Transcript Chapter 8 FRICTION W P F
Chapter 8 FRICTION
W P N F
F
Equilibrium
F m
Motion
F k
P
A horizontal force
P
applied to a block will not at first cause it to move. This is because the
friction force
F
balances
P
.
As the magnitude of
P
increases, the magnitude of
F
increases until it reaches a maximum value
F
m
. If
P
is increased further, the magnitude of
F
drops to slide.
F
k
and the block begins to
P W
F
Equilibrium
F m
Motion
F k
N F
P
The forces
F
m
component
N
and
F
k
are proportional to the normal of the reaction of the surface. We have
F
m
=
m
s
N F
k
=
m
k
N
where m
s
is the
coefficient of static friction
and m
k
is the
coefficient of kinetic friction
. These coefficients depend on the nature and the condition of the surfaces in contact.
W P
N
f
R
F N
=
R
=
R
sin
f
cos
f
F
It is sometimes convenient to replace the normal force
N
and the friction force
F
by their resultant
R
. As the friction force increases and reaches its maximum value
F
m
angle f that
R
= m
s
N ,
forms with the the normal to the surface increases and reaches a maximum value f
s
, called the
angle of static friction
.
W P
N
f
R
F
F N
=
R
=
R
sin
f
cos
f If motion actually takes place, the magnitude of
F
drops to
F
k
; similarly the angle f drops to a lower value f
k
, called the
angle of kinetic friction
. The coefficient of friction and the angle of friction are related by
tan
f s
tan
f
k
=
m
s
=
m
k
W P F
required
N
The magnitude
F
of the friction force is equal to
F
m
= m
s
N
only if the body is about to slide
.
If motion is not impending
,
F
and
N
should be considered as
independent unknowns
to be determined from the equilibrium equations. The value of
F
required to maintain equilibrium should be checked to insure that it does not exceed
F
m
.
W P F
m
= m
s
N
N
If motion is known to be impending
,
F
maximum value
F
m
= m
s
N
has reached its , and this expression may be substituted for
F
in the equilibrium equations.
A B
P
C D
In the analysis of
wedges
, two or more free-body diagrams are generally used to show each friction force and its correct sense.
W Q
q 2 p
r
q
R
f
s L
The analysis of
square
-
threaded screws
(frequently used in jacks, presses and other mechanisms) is reduced to the analysis of a block sliding on an incline by unwrapping the thread of the screw and showing it as a straight line. In doing this,
r
denotes the
mean radius
of the thread,
L
lead
of the screw (the distance through which the screw is the advances in one turn),
W
is the load, and
Qr
is the torque exerted on the screw.
P
1
P
q Dq b
P’ P
2
O
T 1 T 2
For a
flat belt
passing over a cylinder, it is important to determine the direction in which the belt slips or is about to slip. If the drum is rotating, the motion or impending motion of the belt should be determined
relative
to the rotating drum.
P
1
P
q Dq b
P’ P
2
O
If the belt shown is about to slip to the right relative to the drum, the friction force will be directed to the left and the tension will be larger in the right-hand portion of the belt than the left hand portion.
T 1 T 2
Denoting
T
2 as the larger tension, m
s
static friction, and b as the coefficient of as the angle (in radians) subtended by the belt, the two tensions are related by
T
ln =
T
1 m
s
b
T T
2 1
= e
m
s
b