60 – 0.70
Metal on Masonry
Metal on Wood
0.20 – 0.60

15. Characteristics of Dry Friction
Friction acts tangent to the contacting surfaces.
Acts to oppose relative motion.
Maximum static frictional force, Fs is independent on area of contact.
Maximum static frictional force usually greater than kinetic frictional force.
When slipping is about to occur, Fs = s N
When slipping is occurring, Fk = k N
Also need to be aware of tipping.

16. Example 1 (No apparent Impending motion)

17. EX 1

18. By Bx Bx By
100 N
100 N FA FC NA NC

19. Example 2: Impending Motion at All Points

20. EX 2

21. NA  FA FB NB
100 N
FBD:

22. Example 3: Impending Motion at Some Points

23. EX 3

24. FA NA FC NC
100 N Bx By P

25. Bx By Bx By P
100 N
100 N FA FC NA NC

26. Example 4

28. Procedure for Analysis
Draw Free Body Diagrams
Do not Assume Fs = s N
Show Frictional Forces as Unknowns
Determine the number of unknowns and compare with the number of available equilibrium equations.
If there are more unknowns than equations apply frictional equation (Fs = s N) at some or all of the contact surfaces.
Be sure to show Fs acting in the proper direction.

29. Example 5:
W = 20 kg

30. Example 6
Vending machine slides when angle is 25o. Determine s between machine and the bed of the dump truck.

32. Example 7 :
s = 0.25
45o W1 W
Determine the range of values for W1 so that the weight W does not move.

33. s = 0.25 x y N F
45o W1 W
Sliding down the ramp.

34. s = 0.25 x y N F
45o W1 W

35. W1
s = 0.25 W F x y N
45o
Sliding up the ramp.

36. s = 0.25 x y N F
45o W1 W

37. EXAMPLE 8 The coefficients of friction are μs = 0.40 and μk = 0.30
between all surface of contact.
Determine the forces P for which motion of the 27kg block is impending if cable AB
is attached as shown
is removed
18kg
27kg
18kg
27kg

38. 18kg
27kg

39. a) attached

40. b) without cable

41. 18kg
27kg

42. a) attached
18kg
27kg

43. b) without cable

44. EXAMPLE 9
A block of 140 kg weight placed on an inclined surface as shown in Fig.. Determine the required force (P) to move the body upward if the coefficient of friction between the block and the surface is μs = 0.25

45. 140 kg weight
μs = 0.25

46. EXAMPLE 10
A 200Kg block placed on a inclined plane The coefficients of friction between the block and the plane are μs = 0.5 Determine the state of the block if the applied force (p) is 1150 N.

47. 200Kg
μs = 0.5 force
(p) is 1150 N.

48. EXAMPLE 11
A horizontal force of P=100N is just sufficient to hold the crate from sliding down the plane, and a horizontal force of 350 N is required to just push the crate up the plane. Determine the coefficient of static friction between the plane and the crate, and find the mass of the crate.