CHAPTER 6 FRICTION. Expected Outcome:

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1 CHAPTER 6 FRICTIO Expected Outcome: Able to analyze and solve problems involving dry friction using the concept of equilibrium of a particle or a rigid body

2 Application Friction is both problematic and useful in many engineering applications, such as in tires and brakes. 8-2

3 Introduction In preceding chapters, it was assumed that surfaces in contact were either frictionless (surfaces could move freely with respect to each other) or rough (tangential forces prevent relative motion between surfaces). Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called friction forces, will develop if one attempts to move one relative to the other. Types of friction: dry or Coulomb friction fluid friction In this chapter, only dry friction will be consider 8-3

4 The Laws of Dry Friction. Coefficients of Friction Block of weight W is placed on a horizontal surface. Forces acting on the block are its weight and reaction of surface. Small horizontal force P is applied. For the block to remain stationary, in equilibrium, a horizontal component F of the surface reaction is required. F is a static-friction force. As P increases, the static-friction force F increases as well until it reaches a maximum value F m. S is coefficient of static friction. F s m 8-4 Further increase in P causes the block to begin to move as F drops to a smaller kinetic-friction force F k. K is coefficient of kinetic friction. F k k

5 The Laws of Dry Friction. Coefficients of Friction Maximum static-friction force: F s m Kinetic-friction force: F k k k 0.75 s Maximum static-friction force and kineticfriction force are: - proportional to normal force - dependent on type and condition of contact surfaces - independent of contact area 8-5

6 The Laws of Dry Friction. Coefficients of Friction o friction, (P x = 0) o motion, (P x < F) Motion impending, (P x = F m ) Motion, (P x > F m ) 8-6

7 Angles of Friction It is sometimes convenient to replace normal force and friction force F by their resultant R: o friction o motion Motion impending Motion tan tan s s F m s s tan tan k k F k k k 8-7

8 Angles of Friction Consider block of weight W resting on board with variable inclination angle q. o friction o motion Motion impending Motion 8-8

9 Problems involving Dry Friction All applied forces known Coefficient of static friction is known Determine whether body will remain at rest or slide All applied forces known Motion is impending Determine value of coefficient of static friction. Coefficient of static friction is known Motion is impending Determine magnitude or direction of one of the applied forces 8-9

10 Sample Problem 8.1 A 100- force acts as shown on a 300- block placed on an inclined plane. The coefficients of friction between the block and plane are s = 0.25 and k = Determine whether the block is in equilibrium and find the value of the friction force. 8-10

11 1. Draw the FBD of the system 2. Determine values of friction force and normal reaction force from plane required to maintain equilibrium. x 3 F 0 : F 0 F 80 What does the sign tell you about the assumed direction of impending motion? Answer: (-ve) sign shows that your first assumption on the force direction is wrong 8-11 y 4 F 0 : Calculate maximum friction force and compare with friction force required for equilibrium Fm s What does this solution imply about the block? The block will slide down the plane as the Fm is smaller than the force required to maintain the block in equiblirium

12 Wedges Wedges - simple machines used to raise heavy loads. Force required to lift block is significantly less than block weight. Friction prevents wedge from sliding out. Block as free body F W 1 F x y 0 : 0 : s s Wedge as free body F x 0 : s 2 3 s cos6 sin6 P 0 F y 0 : 2 3 cos 6 s sin6 0 Want to find minimum force P to raise block. 8-12

13 2-13

14 2-14

15 References: 1. Beer, Ferdinand P.; Johnston, E. Russell; Vector Mechanics for Engineers - Statics, 8 th Ed., McGraw-Hill, Singapore, 2007.

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