Engineering Mechanics:
Statics
Chapter 6: Friction
Introduction
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Ideal assumption – forces between contacting surfaces act
normal to the surfaces
Real surfaces – there are tangential forces between contacting
surfaces = “Friction forces”
Friction force occurs when one contacting surface tends to slide
along another.
 Minimize the effects: bearings, screws, gears, flow of fluids in
pipe
 Maximize the effects: brakes, clutches, belt drives, wedges
Types of Friction
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Dry friction
- unlubricated surfaces in contact under a tendency to slide
- friction occurs in the direction opposite to the impending motion
- called Coulomb friction
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Fluid friction
- adjacent layers in a fluid are moving at different velocity
Internal friction –solid material under cyclical loading
Dry Friction
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Mechanism of Dry Friction
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Static friction:
Fmax = msN
limiting value for impending motion!!!
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Kinetic friction:
Fk = mkN
Dry Friction
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The direction of R is specified by
tan a = F/N
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When the friction force reaches Fmax, the angle a
reaches a maximum value fs . Thus,
tan fs = ms
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When slippage is occurring, tan fk = mk
The angles fs and fk are called angle of static friction
and angle of kinetic friction which define the limiting
direction of the total reaction R for each case.
Cone of Friction
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If motion is impending, R must be one element of the cone of static friction
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If motion is not impending, R is within the cone. The cone vertex angle is 2fs
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If motion occurs, the angle of kinetic friction is applied. The reaction R must lie
on the surface of cone of vertex angle 2fk
Types of Friction problems
1. Motion is impending (body about to slip)
Fmax = msN
2. Condition of motion is not known –find friction force F from equilibrium
equation
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If F < Fmax (= msN) – body is in equilibrium and friction force = F
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If F = Fmax (= msN) – body is in equilibrium  motion is impending
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If F > Fmax (= msN) – impossible  not in equilibrium
3. Relative motion exist
Fk = mkN
Sample Problem 6/2
Determine the range of values which the mass m0 may have so
that the 100-kg block will neither start moving up the plane nor
slip down the plane
The coefficient of static friction for the contact surfaces is 0.30
Sample Problem 6/4
The homogeneous rectangular block of mass m, width b, and
height H is placed on the horizontal surface and subjected to a
horizontal force P which moves the block along the surface with
a constant velocity. The coefficient of kinetic friction between
the block and the surface is mk. Determine (a) the greatest
value which h may have so that the block will slide without
tipping over and (b) the location of a point C on the bottom
face of the clock through which the resultant of the friction and
normal forces acts if h = H/2
Sample Problem 6/5
The three flat blocks are positioned on the 30 degree incline as shown, and a force
P parallel to the incline is applied to the middle block. The upper block is prevented
from moving by a wire which attaches it to the fixed support. The coefficient of
static friction for each of the three pairs of mating surfaces is shown. Determine the
maximum value which P may have before any slipping takes place.
Problem 6/9
The 30-kg homogeneous cylinder of 400-mm diameter rests
against the vertical and inclined surfaces as shown. If the
coefficient of static friction between the cylinder and the
surfaces is 0.30, calculate the applied clockwise couple M
which would cause the cylinder to slip.
Problem 6/12
50 kg
600 mm
200
mm
75 mm
12 kg
The 50-kg wheel rolls on its hub up the circular incline under the
action of the 12-kg cylinder attached to a cord around the
rim. Determine the angle q at which the wheel comes to rest,
assuming that friction is sufficient to provent slippage. What is
the minimum coefficient of friction which will permit this
position to be reached with no slipping?