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Engineering Mechanics: StaticsEngineering Mechanics: Statics

Chapter 8:

Friction

Chapter 8:

Friction

Chapter ObjectivesChapter Objectives

To introduce the concept of dry friction

and show how to analyze the equilibrium

of rigid bodies subjected to this force.

To present specific applications of

frictional force analysis on wedges,

screws, belts, and bearings.

To investigate the concept of rolling

resistance.

8.1 Characteristics of Dry

Friction

8.1 Characteristics of Dry

Friction

Friction

Retards slipping of the body relative to a

second body or surface which it is in contact

Acts tangent to the surfaces at points of

contact with other body.

Lee says Normal Force is perpendicular to

Frictional force.

Opposing possible or existing motion of the

body relative to points of contact

Two types of friction – Fluid and Coulomb

Friction

8.1 Characteristics of Dry

Friction

8.1 Characteristics of Dry

Friction

Fluid friction exist when the

contacting surface are separated by a

film of fluid (gas or liquid)

Depends on velocity of the fluid and

its ability to resist shear force

Coulomb friction, also known as dry

friction, occurs between contacting

surfaces of bodies in the absence of a

lubricating fluid

a W P h F N X O Write an equilibrium equation – Moment at point O Take Moment about O, W x –Ph= 0 or x = Ph/W The block is on the verge on tipping if N acts at the right corner of the block, x = a/

Note F is on the surface of contact opposite the direction of

motion

Note F is on the surface of contact opposite the direction of

motion

This graph can only be used when there is no tipping.

Theory of Dry Friction  (^) Block will begin to move  Fs is directly proportional to resultant normal force N s s s s N N N F    1 1 1 tan tan tan           ^        F s = μ s N

8.1 Characteristics of Dry Friction -8.1 Characteristics of Dry Friction -MotionMotion Theory of Dry Friction Motion  If the magnitude of P acting on the block is increased so that it is greater than Fs, the frictional force at the contacting surfaces drops slightly to a smaller value Fs, called kinetic frictional force  The block will not be held in equilibrium (P > Fs) but slide with increasing speed

8.1 Characteristics of Dry Friction - Motion8.1 Characteristics of Dry Friction - Motion Theory of Dry Friction  Resultant frictional force F k is directly proportional to the magnitude of the resultant normal force N Fk = μkN  Constant of proportionality μk is called the coefficient of kinetic friction  μk are typically 25% smaller than μs

P N

P

P P

M B

cos 30 ( 1. 05 ) sin 30 ( 1. 2 ) 500 ( 0. 6 ) 0

Assumependingtotip.Reactionforceat A 0.

 What is the force for pending to tip?

If P =198.76N where is the contact point or x? (Apa ni 2X5, 5X2)

1. 6

198. 76 cos 30 ( 1. 05 ) 198. 76 sin 30 ( 0. 6 ) 500 ( ) 0 0

198. 76 cos 30 ( 1. 05 ) 198. 76 sin 30 ( 0. 6 ) 500 ( ) ( 0. 6 ) 0 ............( 1 )

Assumependingtotip.ReactionforceatA 0. 

 x x x x

R

x x R x

M

Ay Ay B X B’ B’

8.1 Characteristics of Dry Friction8.1 Characteristics of Dry Friction Theory of Dry Friction

The graph summarizes the effects regarding friction and shows the variation of frictional force F versus applied load P This is applicable for sliding only not tipping. Static-Frictional Force/Equilibrium Limiting Frictional Force/Motion is impending

8.2 Problems Involving Dry Friction8.2 Problems Involving Dry Friction Types of Friction Problems Equilibrium  (^) Total number of unknowns = Total number of available equilibrium equations  (^) Frictional forces must satisfy F ≤ μ sN; otherwise, slipping will occur and the body will not remain in equilibrium  (^) We must determine the frictional forces at A and C to check for equilibrium Draw the FBD.

8.2 Problems Involving Dry Friction8.2 Problems Involving Dry Friction Types of Friction Problems

If the bars are uniform and have known weights of 100N each, FBD are shown below

There are 6 unknown force components which can be determined strictly from the 6 equilibrium equations (three for each member)