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جوادیان دکتر آقای جوادیان جناب دکتر آقای جناب

What is frictionWhat is friction??

FrictionHard to Live With It, Can’t Live Without It

Mu

Coefficient of Friction

Fn

What’s Stopping You?

FrictionFriction

Friction causes Friction causes objects to slow objects to slow

downdown..Friction creates Friction creates

heatheat..Friction Friction

degrades an degrades an objectobject’’s energys energy

FrictionFriction

Opposes relative Opposes relative motion of two surfacesmotion of two surfaces

Consists of a matched Consists of a matched pair of forcespair of forces::

ObjObj11 pushes Obj pushes Obj22 while while ObjObj22 pushes Obj pushes Obj11

Equal magnitudes, Equal magnitudes, opposite directionsopposite directions

Comes in two typesComes in two types:: static and kineticstatic and kinetic

Places where friction is goodPlaces where friction is good

The soles of shoesThe soles of shoesCar tiresCar tiresThe feet of table legsThe feet of table legsRock climbing holdsRock climbing holdsBrakesBrakesetcetc

Places where friction is badPlaces where friction is bad

In enginesIn engines In transmissionsIn transmissions

On the bottoms of skis On the bottoms of skis and snowboards (To a and snowboards (To a point)point)

When you are trying When you are trying to move a box by to move a box by pushing it along the pushing it along the floorfloor

etcetc

What causes frictionWhat causes friction??

Source of FrictionSource of Friction

Picture of extremely Picture of extremely smooth mica with a smooth mica with a

scanned probe microscopescanned probe microscope

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

Consider 2 Types of Friction

sF

Force of Kinetic Friction

This value represents the relative force necessary to keep an object moving at a constant rate

kF

Force of Static FrictionThis value represents the relative force necessary to make an object move

Types of FrictionTypes of FrictionStatic FrictionStatic Friction

Acts to prevent objects Acts to prevent objects from starting to slidefrom starting to slide

Forces can vary from Forces can vary from zero to an upper limitzero to an upper limit

Kinetic frictionKinetic friction--Sliding FrictionSliding Friction

Acts to stop objects Acts to stop objects that are already slidingthat are already sliding

--Rolling frictionRolling friction

Friction is a Force That Resists Motion

W

fsF

N

Surfaces in Contact

The Pink Block M1 Will not Move Until the Force F (Pull on the scale ) Exceeds the

Force of Static Friction fs.

M1

Spring Scale

Static FrictionStatic Friction

Increases Increases linearlylinearly

For a given pair For a given pair of surfaces, the of surfaces, the ratio of ratio of Frictional force Frictional force to Applied force to Applied force is a constantis a constant..

Applied Force, N

Fri

cti

on

al

Forc

e

Fri

ctio

nal

For

ce

Res

isti

ng

Mot

ion

Force Causing the Object to Move

Kinetic RegionStatic Region

sF

kFMax

kFF s

kFF s

WhyWhy??

--The slightly larger value for static The slightly larger value for static friction results from irregularities and friction results from irregularities and contaminants on the surfaces and is contaminants on the surfaces and is less accurate in general than the less accurate in general than the coefficient of kinetic frictioncoefficient of kinetic friction

--inertiainertia

W

fsF

N

Surfaces in Contact

M1

Spring Scale

sFW

= Force Required to Cause Motion= Weight of Object

= Coefficient of Friction

W

Fs Coefficient of Static

Friction

Example of Static FrictionExample of Static FrictionWhat is the coefficient of What is the coefficient of

static friction between a static friction between a tabletop and a 2 kg block tabletop and a 2 kg block

of wood if a 2 N force is of wood if a 2 N force is required to start the block required to start the block

movingmoving??

Identify knowns and Identify knowns and unknownunknown::

m = 2 kg, applied force = 2 m = 2 kg, applied force = 2 N, v = 0N, v = 0,,

μμss? = ? =

Appropriate equation: f = Appropriate equation: f = μμ N N..

What is NWhat is N ? ?

On a level surface the normal On a level surface the normal force upward is equal to the force upward is equal to the

weight of the object weight of the object downward, i.e. N = W = mg. downward, i.e. N = W = mg.

SoSo,,

f = f = μμ mg or mg or μμ = f/mg = 2 N/(2 = f/mg = 2 N/(2 kg *9.8m/skg *9.8m/s22))

μμ = 0.102 = 0.102

Static & Kinetic Friction Static & Kinetic Friction CoefficientsCoefficients

MaterialMaterialCoefficient of Coefficient of Static Friction Static Friction

SS

Coefficient of Coefficient of Kinetic Friction Kinetic Friction

SS

Rubber on GlassRubber on Glass2.02.0++2.02.0

Rubber on Rubber on ConcreteConcrete

1.01.00.80.8

Steel on SteelSteel on Steel0.740.740.570.57

Wood on WoodWood on Wood0.250.25 –– 0.50.50.20.2

Metal on MetalMetal on Metal0.150.150.060.06

Ice on IceIce on Ice0.10.10.030.03

SynovialSynovial Joints in Joints in HumansHumans

0.010.010.0030.003

Application AnalysisApplication AnalysisSand is often placed on Sand is often placed on

an icy road because the an icy road because the sandsand::

.1.1Decreases the Decreases the coefficient of friction coefficient of friction

between the tires of a between the tires of a car and the roadcar and the road

.2.2Increases the Increases the coefficient of friction coefficient of friction

between the tires of a between the tires of a car and the roadcar and the road

.3.3Decrease the Decrease the gravitational force on a gravitational force on a

carcar

.4.4Increases the normal Increases the normal force of a car on the force of a car on the

roadroad

Using the Gears-IDS Battery to Calculate The Static

W

Fs

Coefficient of Friction

s

Record the Maximum Force (F) (Before the Battery Begins to Move)

W

Fs

Maximum Force F = 110 g

Record the Weight (W ) of the Battery

W

Fs

580 g

The Coefficient of Static Friction Between the Wood Desktop and the Plastic Battery

is Described Algebraically:

W

Fs

= 580 g

= 110 g

s = .190

W

Fk

The Coefficient of Kinetic Friction Can be Found Using the Same Technique

Record the Force Required to Move the Battery at a Constant Rate

The frictional force depends only onThe frictional force depends only on11--the type of surfacesthe type of surfaces

22--how hard the surfaces are pressed how hard the surfaces are pressed togethertogether

The

fricti

onal

force

depends

only

on:-the

type

of

surfaces

how

hard

the

surfaces

are

pressed

together

What is the normal forceWhat is the normal force??

Block at Rest on a TableBlock at Rest on a Table

Normal ForceNormal Force

From NewtonFrom Newton’’s third law we know that if gravity or s third law we know that if gravity or some other force pushes an object (like a block) into a some other force pushes an object (like a block) into a second object (like a table) that second object will be second object (like a table) that second object will be

exerting an equal force back on the firstexerting an equal force back on the first.. Normal force is the force the table exerts back on the Normal force is the force the table exerts back on the

blockblockNormal force is always exerted perpendicular to the Normal force is always exerted perpendicular to the

surfacesurfaceFriction Force is always parallel to the surfaceFriction Force is always parallel to the surface

So if the table is horizontal and gravity is the only force So if the table is horizontal and gravity is the only force on the block Fon the block Fnn = -F = -Fgg

Normal force on a hillNormal force on a hill

Normal force is exerted Normal force is exerted perpendicular to the perpendicular to the surface in accordance with surface in accordance with NewtonNewton’’s Third laws Third law

No unbalanced force so the No unbalanced force so the block is stationary or at block is stationary or at least not acceleratingleast not accelerating

. .

QuestionsQuestions??

SolutionSolution

)20tan(

)20cos(

)20sin(

)20sin()20cos(

)20sin()20cos(

)20sin(

)20cos(

)20cos(

)(

)(

k

k

k

ksurfaceparalleltogf

surfaceparalleltog

nkf

n

gn

gmgmFF

gmF

FF

gmF

FF

Frictional force and normal Frictional force and normal forceforce..

Frictional force is Frictional force is proportional to the proportional to the normal force, f normal force, f αα N. N. On a level surface On a level surface N = W, but what if N = W, but what if someone is lifting someone is lifting up on the objectup on the object??

WonWon’’t that reduce t that reduce the normal forcethe normal force??

Free Body DiagramFree Body Diagram

N + T = W, soN + T = W, so

N = W N = W –– T T..

If T pulls at If T pulls at some angle, some angle,

then just then just decompose decompose

into into componentscomponents..

Lift from person,T

Normal,N

Weight, W

ExampleExample::

A person pulls on a 300 N crate with A person pulls on a 300 N crate with a rope that makes a 30a rope that makes a 3000 angle to angle to the ground. If the coefficient of the ground. If the coefficient of static friction is 0.6, how much static friction is 0.6, how much

tension must the person exert to tension must the person exert to get the crate movingget the crate moving??

Knowns: W = 300 N, Knowns: W = 300 N, θθ = 30 = 30oo, , μμ = 0.6 = 0.6..

Unknown: TUnknown: T? = ? =

Equations: f = Equations: f = μμN. All forces N. All forces balance when at restbalance when at rest..

Horizontal Tension = T cos Horizontal Tension = T cos θθ

Vertical Tension = T sin Vertical Tension = T sin θθ

Net vertical force = N + Tsin Net vertical force = N + Tsin θθ –– W = 0, so W = 0, so

N = W - Tsin N = W - Tsin θθ..

Net horizontal force = Tcos Net horizontal force = Tcos θθ –– f = 0 f = 0

Tcos Tcos θθ = f = = f = μμN = N = μμ(W - Tsin (W - Tsin θθ) , so) , so

Tcos Tcos θθ = = μμ(W - Tsin (W - Tsin θθ))

Tcos Tcos θθ + + μμ Tsin Tsin θθ = = μμWW

T(cos T(cos θθ + + μμ sin sin θθ) = ) = μμWW

T = T = μμW/(cos W/(cos θθ + + μμ sin sin θθ))

T = T = 0.6*300N/(cos300.6*300N/(cos3000

+ .6*sin30+ .6*sin3000))

T = 180N/(0.866+.3)T = 180N/(0.866+.3)

T = 180 N/(1.166)T = 180 N/(1.166)

T = 154 NT = 154 N

Experiment: Does the friction Experiment: Does the friction force depend on surface areaforce depend on surface area??

We stick a 1kg mass on a piece of on We stick a 1kg mass on a piece of on top of the clean surface and, using a top of the clean surface and, using a Newton meter, pull the weight across Newton meter, pull the weight across the table with the string provided at the table with the string provided at constant speedconstant speed..

We put the same weight on a different We put the same weight on a different piece of plexiglass with drastically piece of plexiglass with drastically different surface area and repeatdifferent surface area and repeat

What do you noticeWhat do you notice??

What is rolling friction?

Rolling friction:Rolling friction:

-nature-nature

-normal force-normal force

-diameter-diameter

Rotational Rotational frictionfriction

منابعمنابع

-زاده نمازي دكتر ورزشي فنون زاده- بيومكانيك نمازي دكتر ورزشي فنون بيومكانيك -كماسي ورزش كاربردي كماسي- بيومكانيك ورزش كاربردي بيومكانيك -فرزام ورزش در انسان حركات فرزام- دانش ورزش در انسان حركات دانش

معلميانمعلميان -Mechanical analysis of human -Mechanical analysis of human

motionmotion