MEC 412
Chapter 7: Friction
Learning Outcome
Upon completion of this chapter, student should be able to;
Describe the laws and analyze the problem of dry friction
Determine the application of frictional force analysis.
1
MEC 412
Chapter 7: Friction
7.0 Introduction
Friction is a resistive force that prevents or retards the slipping of
one body with respect to another.
For two surfaces in contact, tangential forces, called friction
forces, will develop if one attempts to move one relative to the
other. However, the friction forces are limited in magnitude and
will not prevent motion if sufficiently large forces are applied.
Two types of friction – fluid and dry (coulomb) friction
Fluid friction exist when the contacting surface are separated by
a film of fluid (gas or liquid). Depends on velocity of the fluid and
its ability to resist shear force
Coulomb friction, also known as dry friction, occurs between
contacting surfaces of bodies in the absence of a lubricating fluid
7.1 Dry friction
Dry friction is described using empirically collected values to
predict the magnitude of this resistance to sliding. This relation
usually depends upon whether there is relative motion or not
between the surfaces
MEC 412
Chapter 7: Friction
• Block of weight W placed on horizontal
surface. Forces acting on block are its weight
and reaction of surface N.
• Small horizontal force P applied to block. For
block to remain stationary, in equilibrium, a
horizontal component F of the surface reaction
is required. F is a static-friction force.
• As P increases, the static-friction force F
increases as well until it reaches a maximum
value Fm.
Fm s N
• Further increase in P causes the block to begin
to move as F drops to a smaller kinetic-friction
force Fk.
Fk k N
MEC 412
Chapter 7: Friction
Static friction force - the force that keeps the block from moving
where
μ sand μk are the static and kinetic coefficients of friction
respectively
• Maximum static-friction force:
Fm s N
• Kinetic-friction force:
Fk k N
k 0.75 s
• 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
MEC 412
Chapter 7: Friction
Four situations can occur when a rigid body is in
contact with a horizontal surface:
• No motion, • Motion impending, • Motion,
• No friction, (Px < Fm) (Px = Fm) (Px > Fm)
(Px = 0)
MEC 412
Chapter 7: Friction
It is sometimes convenient to replace normal force
N and friction force F by their resultant R:
• No friction • No motion • Motion impending • Motion
N F N
F
tan s m s tan k k k
N N N N
tan s s tan k k
MEC 412
Chapter 7: Friction
where
ø = angle with the normal to the surface
Øs = angle of static friction
Øk = angle of kinetic friction
Consider block of weight W resting on board with variable
inclination angle θ.
• No friction • No motion • Motion • Motion
impending
MEC 412
Chapter 7: Friction
7.1.1 Characteristics of dry friction
The frictional force acts tangent to the contacting surfaces in a
direction opposed to the relative motion or tendency for motion of
one surface against another
The maximum static frictional force Fs that can be developed is
independent of the area of contact, provided the normal pressure
is not very low or great enough to severely deform or crush the
contacting surfaces of the bodies
The maximum static frictional force is generally greater than the
kinetic frictional force
However, if one of the bodies is moving with a very low velocity
over the surface of another, Fk becomes approximately equal to
Fs
When slipping at the surface of contact is about to occur, the
maximum static frictional force is proportional to the normal force
When slipping is occurring, the kinetic frictional force is
proportional to the normal force
MEC 412
Chapter 7: Friction
7.1.2 Types of friction problems
In all cases, geometry and dimensions are assumed to be known
Four types of friction problems
- Equilibrium
- Impending motion at all points
- Tipping or Impending motion at some points
- Body is sliding
1). Equilibrium (number of unknowns = # of equations of equilibrium)
P Fx 0 F s N
F Px
W
F F y 0
N Py W
N
No evidence that has reached its maximum value, thus F μsN cannot be
used
MEC 412
Chapter 7: Friction
2). Impending motion at all points (# of unknowns = # of EOE + # of friction
equations)
P Fx 0
Fmax Px F y 0
W
Fmax N Py W
Fmax s N
N
Friction force is in opposite direction of impending motion
3). Tipping or impending motion at some points (# unknowns < # E.O.E. +
# F.E.)
Sliding: must do computations for all the different situations
- assume condition 1, solve
- assume condition 2, solve
etc.
Tipping: - block will slip F s N, x b / 2
- block will tip F S N, x b / 2
MEC 412
Chapter 7: Friction
4).Body is sliding
P Fk Px F y 0
W N Py W
Fk
Fk k N
N
