Force and Friction

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The Meaning of Force

A force is a push or pull upon an object resulting from the object's interaction withanother object. Whenever there is an interactionbetween two objects, there is a forceupon each of the objects. When the interaction ceases, the two objects no longer

experience the force. Forces only exist as a result of an interaction.

Force is a quantity which is measured using the standard metric unit nown as theNewton.

For simplicity sae, all forces !interactions" between objects can be placed into twobroad categories#

contact forces, and

forces resulting from action$at$a$distance

Contact forcesare those types of forces which result when the two interacting objectsare perceived to be physically contacting each other. %xamples of contact forces includefrictional forces, tensional forces, normal forces, air resistance forces, and appliedforces.

Action-at-a-distance forcesare those types of forces which result even when the twointeracting objects are not in physical contact with each other, yet are able to exert apush or pull despite their physical separation. %xamples of action$at$a$distance forcesinclude gravitational forces. For example, the sun and planets exert a gravitational pullon each other despite their large spatial separation. %ven when your feet leave the earth

and you are no longer in physical contact with the earth, there is a gravitational pullbetween you and the %arth. %lectric forces are action$at$a$distance forces. For example,the protons in the nucleus of an atom and the electrons outside the nucleus experiencean electrical pull towards each other despite their small spatial separation. And magneticforces are action$at$a$distance forces. %xamples of contact and action$at$distance forcesare listed in the table below.

Contact ForcesAction-at-a-Distance Forces

Frictional Force &ravitational Force

ension Force %lectrical Force

(ormal Force )agnetic Force

Air *esistance Force

Applied Force

+pring Force

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Type of Force

(and Symbol)Description of Force

Applied Force

Fapp

An applied force is a force which is applied to an object by aperson or another object. f a person is pushing a des acrossthe room, then there is an applied force acting upon the object.he applied force is the force exerted on the des by the person.

Gravity Force

(also known as Weight)

Fgrav

he force of gravity is the force with which the earth, moon, orother massively large object attracts another object towardsitself. -y definition, this is the weight of the object. All objectsupon earth experience a force of gravity which is directeddownward towards the center of the earth. he force of gravityon earth is always equal to the weight of the object as found bythe equation#

Fgrav ! " g

where g #$% !&s' (on arth)

and m / mass !in g"

or!al Force

Fnor!

he normal force is the support force exerted upon an objectwhich is in contact with another stable object. For example, if aboo is resting upon a surface, then the surface is exerting anupward force upon the boo in order to support the weight of theboo. 0n occasions, a normal force is exerted hori1ontallybetween two objects which are in contact with each other. For

instance, if a person leans against a wall, the wall pusheshori1ontally on the person.

Friction Force

Ffrict

he friction force is the force exerted by a surface as an objectmoves across it or maes an effort to move across it. here areat least two types of friction force $ sliding and static friction.hought it is not always the cast, the friction force often opposesthe motion of an object. For example, if a boo slides across thesurface of a des, then the des exerts a friction force in theopposite direction of its motion.

Friction results from the two surfaces being pressed togetherclosely, causing intermolecular attractive forces between

molecules of different surfaces. As such, friction depends uponthe nature of the two surfaces and upon the degree to which theyare pressed together.

he maximum amount of friction force which a surface can exertupon an object can be calculated using the formula below#

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Air *esistance Force

Fair

he air resistance is a special type of frictional force which actsupon objects as they travel through the air. he force of airresistance is often observed to oppose the motion of an object.his force will frequently be neglected due to its negligiblemagnitude !and due to the fact that it is mathematically difficult topredict its value". t is most noticeable for objects which travel athigh speeds !e.g., a sydiver or a downhill sier" or for objectswith large surface areas.

Tension force

he tension force is the force which is transmitted through astring, rope, cable or wire when it is pulled tight by forces actingfrom opposite ends. he tension force is directed along the

length of the wire and pulls equally on the objects on theopposite ends of the wire.

+pring Force

Fspring

he spring force is the force exerted by a compressed orstretched spring upon any object which is attached to it. Anobject which compresses or stretches a spring is always actedupon by a force which restores the object to its rest or equilibriumposition. For most springs !specifically, for those which are saidto obey 2ooe's 3aw", the magnitude of the force is directlyproportional to the amount of stretch or compression of thespring.

ewton,s Three aws of Motion

(ewton's three 3aws of )otion are the foundation of the theory of motion$$e.g., of orbitsand rocets.I. Newton's First Law of Motion: %very object in a state of uniform motion tends toremain in that state of motion unless an external force is applied to it.

his we recogni1e as essentially &alileo'sconcept of inertia, and this is often termedsimply the 3aw of nertia.

II. Newton's Second Law of Motion: (ewton's second law of motion explains how an

object will change velocity if it is pushed or pulled upon.

Firstlythis law states that if you do place a force on an object, it will accelerate, i.e.,

change its velocity, and it will change its velocity in the direction of the force.

It accelerates in t!e direction""""..t!at yo# $#s! it.

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Secondlythis acceleration is directly $ro$ortionalto the force. For example, if you are

pushing on an object, causing it to accelerate, and then you push, say, three times

harder, the acceleration will be three times greater.

If yo# $#s! twice as !ard""""..

It accelerates twice as m#c!.

%!irdly this acceleration is in&ersely $ro$ortional to the mass of the object. For

example, if you are pushing equally on two objects, and one of the objects has five times

more mass than the other, it will accelerate at one fifth the acceleration of the other.

It it ets twice t!e mass"""""..

It accelerates !alf as m#c!.

III. Newton's %!ird Law of Motion: he third law states that for every force t!ere is ane#al and o$$osite force. For example, if you push on a wall, it will push bac on youas hard as you are pushing on it.

If yo# $#s! on it"""""""It $#s!es on yo#.

F*.CT./

Friction is a force that is created whenever two surfaces move or try to move acrosseach other.

Friction always opposes the motion or attempted motion of one surface across

another surface. Friction is dependant on the texture of both surfaces.

Friction is also dependant on the amount of contact force pushing the twosurfaces together !normal force".

0ses1 Advantages and Disadvantages of Friction

here are advantages and disadvantages of friction. +ince friction is a resistance forcethat slows down or prevents motion, it is necessary in many applications to preventslipping or sliding. -ut also, it can be a nuisance because it can hinder motion and causethe need for expending energy. A good compromise is necessary to get just enoughfriction.

4uestions you may have include#

2ow is friction necessary5

2ow is friction a nuisance5

What is a good compromise for using friction5

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.!portant 2ses

n some situations, friction is very important and beneficial. here are many things thatyou could not do without the force of friction.

Walking

6ou could not wal without the friction between your shoes and the ground. As you try tostep forward, you push your foot bacward. Friction holds your shoe to the ground,allowing you to wal. 7onsider how difficult it is to wal on slippery ice, where there islittle friction.

-ear did not heed warning sign

Writing

Writing with a pencil requires friction. 6ou could not hold a pencil in your hand withoutfriction. t would slip out when you tried to hold it to write. he graphite pencil led wouldnot mae a mar on the paper without friction.

A pencil eraser uses friction to rub off mistaes written in pencil lead. *ubbing the eraseron the lead wears out the eraser due to friction, while the particles worn off gather up thepencil lead from the paper.

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Driving car

6our car would not start moving if it wasn't for the friction of the tires against the street.With no friction, the tires would just spin. 3iewise, you could not stop without the frictionof the braes and the tires.

-rae pads in your car help produce friction to slow you down.

his is a closeup of thebrae of a boxcar. hebrae causes frictionagainst the tire, causingit to slow down or stop.

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3ro4le!s fro! friction

Friction can cause problems or be a nuisance that you try to minimi1e.

Makes !ove!ent diffic2lt

Any time you want to move an object, friction can mae the job more difficult. %xcessfriction can mae it difficult to slide a box across the floor, ride a bicycle or wal throughdeep snow.

An automobile would not move forward very well unless its friction was not reduced. 0ilis needed to lubricate the engine and allow its parts to move easily. 0il and ball bearingsare also used in the wheels, so they will turn with little friction

Wastes energy

n any type of vehicle$$such as a car, boat or airplane$$excess friction means that extrafuel must be used to power the vehicle. n other words, fuel or energy is being wastedbecause of the friction.

Fluid friction or air resistance can greatly reduce the gas mileage in an automobile. 7arsare streamlined to reduce friction. -ut driving at highway speeds with your windowsopen can create enough drag on the car to greatly reduce your gas mileage.

5eats parts

he 3aw of 7onservation of %nergy states that the amount of energy remains constant.

hus, the energy that is lost to friction in trying to move an object is really turned toheat energy. he friction of parts rubbing together creates heat.

6ou've seen how people will try to start a fire by vigorously rubbing two stics together.0r perhaps you've seen an automobile spin its wheels so much that the tires start tosmoe. hese are examples of friction creating heat energy. 8ust rub your handstogether to create the same effect.

-esides the problem of losing energy to heat, there is also the threat of a partoverheating due to friction. his can cause damage to a machine.

Wears things o2t

Any device that has moving parts can wear out rapidly due to friction. 3ubrication is usednot only to allow parts to move easier but also to prevent them from wearing out. +omeother examples of materials wearing out due to friction include the soles of your shoesand a pencil eraser.

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Friction can cause problems. When objects rub against each other, thesurfaces are worn away. Friction with the ground causes the heels andsoles of your shoes to wear away.

Co!pro!ise

A compromise is needed between too much friction and not enough.

Fro example, if you wanted to slide a heavy box across the floor, you would want to

reduce the friction between the box and the floor, so that it would be easy to move.3ubrication of some sort is often a way to reduce friction.

62t yo2 wo2ld also want to increase the friction of yo2r shoes on the floor1 so that

yo2 wo2ld 4e a4le to get good traction and 4e a4le to p2sh effectively$ +oles

!ade of r244er !aterial that incl2de treads can red2ce slipping when

walking or r2nning$

Ca2ses of Friction

he causes of the resistive force of friction are molecular adhesion, surface roughness,

and the plowing effect.

Adhesion is the molecular force resulting when two materials are brought into closecontact with each other. rying to slide objects against each other requires breaingthese adhesive bonds. For years, scientists thought that friction was caused by surfaceroughness, but recent studies have shown that it is actually a result of adhesive forcesbetween the materials.

Adhesion

When two objects are brought into contact, many atoms or molecules from one objectare in such close proximity to those in the other object that molecular or electromagnetic

forces attract the molecules of the two materials together. his force is called adhesion.rying to slide one object across the other requires breaing these adhesive bonds.

Adhesion is the essence of friction.

6ou've seen a water drop adhere to a window pane. he force of friction prevents thisliquid from sliding down the solid material. -ut most cases of friction you see concern asolid object sliding or moving against another solid.

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+liding objects against each other requires breaing these millions of contact pointswhere the adhesion force taes effect, only to result in millions of new contact points ofadhesion.

+2rface ro2ghness

All solid materials have some degree of surface roughness. f you looed at what seemsto be a smooth surface under a high$powered microscope, you would see bumps, hillsand valleys that could interfere with sliding motion.

7lose$up view of surface roughness

At one time it was thought that the surface roughness of materials was the cause forfriction. n reality, it only has a small effect on friction for most materials.

f the surfaces of two hard solids are extremely rough, the high points or asperities caninterfere with sliding and cause friction because of the abrasion or wear that can taeplace when you slide one object against the other. his is the sandpaper effect whereparticles of the materials are dislodged from their surfaces. n such a case, the friction iscaused by surface roughness, although the adhesion effect still plays a part in theabrasion.

Defor!ations

+oft materials will deform when under pressure. his also increased the resistance tomotion. For example, when you stand on a rug, you sin in slightly, which causesresistance when you try to drag your feet along the rug's surface. Another example ishow rubber tires flatten out at the area on contact with the road.

When materials deform, you must plow through to move, thus creating a resistive

force.

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9ushing object on soft surface

When the deformation becomes large, such that one object sins into the other,streamlining can affect the friction, similar to what happens in fluid friction.

Types of friction

he classic law of friction states that friction is the product of a coefficient and a force.

here are two main types of friction# +tatic and :inetic

+tatic and 7inetic Friction

Friction is a ey concept when you are attempting to understand car accidents. heforce of friction is a force that resists motion when two objects are in contact. f you looat the surfaces of all objects, there are tiny bumps and ridges. hose microscopic peasand valleys catch on one another when two objects are moving past each other.

his explanation is a little simplified. here are other processes at wor, includingchemical bonding and electrical interactions.

he level of friction that different materials exhibit is measured by the coefficient offriction. he formula is ; / f < (, where ; is the coefficient of friction, f is the amount offorce that resists motion, and ( is the normal force. (ormal force is the force at whichone surface is being pushed into another. f a roc that weighs => newtons is lying on theground, then the normal force is that => newtons of force. he higher ; is, the more forceresists motion if two objects are sliding past each other.

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+tatic friction

+tatic friction is friction between two solid objects that are not moving relative to eachother. For example, static friction can prevent an object from sliding down a slopedsurface. he coefficient of static friction, typically denoted as s, is usually higher thanthe coefficient of inetic friction.

he static friction force must be overcome by an applied force before an object canmove. he maximum possible friction force between two surfaces before sliding beginsis the product of the coefficient of static friction and the normal force# . When there is nosliding occurring, the friction force can have any value from 1ero up to . Any forcesmaller than attempting to slide one surface over the other is opposed by a frictionalforce of equal magnitude and opposite direction. Any force larger than overcomes theforce of static friction and causes sliding to occur. he instant sliding occurs, static

friction is no longer applicable and inetic friction becomes applicable.

An e+am$le of static friction is t!e force t!at $re&ents a car w!eel from sli$$in asit rolls on t!e ro#nd. ,&en t!o#! t!e w!eel is in motion t!e $atc! of t!e tire incontact wit! t!e ro#nd is stationary relati&e to t!e ro#nd so it is static rat!ert!an inetic friction.

he maximum value of static friction, when motion is impending, is sometimes referredto as limiting friction, although this term is not used universally.

7inetic friction

:inetic !or dynamic" friction occurs when two objects are moving relative to each otherand rub together !lie a sled on the ground". he coefficient of inetic friction is typicallydenoted as , and is usually less than the coefficient of static friction for the samematerials.

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8a!ples of kinetic friction#

:inetic friction is when two objects are rubbing against each other. 9utting a boo flat ona des and moving it around is an example of inetic friction. he graphicalrepresentation of static and inetic friction is shown below.

+ome common values of coefficients of inetic and static friction#

S#rfaces (static) (inetic)

+teel on steel >.?@ >.=?

&lass on glass >.@ >.@>

)etal on )etal!lubricated"

>.B= >.>C

ce on ice >.B> >.>D

eflon on eflon >.>@ >.>@

ire on concrete B.>> >.E>

ire on wet road >.C> >.@>

ire on snow >.D> >.>

*ed2cing Friction9

A common way to reduce friction is by using a lubricant, such as oil, that is placed

between the two surfaces, often dramatically lessening the coefficient of friction. he

science of friction and lubrication is called tribology. +uper lubricity, a recently$

discovered effect, has been observed in graphite# it is the substantial decrease of friction

between two sliding objects, approaching 1ero levels $ a very small amount of frictional

energy would be dissipated due to electronic and


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Co!ponent of the force acting on the o4:ect (+trings1 p2lleys1 and inclines)9

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Figure:Block suspended by a string

Figure:Block suspended by three string

Figure:Block sliding over a smooth table,

pulled by a second block

Figure:An Atwood machine

Figure:Block sliding down an inclineFigure:Block dragged over a horizontal surface


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/roblems

B. A bloc of mass m / B= g held by a cord on a frictionless inclined plane. What is the

tension in the cord if / ?o5 What force does the plane exert on the bloc5

. A bloc rests on an inclined plane surface. he angle of inclination is increased until it

reaches a critical angle of @=>, after which the bloc begins to slide. Find the coefficient of

static friction

D. wo blocs connected by a cord that passes over a mass less, frictionless pulley. 3et m /

B.D g and ) / .E g. Find the tension in the cord and the magnitude of the acceleration

of the two blocs.

@. A sphere of mass D.>xB>$@ g is suspended from a cord. A steady hori1ontal bree1e

pushes the sphere so that the cord maes a constant angle of D? owith the vertical. Find

!i" the magnitude of the push and !ii" the tension in the cord.

=. A bartender slides a beer stein of mass >.@= g hori1ontally along the bar with an initial

speed of D.= m=. 2ow far does the sled go before stopping5

?. An elevator and its load have a combined mass of BC>> g. Find the tension in the

supporting cable when the elevator, originally moving downward at B m> m>

g5

. An electron with a speed of B. H B>?m$BC( acts on it. he mass of the electron is .BBH B>$DB g.

Ietermine the vertical distance the electron is deflected the time it has moved D> mm

hori1ontally.

B>. A woman pulls a loaded sled of mass m / ?= g along a hori1ontal surface at constant

velocity. he coefficient of inetic friction k between the runners and the snow is >.B>,

and the angle is @o. !i" What is the tension in the rope5 !ii" What is the normal force

with which the snow pushes vertically upward on the sled5

BB. A CE g crate is dragged across a floor by pulling on a rope attached to the crate and

inclined @J above the hori1ontal. !i" f the coefficient of static friction is >.@?, whatminimum force magnitude is required from the rope to start the crate moving5 !ii" f the

coefficient of inetic friction / >., what is the magnitude of the initial acceleration of the

crate5

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Force and Friction