EAS 208 (Fall 2010)
Coulomb Friction
Assume the block
A
shown in the Figure below. The block is resting on the surface, and
the coefficient of static friction between the block
A
and the surface is
s
μ
. In addition,
an external force
is applied on block
ext
F
A
.
The F.B.D. (free body diagram) of block
A
is shown in the Figure below:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
From the F.B.D. of block
, applying Newton’s second law in each direction (
A
x
–
y
direction) we obtain the equations of motion for block
:
A
x
A
x
A
A
ext
A
A
F
m a
m X
F
f
m X
Σ
=
=
⇒
−
=
&&
&&
(1)
y
A
y
A
A
A
A
F
m a
m Y
N
m g
m Y
Σ
=
=
⇒
−
=
&&
&&
A
f
(2)
If we assume that block
is stationary then the equations of motion become (from Eq. 1
and Eq. 2):
A
0
ext
A
A
ext
F
f
m X
F
−
=
=
⇒
=
&&
(3)
0
A
A
A
A
N
m g
m Y
N
m g
−
=
=
⇒
=
&&
(4)
We can study two limiting cases.
CASE A
Assume that the external force
is zero. From Eq. 3:
ext
F
0
ext
F
f
f
=
⇒
=
(5)
Therefore, if there is no external force, from equilibrium the friction force is
.
0
f
=
CASE B
The maximum value that the static friction can take before block
slides on the surface
is given by the relation:
A
max
s
s
f
f
N
μ
=
=
(6)
The normal force from Eq. 4 is
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 MehdiAhmadizadeh
 Friction, external force, Fext, external force Fext

Click to edit the document details