Download Dry Friction

CE 201 - Statics
Chapter 8 – Lecture 1
FRICTION
 We used to assume that surface of contact between
two bodies are smooth

Reaction is assumed normal to surface of contact
F
 In reality, surfaces are rough
Ff
Fn
Characteristics of Dry Friction
What is friction?
Friction is a force of resistance acting on a body
preventing it from slipping. The friction force is
always tangent to the surface at point of contact and
its direction is opposite to the possible motion of the
body.
Theory of Friction
 Consider block of weight W on a
rough surface
W
P
 Surface of contact of the block is non-
rigid or deformable
 N is upward to balance W and Ff is to
the left to prevent P from moving the
block.
 Close look at the contacting surfaces
Ff
Nn
Equilibrium
 For simplicity, the resultants N and F
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

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will be used.
F is tangent to the surface and opposite
to P
N is found from the distribution of
Nn and is upward to balance W
N acts at a distance X right to W line
of action
X is necessary for the tipping effect
Take moment about O
WX = Ph
 X = Ph / W
The block will be on the verge of
tipping if X = a/2
a/2 a/2
W
P
h
O
F
X
N
Impending Motion
As P increase, F will increase till it reaches a maximum
value Fs called the limiting static frictional force
Any further increase in P will cause deformation at the
points of contact and consequently the block will move. Fs
was found to be directly proportional to N
Fs = s N
Where s is the coefficient of static friction and is
dimensionless.
a/2 a/2
Impending Motion
W
P
h
O
Fs
X
N
Motion
If P was increased to be greater than Fs, the frictional force
slightly drops to Fk called the kinetic frictional force.
Since P > Fk , the block will move.
Fk was found to be:
Fk = k N
Where k is the coefficient of kinetic friction and is
approximately 25% less than s
a/2 a/2
Impending Motion
W
P
h
O
Fk
X
N
Characteristics of Dry Friction
 Frictional force is tangent to the surface opposite
to motion
 Maximum Fs is independent of the area of contact
 Maximum Fs is greater than maximum Fk
 If one body is moving with very low velocity, then
Fs = Fk or s = k
 When body is about to move, then Fs = s N
 When body is moving, then Fk = k N
Angle of Friction
 If block is stationary
Fs  s N
 If block is on the verge of moving
Fs = s N
 If block is moving
Fk = k N
Angle of Friction
At equilibrium, Fs and N combine to have a resultant Rs, the angle of
static friction s is:
s = tan-1 ( Fs / N) = tan-1 (s N / N) = tan-1 s
If the block is in motion, then the angle of kinetic friction :
k = tan-1 ( Fk / N) = tan-1 (k N / N) = tan-1 k
By comparison, s  k
W
W
Impending Motion
Motion
P
P
Fs
Fk
s
N
k
Rs
N
Rk
Angle of Response
To measure the coefficient of friction experimentally,
a block is placed on a plane of different material than
the block.
The plane is inclined to the angle s
The block is on the verge of moving
Fs = s N
Angle of Response
At equilibrium
Fs = W sin s
N = W cos s
s
Since Fs = s N
W sin s = s ( W cos s )
s = tan-1s
W
s
Fs = s N
s is called the angle of response
s = tan s
N