Extended Essay Ver 7

IB Physics Extended Essay 002272-091

Ashish Tayal

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Candidate Name - Ashish Tayal Candidate No – 002272-091 Session May 2010 Word Count: 3,220 [1 March 2010]

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

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Ashish Tayal

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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 Bibliography

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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 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 1 http://www.virginia.edu/ep/SurfaceScience/friction.html 2 http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-800Fall-2004/EDEB0AEE-FEB5-48DD-B3AD83F2422FAF07/0/ch1_trib_intro.pdf

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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 μsN 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=μkN where µ k 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.

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

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

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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 mgsinθ 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 remain the same mgsinθwould also remain the same for all the different trials for a particular 11 / 27


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

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

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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 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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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. 15 / 27


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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, mgsinθ, was not subtracted from the mass added. Uncertainty of the trials has been calculated using the formula: Max-Min2 Wood on Wood Object 1 Area (cm²) 94.3 188.5 282.8

Object 2

Surface Area (cm²) 94.25 Trial 1 152.0 167.0 170.0

(cm²) 55.9 111.8 167.7

Object 3

Trial 1 94.0 105.0 110.0

110.5 221.0 331.5

Trial 1 185.0 187.0 192.0

Added Trial 2 182.0 186.0 190.0

Trial 5 152.0 165.0 168.0

Avera ge 154.2 163.8 171.0

Uncertai nty ± 2.5 3.5 3.5

Object Mass 172.8 grams

Added Mass (grams) Trial Trial Trial 2 3 4 96.0 92.0 94.0 102.0 106.0 104.0 112.0 104.0 112.0

Surface Area (cm²) 110.5

Area (cm²)

Added Mass (grams) Trial Trial Trial 2 3 4 155.0 155.0 157.0 162.0 165.0 160.0 172.0 175.0 170.0


Area


Trial 5 85.0 103.0 111.0

Avera ge 92.2 104.0 109.8

Uncertai nty ± 5.5 2.0 4.0

Object Mass: 288.6 grams

Mass (grams) Trial Trial 3 4 181.0 180.0 190.0 188.0 192.0 189.0

Trial 5 182.0 187.0 188.0

Avera ge 182.0 187.6 190.2

Uncerta inty ± 2.5 2.0 2.0

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Wood on glass Object 1 Area (cm²) 110.5 221.0 331.5

Object 2 Area (cm²) 78.0 156.0 234.0

Surface Area (cm²) 110.5 Added Trial 1 137.0 140.0 138.0


Mass (grams) Avera Trial Trial ge 2 3 138.0 134.0 136.3 137.0 136.0 137.7 135.0 135.0 136.0




Added Mass (grams) Avera Trial Trial Trial ge 1 2 3 92.0 95.0 93.5 92.0 87.0 90.0 89.7 93.0 89.0 95.0 92.3


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Wood on rubber Object 1 Area (cm²) 55.4 110.7 166.1

Object 2 Area (cm²) 56.6 113.1 169.7



Added Mass (grams) Avera Trial Trial Trial Trial ge 1 2 3 4 235.0 237.0 247.0 245.0 241.0 254.0 256.0 262.0 259.0 257.8 270.0 272.0 267.0 271.0 270.0




Added Mass (grams) Avera Trial Trial Trial Trial ge 1 2 3 4 149.0 154.0 152.0 155.0 152.5 156.0 159.0 159.0 157.0 157.8 167.0 162.0 165.0 166.0 165.0


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Graphical Representations

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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 6 http://depts.washington.edu/nanolab/ChemE554/Summaries%20ChemE%20554/Introduction %20Tribology.htm

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thin layer of oxide, adsorbed water, or grease. This film has a low mechanical strength therefore 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 Anon. Friction Mit Physics lECTURE. 2010 February 24 —. Introductionn to Tribology. 24 February 2010 . EN3: Introduction to Engineering and Statics, Friction. 24 February 2010 . 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 . Anon. Friction Mit Physics Lecture. 2010 February 24 .

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Extended Essay Ver 7

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