Document related concepts
Transcript
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‫جناب آقای دکتر جوادیان‬
What is friction?
What’s Stopping You?
Mu
F
n
Friction
Hard to Live With It, Can’t Live Without It
Coefficient of Friction
Friction
Friction causes
objects to slow
down.
Friction creates
heat.
an object’s energy
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
Friction
Opposes relative motion of
two surfaces
Consists of a matched pair
of forces:
Obj1 pushes Obj2 while Obj2
pushes Obj1
Equal magnitudes, opposite
directions
Comes in two types:
static and kinetic 
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Places where friction is good
The soles of shoes
Car tires
The feet of table legs
Rock climbing holds
Brakes
etc
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In engines 
In transmissions 
On the bottoms of skis 
and snowboards (To a
point)
When you are trying to 
move a box by pushing it
along the floor
etc 
What causes friction?
Source of Friction
At the microscopic level even the
smoothest of surfaces is dotted
with little “mountain peaks”.
The tips of the peaks are the only
parts that touch the other material.
Only a very small portion of the
apparent surface area is in contact
with the other surface
This causes extremely high
pressures to form on the parts that
touch. This causes the two
surfaces to become “welded”
almost at the points of contact
Picture of extremely smooth
mica with a scanned probe
microscope

Consider 2 Types of Friction
Fs
Force of Static Friction
This value represents the relative force necessary
to make an object move
Fk
Force of Kinetic Friction
This value represents the relative force necessary
to keep an object moving at a constant rate
Types of Friction
Static Friction

Acts to prevent objects from
starting to slide
Forces can vary from zero to
an upper limit
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
Kinetic friction 
-Sliding Friction 
Acts to stop objects that
-Rolling friction
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Friction is a Force That
N
Resists Motion
F
fs
M1
Surfaces in
Contact
Spring Scale
W
The Pink Block M1 Will not Move Until the
Force F (Pull on the scale ) Exceeds the
Force of Static Friction fs.
Increases 
linearly
For a given pair
of surfaces, the
ratio of
Frictional force
to Applied
force is a
constant.

Frictional Force
Static Friction
Applied Force, N
Fs
Fs  Fk
Max
Fk
Fs  Fk
Static
Region
Kinetic Region
Force Causing the Object to Move
Why?
-The slightly larger value for static friction
results from irregularities and
contaminants on the surfaces and is less
accurate in general than the coefficient of
kinetic friction
-inertia 

F
s 
W
Coefficient of Static
Friction N
F

fs
M1
Surfaces in
Contact
Spring Scale
W
s
F
W
= Coefficient of Friction
= Force Required to Cause Motion
= Weight of Object
Example of Static Friction
What is the coefficient of
static friction between a
tabletop and a 2 kg block
of wood if a 2 N force is
required to start the block
moving?
Identify knowns and
unknown:
m = 2 kg, applied force = 2
N, v = 0,
μs = ?
Appropriate equation: f = μ N.
What is N?
On a level surface the normal force
upward is equal to the weight of
the object downward, i.e. N = W
= mg. So,
f = μ mg or μ = f/mg = 2 N/(2 kg
*9.8m/s2)
μ = 0.102
Static & Kinetic Friction
Coefficients
Material
Coefficient of
Coefficient of
Static Friction S Kinetic Friction S
Rubber on Glass
2.0+
2.0
Rubber on Concrete
1.0
0.8
Steel on Steel
0.74
0.57
Wood on Wood
0.25 – 0.5
0.2
Metal on Metal
0.15
0.06
Ice on Ice
0.1
0.03
Synovial Joints in
0.01
0.003
Humans
Application Analysis
Sand is often placed on
sand:
Decreases the
coefficient of friction
between the tires of a
Increases the coefficient
of friction between the
tires of a car and the
Decrease the
gravitational force on a
car
Increases the normal
force of a car on the
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.1
.2
.3
.4
Using the Gears-IDS Battery to
Calculate The  s Static
F
s 
W
Coefficient of Friction
Record the Maximum Force (F)
(Before the Battery Begins to Move)
Maximum Force F = 110 g
F
s 
W
Record the Weight
(W ) of the Battery
F
s 
W
580 g
The Coefficient of Static Friction Between
the Wood Desktop and the Plastic Battery is
Described Algebraically:
F
s 
W
s
= .190
= 110 g
= 580 g
The Coefficient of Kinetic Friction Can
be Found Using the Same Technique
F
k 
W
Record the Force Required to Move
the Battery at a Constant Rate
r
r
f
f
t
The frictional force depends only on 
1-the type of surfaces 
2-how hard the surfaces are pressed 
together
What is the normal force?
Block at Rest on a Table
Normal Force
From Newton’s third law we know that if gravity or some
other force pushes an object (like a block) into a second
object (like a table) that second object will be exerting

an equal force back on the first.
Normal force is the force the table exerts back on the 
block
Normal force is always exerted perpendicular to the 
surface
Friction Force is always parallel to the surface 
So if the table is horizontal and gravity is the only force
on the block Fn = -Fg

Normal force on a hill
Normal force is exerted 
perpendicular to the surface in
accordance with Newton’s
Third law
No unbalanced force so the 
block is stationary or at least
not accelerating
.
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Questions?
Solution
Fn  Fg  cos( 20)
Fn  m  g  cos( 20)
Ff  k  Fn
Fg ( paralleltosurface)  m  g  sin( 20)
Ff  Fg ( paralleltosurface)  m  g  cos( 20)  k  m  g  sin( 20)
cos( 20)  k  sin( 20)
sin( 20)
k 
cos( 20)
k  tan( 20)
Frictional force and normal
force.
Frictional force is 
proportional to the
normal force, f α N.
On a level surface N
= W, but what if
someone is lifting up
on the object?
Won’t that reduce the
normal force?

Free Body Diagram
N + T = W, so Normal,
N
N = W – T.
If T pulls at
some angle,
then just
decompose
into
components.
Lift from
person,T
Weight, W
Example:
A person pulls on a 300 N crate with a
rope that makes a 300 angle to the
ground. If the coefficient of static
friction is 0.6, how much tension
must the person exert to get the
crate moving?
Knowns: W = 300 N, θ = 30o, μ = 0.6.
Unknown: T = ?
Equations: f = μN. All forces balance
when at rest.
Horizontal Tension = T cos θ
Vertical Tension = T sin θ
Net vertical force = N + Tsin θ – W = 0,
so
N = W - Tsin θ.
Net horizontal force = Tcos θ – f = 0
Tcos θ = f = μN = μ(W - Tsin θ) , so
Tcos θ = μ(W - Tsin
θ)
Tcos θ + μ Tsin θ =
μW
T(cos θ + μ sin θ) =
μW
T = μW/(cos θ + μ
sin θ)
T=
0.6*300N/(cos300
+ .6*sin300)
T = 180N/(0.866+.3)
T = 180 N/(1.166)
T = 154 N
Experiment: Does the friction force
depend on surface area?
We stick a 1kg mass on a piece of on top
of the clean surface and, using a Newton
meter, pull the weight across the table
with the string provided at constant
speed.
We put the same weight on a different 
piece of plexiglass with drastically
different surface area and repeat
What do you notice? 

What is rolling friction?
Rolling friction:
-nature
-normal force
-diameter
Rotational friction
‫منابع‬
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‫دكتر نمازي زاده‬
‫بیومكانیك فنون ورزشي‬‫بیومكانیك كاربردي ورزش كماسي‬‫دانش حركات انسان در ورزش فرزام معلمیان‬‫‪-Mechanical analysis of human motion‬‬
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