1 6 Friction. 2 Objectives Students must be able to Utilize theory of dry friction –Describe...
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1 6 Friction. 2 Objectives Students must be able to Utilize theory of dry friction –Describe theory of dry friction –Describe physical meanings of frictional
2 Objectives Students must be able to Utilize theory of dry
friction Describe theory of dry friction Describe physical meanings
of frictional effects Describe and differentiate between static and
kinetic coefficients of friction Describe the angles of frictions
Add friction into the analyses of objects and structures in
equilibrium
Slide 3
3 Objectives Students must be able to Describe and analyze
machines with frictions Wedges Threads, screws Belts Disks and
clutches Collar, pivot, thrust and journal bearings Outline rolling
resistance Describe the physical meanings of rolling resistance
Differentiate between frictions and rolling resistance
Slide 4
4 Section A: Frictional Phenomena Characteristics, theory,
coefficient of friction, angle of friction We will study this Part
first. Topic in textbook Section B: Applications Wedges Screws
Journal Bearings Thrust Bearings; Disk friction Flexible Belts
Rolling Resistance
Slide 5
5 Dry Friction Force of resistance acting on a body which
prevents or retards slipping of the body relative to a surface with
which it is in contact. roughnesses of the contacting surfaces.
Friction exists? Magnitude: frictions magnitude limitation will be
discussed later Direction: tangent to the contacting surface and
opposed to the relative motion or tendency for motion Line of
Action (Point of application): contact surface
Slide 6
6 Friction Model Frictional force F In equilibrium N FBD is
correct? N W F P a/2 h x If x > a/2 ? The object is toppling
(not in equilibrium) Slipping and/or Tipping Effect The N at right
side is supporting force more than its left side. x-limit Slipping
toppling modeling The application point (x) of N increases with
force P F-limit y x Equilibrium
Slide 7
7 Motion Slipping / Sliding Relative sliding (translation
motion) between two surfaces Toppling / Tippling Fall over
(rotation) about the edge Topple, tipping, rolling, tumble, trip N
N F P a/2 h x
Slide 8
8 Experiment for determining Friction P m FBD P mg N F F P
Kinetic friction (motion) Object with motion (steady state) :
coefficient of kinetic friction F=P Static friction (no motion)
Object at rest (no motion) : coefficient of static friction F s:max
FkFk = s N = k N : constant on 2 certain contacting surfaces
impending motion (on the verge of motion)
Slide 9
9 Angle of Friction P mg N F s = arctan( s ) = angle of (max)
static friction k = arctan( k ) = angle of kinetic friction (object
at rest) (object in motion) R Not depend on N not depend on
P,v,a
Slide 10
10 Dry Friction Characteristics Frictional force acts
tangentially to the contacting surfaces, opposing the relative or
tendency for motion. F s is independent of the area of contact,
provided that the normal pressure is not very low nor great enough
for deformation of the surfaces. In equilibrium: Impending
slipping: = s Slipping: = k Very low velocity: k s Dry
Friction
12 y x Sample 6/1 Determine the maximum angle which the
adjustable incline may have before the block of mass m begins to
slip. The coefficient of static friction between the block and the
inclined surface is s. W=mg N F Impending Slip: W=mg x H/2 Three
force member Ans 3 eq., 3 unknowns Possibility of toppling? (for
slipping)
Slide 13
13 6/125 A uniform block of mass m is at rest on an incline z.
Determine the maximum force P>0 that can be applied to the block
in the direction shown before slipping begins. The coefficient of
static friction between the block and the incline is P mg x y z N
At this max P, object is about to move at which direction?
Slide 14
14 Example Friction 2 #1 Will this crate slide or topple over?
Dry Friction
Slide 15
4 Unknowns: P, F, N, x 1) about to slip 2) about to tip Two
possibilities 4 th Eq. Check condition : 2 nd Eq. 3 rd Eq. Check
condition : 1 st Eq. Its time consuming, Better to know it
exactly
Slide 16
16 The block of mass m is homogeneous, moving at a constant
velocity. The coefficient of kinetic friction is -Determine a) the
greatest value that h may have so that the block will not tip over
b) The location of point C on the bottom face of the block through
with the resultant of the friction and normal force act if h =
H/2.
Slide 17
17 -The block of mass m is homogeneous, moving at a constant
velocity. The coefficient of kinetic friction is -Determine a) the
greatest value that h may have so that the block will not tip over
P mg F N on the verge of tipping The box is in Equilibrium (no
acceleration) F N Three force member in Statics Ans Solution 1
Moving h=? Concurrent at one point OR parallel Moving With no
acceleration = ? on the verge of tipping
Slide 18
18 mg P -The block of mass m is homogeneous. -The block is
moving at a constant velocity. -Determine b) The location of point
C on the bottom face of the block through with the resultant of the
friction and normal force act if h = H/2. F N x Three force member
Ans Solution 1 C =? =H/2 N Moving with constant velocity Moving The
box is in Equilibrium (no acceleration) Concurrent at one point OR
parallel h=H/2
Slide 19
19
Slide 20
20 static friction kinetic friction or Dry Frictions Problem
Equilibrium eq. + Inequality: hard to deal Equilibrium eq. +
Kinetic friction Kinetic motion is known. fricitional eq. Moving at
constant vel. Friction
Slide 21
21 Equilibrium eq. Static friction + In static equilibrium Only
equilibrium eq. can be used to determine unknown values. Friction
is determined by equilibrium eqs. However, F must
