Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 36:Friction

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 2 Chapter 8 Objectives to introduce the concept of dry friction to analyze the equilibrium of rigid bodies subjected to dry friction force to present specific applications of dry friction force analysis on wedges

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 3 Lecture 36 Objective to introduce the concept of dry friction to analyze the equilibrium of rigid bodies subjected to dry friction force

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 4 Friction – What is it? Resistance force  Sliding, rolling, twisting Tangent to normal contact surface between two bodies Acts in a direction opposite to relative motion or tendency for motion

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 5 Types of Friction Fluid Friction  Contact surface separated by fluid  Fluid may be a liquid or gas  Fluid mechanics

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 6 Types of Friction Dry Friction  Coulomb friction  Non-lubricated contact surface

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 7 Dry Friction Classical Model  Mechanical  Surface roughness Other Factors  More complex process  Scale dependent Macro  nano scale  Parameters with varying importance e.g. compare friction between two ‘rough’ sheet metal and two polished sheet metal surfaces e.g. compare friction between two rough glass and two smooth glass (microscope plates) surfaces

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 8 Dry Friction – Classical Model Mechanical  Surface roughness Frictional component,  F Normal Force,  N

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 9 Dry Friction – Classical Model (cont.) Distributed Contact Forces  Normal  Tangential (Frictional) Resultant Forces

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 10 Normal Force, N N  F NN  F

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 11 Static Friction Force, F s Equilibrium (P < F s )  s  coefficient of static friction Why is F s  N?

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 12 Static Friction Force, F s (cont.) Impending Motion (P = F s =  s N) Impending Motion Applied Force Friction Force FsFs P = F s No Motion

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 13 Friction Force Assumptions  Proportional to normal force  Independent of the contact area  Independent of velocity Valid for a Wide Range of Practical Conditions

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 14 Friction Force (cont.) Can Breakdown  Contact conditions  Variable friction coefficient e.g. Tires in snow or mud

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 15 Motion (P > F k =  k N)  Block is in motion Constant velocity Kinetic friction coefficient ~25% less than static   F k < F s  Complex phenomenon  k  coefficient of kinetic friction where  k <  s Constant Velocity Static Friction Force, F k

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 16 Variation of Friction Force Three Phases  Static friction Equilibrium  Limiting static friction Maximum value Impending motion  Kinetic friction Motion Impending Motion Applied Force Friction Force FsFs P = F s No Motion Kinetic Static

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 17 Variation of Friction Force (cont.) Three Characteristics  Experimental measurements  Range where static friction exceeds kinetic friction  General decrease in friction force magnitude and coefficient  General constant kinetic friction force Applied Force Friction Force FsFs P = F s No Motion Kinetic Static

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 18 Determination of Friction Coefficient Static: Angle to cause motion Kinetic: Angle to cause motion with constant velocity Exercise: Sum forces on axes parallel and perpendicular to plane

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 19 Impending Motion / Tipping? How to Determine?  Number of Unknowns? F s, N, P, and x

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 20 Impending Motion / Tipping? (cont.) Assume Impending Motion   Slipping What is Known or Assumed? What is to be Solved?  P, N, x Check?

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 21 Impending Motion / Tipping? (cont.) Assume Tipping What is Known? What is to be Solved?  P, N, F Check?

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 22 Comprehension Quiz A 10 N block is in equilibrium. What is the magnitude of the friction force between this block and the surface?  A) 0 N  B) 1 N  C) 2 N  D) 3 N Answer: C

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 23 Textbook Problems

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 24 Textbook Problems

ENGI 1313 Statics I – Lecture 36© 2007 S. Kenny, Ph.D., P.Eng. 25 References Hibbeler (2007) mech_1