Slide 1

ENGI 1313 Mechanics I

Lecture 36:

Friction

Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]


Slide 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


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 3

Lecture 36 Objective
to introduce the concept of dry friction
 to analyze the equilibrium of rigid bodies
subjected to dry friction force


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 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


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 5

Types of Friction


Fluid Friction
Contact surface separated by fluid
 Fluid may be a liquid or gas
 Fluid mechanics


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 6

Types of Friction


Dry Friction
Coulomb friction
 Non-lubricated
contact surface


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 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

•
7

two polished sheet metal surfaces
e.g. compare friction between two rough glass and two
smooth glass (microscope plates) surfaces
© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 8

Dry Friction – Classical Model


Mechanical


Surface roughness

Frictional component, F

Normal Force, N
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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 9

Dry Friction – Classical Model (cont.)


Distributed Contact Forces
Normal
 Tangential (Frictional)




Resultant Forces


F



x

0

P F




F

y

0

N W
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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 10

Normal Force, N
F

F



N
N  W  mg

10



N
N  W  F sin 

© 2007 S. Kenny, Ph.D., P.Eng.

N
N  W  F sin 

ENGI 1313 Statics I – Lecture 36


Slide 11

Static Friction Force, Fs


Equilibrium (P < Fs)
Fs   s N   s mg

Why is Fs N?



s  coefficient of static friction

 s  tan

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© 2007 S. Kenny, Ph.D., P.Eng.

1

 Fs 

  tan
N 

1

 sN 

  tan
 N 

ENGI 1313 Statics I – Lecture 36

1

s


Slide 12

Static Friction Force, Fs (cont.)


Impending Motion (P = Fs = sN)
Fs   s N   s mg



Impending Motion

Friction Force

Fs

P = Fs
No Motion
Applied Force

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 13

F  N

Friction Force


Assumptions
Proportional to normal force
 Independent of the contact area
 Independent of velocity




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Valid for a Wide Range of Practical
Conditions

© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 14

Friction Force (cont.)


Can Breakdown
Contact conditions
 Variable friction coefficient


e.g. Tires in snow or mud

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 15

Constant Velocity

Static Friction Force, Fk


Motion (P > Fk = kN)


Block is in motion

• Constant velocity
F k   k N   k  mg



k  coefficient of kinetic friction where k < s

 k  tan

1

 Fk 

  tan
N 

1

 kN 

  tan
 N 

1

k

• Kinetic friction coefficient ~25% less than static
 Fk < Fs
 Complex phenomenon


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 16

Variation of Friction Force


Three Phases


Static friction

Impending Motion

• Equilibrium
Limiting static friction

• Maximum value
• Impending motion


Kinetic friction

• Motion

Fs
Friction Force



Kinetic

Static
P = Fs

No Motion
Applied Force

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 17

Variation of Friction Force (cont.)
Three Characteristics








17

Experimental
measurements
Range where static
friction exceeds kinetic
friction
General decrease in
friction force magnitude
and coefficient
General constant
kinetic friction force
© 2007 S. Kenny, Ph.D., P.Eng.

Fs
Friction Force



Kinetic

Static
P = Fs

No Motion
Applied Force

ENGI 1313 Statics I – Lecture 36


Slide 18

Determination of Friction Coefficient

Exercise: Sum forces on axes parallel and perpendicular to plane

Static: Angle to
cause motion
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© 2007 S. Kenny, Ph.D., P.Eng.

Kinetic: Angle to cause
motion with constant velocity
ENGI 1313 Statics I – Lecture 36


Slide 19

Impending Motion / Tipping?


How to Determine?


Number of Unknowns?

• Fs, N, P, and x

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 20

Impending Motion / Tipping? (cont.)


Assume Impending Motion




Slipping

What is Known or Assumed?
F   s N   s mg



What is to be Solved?






P, N, x

Check?
0  x  b/ 2

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 21

Impending Motion / Tipping? (cont.)
Assume Tipping
 What is Known?


x  b/ 2



What is to be Solved?




P, N, F

Check?
F   s N   s mg

21



© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 22

Comprehension Quiz 21-01


A 10 N block is in equilibrium. What is the
magnitude of the friction force between this
block and the surface?







22

A) 0 N
B) 1 N
C) 2 N
D) 3 N

Answer: C
© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 23

Textbook
Problems

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 24

Textbook
Problems

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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36


Slide 25

References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1


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© 2007 S. Kenny, Ph.D., P.Eng.

ENGI 1313 Statics I – Lecture 36