extended essay ver 7

IB Physics Extended Essay:Does The Static Frictional Force Acting Between Two Surfaces Have Correlation With Surface Area In Contact

Candidate Name - Ashish TayalCandidate No – 002272-091

Session May 2010Word Count: 3,220

[1 March 2010]

IB Physics Extended Essay Ashish Tayal - 002272-091

Abstract

Friction forces are the forces that hinder movement of the objects that are in contact with each

other. Mathematical approximation allows us to calculate the variation of friction acting on a

body with its mass. Theoretically, formula suggests friction to be independent of the surface

area, but my intuition tells me of a possible positive correlation between surface area and static

friction therefore this research.

The scope of this research is to compare the change in frictional force between two surfaces and

its surface area that are in contact; compare the results with those predicted hypothetically; and

compare change in the fractional force with surface area for different materials which includes

materials with both high frictional coefficients (rubber) and low frictional coefficients (glass). To

investigate, an apparatus comprising of an inclined plane and a pulley was created. Objects of

different masses and surface area were created from wooden blocks. The magnitude of friction

was determined by finding out the minimum additional mass need to move the object on the

inclined plane. Trials were repeated also on glass and rubber surfaces.

Contrary to the theory, positive correlation between surface area and fiction was observed in case

of objects high frictional coefficient (wood on wood, rubber on wood). However friction is found

to be independent of surface are in case of surface with low frictional coefficients (wood on

glass). The major limitations to this research are the normal wear and tear of the object during

repeated trials and the impact of chemical including oil / wetness left on the object / surface by

use of taps, bare hands etc. which may impact the accuracy of results. Elementary nature of the

apparatus use might also have resulted in inaccurate reading impacting results.

Word count – 289

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Acknowledgement

I would like thank the faculty members of Indus International School, who encouraged and supported through my research.

My grateful thanks go to Mr. Jay Kumar Pillai, my physics teacher, who provided his support all through my research.

I am thankful to Mr. Sukumar, Physics Lab Assistant, who patiently worked with me and whose cooperation was critical to completion of this research.

Special thanks also to Ms. Meenakshi Myer and Ms. Kavita Sinha, faculty members of Indus International School, for their encouragement & support that helped me complete my extended essay successfully.

Last but not least I would like to thank my father, Sushil Tayal, for his help in building the apparatus for this research and the encouragement he provided throughout my project.

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Table of Contents

Table of Contents.............................................................................................................................4

Introduction......................................................................................................................................5

Background Information..................................................................................................................7

Scope................................................................................................................................................9

Hypothesis:....................................................................................................................................10

Procedure.......................................................................................................................................11

Observations and Results...............................................................................................................16

Analysis of Results........................................................................................................................23

Limitations.....................................................................................................................................25

Bibliography..................................................................................................................................27

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Introduction

Aristotle had noticed that when an object is pushed on the floor with a constant force, the object

moves with a constant velocity. In modern sense, this would be hard to comprehend as in terms

of Newtonian mechanics a constant force acting on a body must cause it to accelerate. The

answer to this is that Aristotle had taken into consideration that frictional force is always acting

naturally on a body1 whereas in Newtonian mechanics, the effect of frictional forces acting on

the body must be calculated separately from the kinematical equation. Frictional forces can be

defined as the forces that oppose the movement of two bodies in contact with each other.

Frictional forces are vital to us in everyday life and have its innumerable benefits. The very

reason that we can walk is because of the friction between the soles of our feet and the ground

that we stand on. Also if there was no friction then tyres of automobiles would keep slipping in

their places and the vehicles would not move forward. However in many situations frictional

forces act as a hindrance causing a lot of waste of useful energy such as the moving parts of a

combustion engine. It is estimated that each year in the USA alone 6% of the GDP is spent only

on overcoming the hindrance that is caused by friction!2

Frictional forces are classified into two types, static and kinetic. Static frictional force is the one

which prevents a wooden body at rest from moving. The minimum amount of force that needs to

be exerted on a body just to get it moving is the amount force required to overcome the static

frictional force between the object and the surface on which it is at rest. Kinetic frictional force

acts on a body while it is moving; kinetic frictional force converts the kinetic energy of a moving

object into heat energy; a very simple example of this would be rubbing our palms together.

The most common generalizations of friction helps us come up with a correlation between an

objects mass and the frictional force acting on it; yet this does not account for the impact of the

size of the object. From common sense one can deduce that the main cause of friction is the

1 http://www.virginia.edu/ep/SurfaceScience/friction.html

2 http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-800Fall-2004/EDEB0AEE-FEB5-48DD-B3AD-83F2422FAF07/0/ch1_trib_intro.pdf

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http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-800Fall-2004/EDEB0AEE-FEB5-48DD-B3AD-83F2422FAF07/0/ch1_trib_intro.pdf

http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-800Fall-2004/EDEB0AEE-FEB5-48DD-B3AD-83F2422FAF07/0/ch1_trib_intro.pdf

http://www.virginia.edu/ep/SurfaceScience/friction.html


roughness of the surfaces and hence based on this reasoning intuition tells us that the frictional

force acting on the object should increase and if so does there exist any direct mathematical

relation between the two? This has lead to choosing the research topic as “Does the static

frictional force acting between two surfaces have correlation with surface in contact?”

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Background Information

When an object is at rest, a force needs to be exerted on the object so that it begins to move; this

force is required to overcome the static frictional force acting between the object and the surface

on which it is resting. Theoretically, the magnitude of the maximum frictional force that acts on

an object can vary anywhere between 0 and μs N where N is equal to its normal reaction force

and µs is the coefficient of static friction between the two surfaces. In case of an object resting on

a flat surface the objects weight is equal to its normal reaction force. This is an empirical

quantity (constant) which can be determined only by experimentation of different surfaces and

cannot be derived mathematically. When the applied force exceeds static frictional force, the

object begins to move. Friction continues to oppose the movement and this is known as the

kinetic frictional force. Kinetic friction can be approximated by the formula F=μk N where µk is

the coefficient of kinetic friction, usuallyμs>μk. This implies that a greater amount of force needs

to be exerted on an object that is at rest to get moving than what is required to keep an object in

motion to continue moving.

3

(A graphical representation of how the frictional force acting on an object changes with the force being applied)

3 http://academicearth.org/lectures/friction

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http://academicearth.org/lectures/friction


On any two regular surfaces that are in contact with each other, there exist irregularities and

fibres that protrude from the surfaces. Due to the force exerted by the weight one object on the

other these irregularities get locked into each other. This is the root cause of static friction

between two objects. In order to get the objects to move past each other, we need to exert a force

to push the objects out of place and overcome the mechanical interlocking. Mechanical

interlocking is high between objects whose surfaces are rough in nature, however there does

exist a small magnitude of frictional force between the two very smooth surfaces as well. The

cause of this can be understood by going at a microscopic level. When two objects come into

contact with each other, their molecules are pushed into contact with each other and the

electrostatic forces of attraction start acting between the molecules of these surfaces. The

oppositely charged particles present in both the molecules establish forces of attraction. The

positively charged protons present in the nucleus of one molecule get attracted to the negatively

charged electrons present in the outer shells of the atoms of the other molecules.

The forces of attraction that occur between two surfaces of objects made from the same material

are known as cohesive forces of attraction and for different materials are known as adhesive

forces of attraction. When dealing with static forces of friction between two similar objects it

would be the cohesive forces that are the contributors to static friction and similarly between two

objects of different materials it must be the adhesive forces. The coefficient of friction between

any two surfaces would largely depend on the magnitude of these cohesive or adhesive forces.

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Scope

The scope of this research includes:

1) to compare the change in frictional force between two surfaces and its surface area that

are in contact

2) analyse the difference between results obtained and those predicted hypothetically; and

3) compare change in the fractional force with surface area for different materials which

includes materials with both high and low frictional coefficients.

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Hypothesis:

As the surface area of an object increases, the frictional force acting between them would

increase because of increased number of molecules that are brought into contact with each other

hence increasing the magnitude of the adhesive forces between them.

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Procedure

To study the correlation between the static frictional force that acts on an object and its surface

area, objects made of wooden blocks were used. The wooden blocks were used to create objects

of different surface areas with constant mass. Trials were performed for one particular surface

area and then the blocks were re arranged to form a second surface area and then repeated the

trials. Once the results for a particular material have been obtained the procedure was repeated to

gather data for different materials such as wood on rubber, wood on glass etc in order to see if

the correlation stand true / differs in a scenarios of very high and very low coefficients of friction

respectively.

Independent Variable: Surface area of the object

Dependant Variable: The magnitude of the static frictional force measured by measuring the

mass of the weights that are added to the pan

Controlled Variable: Mass of the object, since the objects of each observation are made

from the same number of blocks but arranged differently for different

surface areas, the total mass still remains the same.

The material of the blocks of the objects is same for all trials of surface

area. The blocks were all cut from the same original source in order to

control the roughness and unevenness of the surfaces.

To determine the frictional force a method consisting of a pulley and weights was devised.

(Refer the diagram below). A wooden inclined plane was used with a pulley fixed at its upper

edge. The benefit of using an inclined plane is that the magnitude of the force that needs to be

measured increases. The tension in the string is the sum of the static frictional force and mg sin θ

where θ is the angle of inclination. Our objective is to see if there is a change in the mass needed

to get the object to move with an increase in surface area. Since the mass of the object would

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remain the same mg sin θwould also remain the same for all the different trials for a particular

object. Increase in the frictional force with surface area shall require increased mass to be added

to the pan.

4

An object consisting of 3 wooden blocks are taped together, with surface area of its base

measured, was placed on top of the incline plane. A string was then tied to the object, passed

over a pulley and the incline plane (30°) was kept at the edge of a table so that the string would

hang freely from the pulley. A pan was tied to the other end of the string to add masses. The

inclined plane was inclined for a moderate amount of inclination throughout the experiment and

the angle of inclination was kept constant at angle throughout the observation for a particular

objects.

4 http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

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http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html


The frictional force can be determined by adding weights to the pan that is tied to the string. The

tension in the string pulling the object will be caused by the force of gravity acting on the pan

and opposes the static frictional force. At the point where tension in the string exceeds the static

frictional force, the object should start to move. Weights were added gradually with a small

difference between the successive additions in order to increase the accuracy. After each weight

was added a slight tapping was provided to the surface. (The tapping helps overcome the cold

welds that are formed between the object and the surface on which it is resting. Cold welds are

temporary intermolecular forces of attraction that are set up between the two surfaces because

of which the force that needs to be applied to move the object form rest would be more than the

actual static friction force.5 The tapping provided was kept consistent). When the object just

moved slightly it was considered to have overcome the frictional force and the mass added to the

pan was noted. 3 to 5 such trials were performed.

After this, the blocks of the object were repositioned and taped in order to get a larger surface

area. (See the picture below). The total number of blocks however remained the same hence

keeping the mass constant. The trials were repeated for the new surface area. After the collection

of data for the second area, the blocks were again repositioned in order to have a larger surface

area with all three blocks in contact, and the trials were repeated.

5 http://www2.swgc.mun.ca/physics/images/inclined_plane2M.jpg

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Results from the experiments recorded in the format given below:-

Area(cm2) Trial 1(g) Trial 2(g) Trial 3(g) Average

Once the experiment was performed for one particular object, the procedure was then repeated

for new objects having different initial surface areas and mass.

Once the data was gathered for wooden objects on wooden surfaces trials were then carried out

to see the change in the correlation, if any, on extremely smooth surfaces where the coefficient of

friction is very low and on a material like rubber where the coefficient friction is very high.

For the experiment on a very smooth surface, a plain glass of 4mm thickness was used. The glass

was stuck on to the surface of the inclined plane and the angle of inclination was readjusted to

complete the experiment. Considering the smooth surface of glass the angle of inclination was

kept at 20°. Observations for different blocks were made in the same manner as before and the

results were tabulated in the same format.

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To investigate the change in friction with surface area for a material that has property of large

friction, a thin rubber sheets were stuck beneath the surface of the wooden blocks that were

being used. Since the frictional force between the two was of a large magnitude hence the pan

had to be loaded with a lot of heavy weights which caused a lot of stress on the pulley and

reduced the accuracy of the readings, therefore, the angle of inclination was reduced to zero.

Trials were carried out in the similar manner as above and the results were tabulated in a similar

format.

All the results recording were then populated on the spreads sheet for analysis and graphs were

plotted.

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Observations and Results

As we know that the mass added to the pan is sum of the frictional force and the force of gravity

acting down the inclined plane. For each of the observations the mass of the object does not

change as the numbers of blocks that have been used remain constant. Similarly the mass of the

pan remains constant for all observations. Since our objective is to track the change in the mass

that needs to be added to the pan in each trial and not to determine the actual value of the friction

acting on the objects the mass of the pan was not added to the average of the trials and similarly

the force of gravity, mg sin θ ,was not subtracted from the mass added.

Uncertainty of the trials has been calculated using the formula: Max−Min

2

Wood on Wood

Object 1 Surface Area (cm²) 94.25 Object Mass 283.2 gramsArea (cm²)

Added Mass (grams)Average Uncertainty

±Trial 1 Trial 2 Trial 3 Trial 4 Trial 594.3 152.0 155.0 155.0 157.0 152.0 154.2 2.5

188.5 167.0 162.0 165.0 160.0 165.0 163.8 3.5282.8 170.0 172.0 175.0 170.0 168.0 171.0 3.5

Object 2 Surface Area (cm²) 55.9 Object Mass 172.8 gramsArea Added Mass (grams)

Average Uncertainty±(cm²) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

55.9 94.0 96.0 92.0 94.0 85.0 92.2 5.5111.8 105.0 102.0 106.0 104.0 103.0 104.0 2.0167.7 110.0 112.0 104.0 112.0 111.0 109.8 4.0

Object 3 Surface Area (cm²) 110.5 Object Mass: 288.6 gramsArea Added Mass (grams) Averag

e

Uncertainty±(cm²) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

110.5 185.0 182.0 181.0 180.0 182.0 182.0 2.5221.0 187.0 186.0 190.0 188.0 187.0 187.6 2.0331.5 192.0 190.0 192.0 189.0 188.0 190.2 2.0

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Wood on glass

Object 1 Surface Area (cm²) 110.5 Object Mass 288.6 grams

Area Added Mass (grams) Average

Uncertainty±(cm²) Trial 1 Trial 2 Trial 3

110.5 137.0 138.0 134.0 136.3 2.0221.0 140.0 137.0 136.0 137.7 2.0331.5 138.0 135.0 135.0 136.0 1.5



Uncertainty±(cm²) Trial 1 Trial 2 Trial 3

78.0 92.0 95.0 93.5 1.5156.0 92.0 87.0 90.0 89.7 2.5234.0 93.0 89.0 95.0 92.3 3.0

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Wood on rubber



Uncertainty±(cm²) Trial 1 Trial 2 Trial 3 Trial 4

55.4 235.0 237.0 247.0 245.0 241.0 6.0110.7 254.0 256.0 262.0 259.0 257.8 4.0166.1 270.0 272.0 267.0 271.0 270.0 2.5



Uncertainty±(cm²) Trial 1 Trial 2 Trial 3 Trial 4

56.6 149.0 154.0 152.0 155.0 152.5 3.0113.1 156.0 159.0 159.0 157.0 157.8 1.5169.7 167.0 162.0 165.0 166.0 165.0 2.5

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Graphical Representations

50.0 100.0 150.0 200.0 250.0 300.0145.0

150.0

155.0

160.0

165.0

170.0

175.0

f(x) = 0.0891246684350133 x + 146.2

Wood on Wood Object 1

Surface Area cm

Adde

d M

ass (

g)

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40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.080.0

85.0

90.0

95.0

100.0

105.0

110.0

115.0

f(x) = 0.15742397137746 x + 84.4


Surface Area cm

Adde

d M

ass (

g)

50.0 100.0 150.0 200.0 250.0 300.0 350.0176.0

178.0

180.0

182.0

184.0

186.0

188.0

190.0

192.0

f(x) = 0.03710407239819 x + 178.4


Surface Area

Adde

d M

ass (

g)

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50.0 100.0 150.0 200.0 250.0 300.0 350.080.0

90.0

100.0

110.0

120.0

130.0

140.0

150.0

f(x) = − 0.00150829562594118 x + 137

Wood on Glass Trial 1

Surface Area

Adde

d M

ass (

g)

60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0 220.0 240.0 260.060.0

65.0

70.0

75.0

80.0

85.0

90.0

95.0

100.0

f(x) = − 0.00747863247863269 x + 93

Wood on Glass Trial 2

Surface Area

Adde

d M

ass (

g)

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40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0225.0

230.0

235.0

240.0

245.0

250.0

255.0

260.0

265.0

270.0

275.0

f(x) = 0.26196928635953 x + 227.25

Rubber on Wood Trial 1

Surface Area

Adde

d M

ass (

g)

40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0146.0

148.0

150.0

152.0

154.0

156.0

158.0

160.0

162.0

164.0

166.0

f(x) = 0.1105216622458 x + 145.916666666667

Rubber on Wood Trial 2

Surface Area

Adde

d M

ass (

g)

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Analysis of Results

The graphs of the recordings show how the mass, needed to get the object to move, changes with

its surface area. The results show a positive correlation between the static frictional force acting

on an object and its surface areas in contact. Furthermore it is evident from the results that the

higher the frictional force between the two surfaces, greater is the correlation between friction

and the surface area of each object.

Hypothetically, friction is independent of surface area because the pressure acting downward

reduces as the surface area of the body is increases. However, from the results of the experiment

it is evident that effect of the reduction in pressure is far less than compared to the increase in the

forces of attraction (adhesive forces) between the atoms, particles at the microscopic scale that

come into contact with each other. When the surface area of an object is increased, the area of

the particles that comes into contact with each other increase. This contact area is also known as

the “True Contact Area”. With an increase in the apparent area of contact, the molecules that are

present on both the surfaces are brought into contact with each other and this generates

electrostatic forces of attraction between them. Thus what were described as adhesive bonds

between the surfaces earlier increases and the amount of force that needs to be applied to

overcome these bonds has to increase.

We may define magnitude of static friction as the sum of all the adhesive bonds that are formed

at the points of contact between two surfaces that are in contact with each other; hence an

increase in surface area shall increase the area of contact thereby increasing magnitude of the

adhesive forces.

As per Coulombs’ law of electrostatics, the force of attraction between two charged particles is

directly proportional to the size of the charges and inversely proportional to the separation of the

charges. While increasing the surface area of the objects in the trials, more charged particles

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were brought closer to each other, therefore, the electrostatic force attraction between the two

shall increase.

By comparing the results obtained from the two different types of surfaces it is clear that whilst a

body is in contact with a relatively smooth surface the ‘True Contact Area’ is much lower than

that of a relatively rougher surface. This why we see that the dependence on surface area

negligible on glass (in other words it is independent of surface area on glass).

From the data gathered and graphs shown above, it is inferred that the interdependence of

friction and surface areas is showing a linear progression. As the gradient of the straight line is

steeper for rubber on wood than wood on wood, it indicate higher interdependence of friction

and surface areas for rubber than that of wood.

From the results we can propose that F=μN+kA , with k being the constant of proportionality

between the two surfaces that in contact with each other and the value of k must be determined

experimentally for different pairs of surfaces.

The overall conclusion of this experiment is that there exists a correlation between the static

frictional force of an object and the surface area in contact however it is depending on the kind of

material used for investigation. The assumption that is made about friction being totally

independent of the surface area is only hypothetical. The assumption holds true only for

extremely smooth surfaces.

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Limitations

There are limitations to the procedure that was adopted to determine the magnitude of friction.

Since the same surface of the inclined plane was used for a large number of trials, the surface

was worn out after being rubbed continuously by the objects. With roughness of the surface

reduced, the possibility of reduced adhesive bonds is high which in turn could affect the accuracy

of the readings.

When tape was removed from wooden blocks and they were re-taped in a different position the

tape had left marks on surfaces. This may affect the frictional force that would act between the

two surfaces. The uniformity of the wooden blocks could be lost when the tape is removed from

the surface, and rough particles could get removed from the surface along with tap thus altering

the uniformity of the surface and this would affect both the bonding and the mechanical

interlocking of the surfaces.

The frictional force between two surfaces can reduce considerably when small layer grease, oil,

water or another substance forms on any of the surfaces being investigated. This may have been

a source error in the experiments as while transferring and storing the apparatus or when

performing trials the hands may have come into contact with the surfaces being investigated and

oil from palms and fingers could have been transferred to the surface. That would have provided

a lubricating effect to the surfaces thereby reducing the magnitude of friction acting on the

surfaces. Had this been avoided it may have been possible to have achieved a greater difference

the value friction with an increase in the area.

According to another theory on friction, when an object rests on top of another surface only a

few points on its surface, known as ‘asperities’, actually come into contact. Nobody has really

been able to determine with certainty how many there actually are6. However, the true contact

area, at asperity tips, is much smaller than the surface area. Each asperity tip is covered with a

thin layer of oxide, adsorbed water, or grease. This film has a low mechanical strength therefore 6 While performing trials it was noticed that at times when the object was left on the surface for long periods of time a slightly higher mass was needed to be added to get the object to move and the reading would be inconsistent with all the other trials. Hence a small amount of tapping is required to counteract this effect.

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deforms and allow the two asperities to slide past each other, when the tangential force per unit

area acting on the film reaches the shear strength of the film. Considering the apparatus used in

this research, this element could not be investigated. Deeper investigation into this could have

provided different readings and results.

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Bibliography

BIBLIOGRAPHY Anon. Friction Mit Physics lECTURE. 2010 February 24 <http://academicearth.org/lectures/friction>—. Introductionn to Tribology. 24 February 2010 <http://depts.washington.edu/nanolab/ChemE554/Summaries%20ChemE%20554/Introduction%20Tribology.htm>.EN3: Introduction to Engineering and Statics, Friction. 24 February 2010 <http://www.engin.brown.edu/courses/en3/Notes/Statics/friction/friction.htm>.Feynmen, Richard P and Robert Leighton. Feynman Lectures Vol.1. New Delhi: NAROSA PUBLISHING , 2003.Kurtus, Ron. Resistive force of friction . 20 August 2208. 2009 February 24 <http://www.school-for-champions.com/science/friction.htm>.Anon. Friction Mit Physics Lecture. 2010 February 24 <http://academicearth.org/lectures/friction>.

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