Statics Chapter 8 Friction -...

Statics

Chapter 8

Friction

Eng. Iqbal Marie

iqbal@hu.edu.jo

Hibbeler, Engineering Mechanics: Statics,13e, Prentice Hall

• 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.

Introduction

• There are two types of friction: dry or Coulomb friction

and fluid friction. Fluid friction applies to lubricated

mechanisms.

8.1 - Characteristics of Dry Friction

Definition: friction is the force that opposes relative movement

between two surfaces in contact.

The friction force is always tangent to the surfaces at the point of

contact.

Theory of Dry Friction

Dry friction can be modeled by considering pulling

horizontally with a force P on a block of uniform

density and weight W, resting on a horizontal

surface (floor)

The contact surfaces are considered non-rigid, or

deformable.

The rest of the block, however, is considered rigid.

A free body diagram on the block shows the

reactions the floor exerts on the block.

These reactions are both distributed forces:

DNn - normal force

DFn - friction force tangential to the surface

Equilibrium implies that:

- the normal forces DNn must act upwards,

to balance the weight W;

- the friction forces DFn must act to the left,

to balance the force P pulling to the right.

A magnified view of the contact between the

two surfaces shows how these normal and

frictional forces develop.

Irregularities (bumps and dents) cause a reactive force DRn to develop at

each bump.

These forces act at all points of contact, generating the distributed forces

DNn and DFn.

T he distributed forces will be replaced by their resultants N and F ,

F is always tangent to the contact surfaces, opposite

to the direction of P.

N is always normal to the contact surfaces, directed

upwards, and its point of application will depend on

the distribution of DNn

Tipping - depending on the magnitude of the forces W and P and the

height h of the line of action of P, the block may tip over, before it starts

sliding.

sliding condition tipping condition

Impending (about to happen) Motion

if: h is small

then: the friction force F may not be strong

enough to balance P and prevent motion, and

the block will start to slide before it tips over.

If P is slowly increased, the tangential friction

reaction F will also increase, and the body will not move

until it reaches a maximum value FS, called limiting static frictional force.

At this point, equilibrium is unstable, and the slightest increase in F will cause

the block to slide.

or: the surfaces are very slick (slippery)

NF SS

S is called coefficient of static friction, and is a

constant for pairs of surfaces (see table).

SSS

SN

N

N

F

111 tantantan

S is called angle of static friction

• Further increase in P causes the block to begin

to move as F drops to a smaller kinetic-

friction force Fk.

Experiments show that the frictional force resisting P

now drops slightly to a value Fk < FS .

The block will not be in equilibrium, but will accelerate,

because P > FS .

NF kk

kkk

kN

N

N

F

111 tantantan

k is called angle of kinetic (dynamic) friction

• Maximum static-friction force:

NFs s

• Kinetic-friction force:

sk

kk NF

75.0

• Maximum static-friction force and kinetic-friction force are:

- proportional to normal force

- dependent on type and condition of contact surfaces

- independent of contact area

Four situations can occur when a rigid body is in contact with a

horizontal surface:

• No friction,

(Px = 0)

• No motion,

(Px < Fm)

• Motion impending,

(Px = Fm)

• Motion,

(Px > Fm)

8.2 Problems Involving Dry Friction

Types of Friction Problems - There are three

types of friction problems. They can be classified

from the free body diagram and from the number

of unknowns and available equilibrium equations.

#1 - Equilibrium - requires that the number

of unknowns and the number of equilibrium

equations are the equal.

F s N for all friction forces,

otherwise, slipping will occur and equilibrium

will be violated.

#2 - Impending Motion at All Points - in this case,

the total number of unknowns is equal to the total number of equations of equilibrium plus the total

number of available frictional equations F N.

Example find the smallest angle q at which the 100 N

bar can be placed against the wall without slipping.

Solution: There are five unknowns:

0 , 0 , 0 Oyx MFF

There are three equations of equilibrium:

, , , , BBAA NFNF

and two friction equations:

BBBAAA NFNF ,

Example: determine the force P that will make one

of the two 100 N bars in the figure slip.

there are seven unknowns:

PBBNFNF yxCCAA , , , , , ,

six equations of equilibrium (three per bar) , and

two friction equations

Only one solution is possible: in practice, the

one with smaller P (solve the problem for both cases).

#3 - Impending Motion at Some Points - the total number of unknowns is less to the total number of equations of equilibrium plus the total number of available frictional equations . More than one possibility of motion or impending motion

will exist. The solution must determine which motion will actually

occur.

Eg. 8.1

Eg. 8.1

:0 xF 0lb 300 - lb 10053 F

lb 80F

:0 yF 0lb 300 - 54 N

lb 240N

Calculate maximum friction force and compare with friction force

required for equilibrium.

The block will slide down the plane.

lb 60lb 24025.0 msm FNF

• If maximum friction force is less than friction force required for

equilibrium, block will slide. Calculate kinetic-friction force.

lb 24020.0

NFF kkactual

lb 48actualF

Actual friction force is directed up and to the right;

also the forces acting on the block are not balanced