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Statics
Chapter 8
Friction
Eng. Iqbal Marie
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
