Friction Contact friction is the force that develops between two surfaces in contact as they attempt to move parallel to their interface.

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1 Friction Contact friction is the force that develops between two surfaces in contact as they attempt to move parallel to their interface. Typically, friction is separated into two cases: static and kinetic. Static friction refers to the condition where the two surfaces are not moving with respect to one another. You push, i.e. apply a force, on your refrigerator and yet it does not move. This is an example where static friction is present. Kinetic friction is felt when you rub your hand across the carpet. Friction is both an enormously important and complex force. It is estimated that in developed countries 4% of GNP (USA $600b) is lost to due to overcoming friction. The frictional force between two surfaces depends on a vast number of variables, including material composition, surface roughness, humidity, velocity, temperature etc. Given all this complexity, it is not surprising that friction defies being described by any simple rules. It is important to remember this as we develop empirical expressions in an attempt to describe friction. Let s think about a common situation, an object is located on a surface, say a book at rest on a table, and a lateral force is applied. The free-body diagrams looks like this: F Friction F Applied There are three possibilities FApplied FFriction, FApplied FFriction and FApplied FFriction. For a book at rest, the last of these is clearly a nonphysical condition. The book is pushed to the right and yet accelerates to the left. Although this is certainly unreasonable, there are many students who unknowingly apply this condition. If the book is already in motion, all three conditions are possible. How can we determine the magnitude of the frictional force? Let s begin by considering a specific application of the external force. The applied force will start at zero and increase linearly with time until the book begins to move. After the book has started to accelerate, the applied force will remain constant. What is the frictional force during this experiment? As the force is starting to be applied the book remains stationary. This means that the frictional force is equal in magnitude and opposite in direction to the applied force. At some point the book breaks free and begins to accelerate. At this time the applied force stops increasing. How does the frictional force respond? In many cases it is measured that the books accelerates uniformly (i.e. constant acceleration). Since the applied force is constant, this means that the frictional force must also be constant, but with a magnitude smaller than the applied force. The sketch below shows the forces during this experiment.

2 F Applied Force F Net time F Friction There are two different regions of this experiment, in the first phase the book is stationary, or static, and the second where the book is moving. These phases are referred to as static and kinetic. There are two important magnitudes of the frictional force that delineate these regions. The first is the maximum force that friction can be applied in the static region; the second is the constant force in the kinetic region. It is found experimentally that these special forces are often proportional to the normal force between the objects. Consider the static phase, empirically the maximum force is found to behave as F N. Up till the time that this maximum force is reached the magnitude static,max static of the static frictional force was equal to the applied force. This can be summarized as Ffric, static Fapplied for Fapplied static N Notice that this is just the magnitude; the direction opposes the tangential component of the applied force. The constant static hides a considerable amount of information. In principle it depends on all the variables mentioned before: material composition, surface roughness, humidity, temperature, length of time in contact. In practice if you really care, you need to measure the value experimentally. Turning to the kinetic part of the experiment, here the book is sliding and the magnitude of the frictional force is constant. Again, it is often found experimentally that the kinetic frictional force is proportional to the normal force. This can be expressed as Ffric, kinetic kinetic N, the

3 direction is opposite the velocity. As before kinetic hides a wealth of information. Perhaps the most surprising aspect is that this expression for kinetic frictional force does not depend on the relative velocity of the objects. In truth if often does. There are numerous situations where the kinetic friction actually decreases as the speed increases. However, for simplicity this is frequently ignored. One other important implication of these empirical relations is that the frictional force does not depend on the surface area of contact. Again, this is surprising because the force arises due to contact between the surfaces, how can the contact area not matter? To understand this we need to look at the microscopic origin of friction. Examining the area of contact between the two surfaces, a microscope would show something like this: The red surface is starting to be forced to the right. At this point the static friction is large enough to cancel the applied force and the objects are not moving with respect to one another. This is the static phase. As more force is applied the three contacting asperities begin to deform, i.e. they act just like springs. The more force that is applied the more they are compressed and like any spring the larger reaction force they exert. This behavior explains the response of the surfaces during the static frictional phase. The springlike compression allows the frictional force to exactly cancel the applied force. This is exactly the same mechanism used to explain the normal force. Turning to the transition to the kinetic frictional phase, a couple things can happen. First, the asperities can exceed their elastic limit and either be deformed or sheared off. The second thing that can happen is that the normal components of the forces on the asperities can momentarily separate removing the contact points. It is likely that both effects occur to varying extent. Once the surfaces begin moving it is more difficult for the asperities to reengage. This is a natural explanation for why the kinetic friction is typically less than the static. It is also plausible that this is why the kinetic friction often decreases with velocity. With increased velocity the asperities have less time to adhere to one another. The time dependence of the adhesion of the contact points is enormously complicated, not well understood and a subject of much current research. Once we have this microscopic picture we can understand the seemingly strange observation that the macroscopic surface area of contact often does not play a major role in the frictional force.

4 We need to make a distinction between the macroscopic surface area that is measured with a ruler and the microscopic contact area. The normal force arises due to the forces placed on the asperities; this is the actual microscopic contact area. Consider a block of wood that is rectangular in shape. When the large surface of the block is in contact there is a certain pressure or force/area. This pressure allows N asperities to come into contact. Now flip the block so a smaller side is in contact. This means that the pressure is larger. You might expect that the number of asperities would be reduced because the macroscopic area is smaller; however this is not the case. Since the pressure is larger, the surfaces are forced closer and more asperities per unit area come in contact. Assuming a linear system, like a spring, the number of asperities in contact would be proportional to the product of the pressure and the macroscopic surface area, but this is just the weight of the block. Since that is a constant, then the number of asperities, or the microscopic contact area, is constant, independent of what side of the block is in contact. With an equal number of asperities in contact for the two situations, it is reasonable to see why the frictional force would be the same. Once again, the linearity of the material spring system allows us to explain an initially nonobvious result.

5 We have discussed what is often called the standard model of friction. Static friction Kinetic friction FApplied Force F Net time F kinetic N k F Friction F static,max N s It is a very approximate description of the complex phenomena. There are many situations that do not follow this model. One rather common exception is the expectation that the coefficients of friction should increase with more surface roughness. It is relatively easy to find counter examples to this. Take glass as an example, ground glass has a lower coefficient of friction than does polished glass. This is why glass stoppers in chemical containers have their surfaces roughened; it lowers the friction need to remove the stopper. An extreme example of this is when two flat clean metal surfaces are put into a vacuum. The surface roughness is very low; however the surfaces can become almost impossible to separate. This is called a cold weld. The materials have formed atomics bonds between the surfaces and in some sense have lost the interface that separates them. In a vacuum to reduce this possibility joints are made of two dissimilar materials that have a reduced chance of making bonds. Under non-vacuum conditions cold welding can be avoided by using placing a third material between the surfaces. This keeps the asperities from becoming atomically close and bonding. If you would like to reduce kinetic friction, the obvious solution is to, if possible, use a lubricant. I hope that you keep your bike chain lubricated and oil in the engine of your car. If you don t it will cost you big bucks a bit down the road. From our microscopic picture of friction it is clear what role a lubricant plays. It can effectively smooth out the surfaces by filling in the gaps between asperities. A lubricant also reduces the adhesion/bonding between asperities. The materials with the lowest coefficient of friction are wet ice on ice, with kinetic.03. Ice is slippery because it typically self-lubricates with a layer of water several molecules thick. As a

6 fun fact, the friction in your synovial joints (i.e. knee) is even lower than that for wet ice. The cartilage and fluid reduce the coefficient of friction to kinetic.003 Lubricants do not have to be fluid. Graphite, a form of carbon, is often used as a lubricant. The crystal structure of graphite has strongly bonded sheets with very weak inter-sheet bonding. When you rub your pencil lead (graphite) on a piece of paper the weakly bonded sheets exfoliate and deposit on the paper leaving a dark trace. When graphite is placed between two moving surfaces the sheets both prevent adhesion and slide across one another very easily. A gem cannot be polished without friction, nor a person perfected without trials -Chinese Proverb Below are three tables of various coefficients of friction. You will notice a fair bit of variation, this is due to all the complexity and particular circumstances of the measurement situation.

7 Coefficient of friction for a range of material combinations combination Static Dynamic dry lubricated dry lubricated steel-steel copper-steel steel-cast iron cast iron - cast iron friction material - steel steel-ice steel-wood wood-wood leather-metal rubber-metal plastic-metal plastic-plastic The coefficient of friction between two materials in relative sliding may depend on contact pressure, surface roughness of the relative harder contact surface, temperature, sliding velocity and the type of lubricant whether the level of contamination. It's the reason that the data found in the many reference tables available may show a large variation.

8 Coefficient of Friction Table Material 1 Material 2 Coefficient Of Friction Dry Greasy Static Sliding Static Sliding Aluminum Aluminum Aluminum Mild Steel 0.47 Brake Material Cast Iron Brake Material Cast Iron (Wet) Brass Cast Iron 0.3 Brick 0.6 Bronze Cast Iron 0.22 Bronze Steel 0.16 Cadmium Cadmium 0.05 Cadmium Mild Steel 0.46 Cast Iron Cast Iron Cast Iron Oak Chromium Chromium Copper Cast Iron 0.29 Copper Copper 0.08 Copper Mild Steel Copper-Lead Alloy Steel 0.22 Diamond Diamond Diamond Metal 0.1 Glass Glass Glass Metal Glass Nickel 0.56 Graphite Graphite 0.1 Graphite Steel 0.1 Graphite (In vacuum) Graphite (In vacuum) Hard Carbon Hard Carbon Hard Carbon Steel Iron Iron Lead Cast Iron 0.43 Leather Leather Metal(Clean) 0.2 Leather Metal(Wet) Leather Oak (Parallel grain) 0.52 Magnesium Magnesium Nickel Nickel Nickel Mild Steel

9 Nylon Nylon Oak Oak (parallel grain) 0.48 Oak Oak (cross grain) Platinum Platinum Plexiglas Plexiglas 0.8 Plexiglas Steel Polystyrene Polystyrene 0.5 Polystyrene Steel Polythene Steel Rubber Asphalt (Dry) Rubber Asphalt (Wet) Rubber Concrete (Dry) Rubber Concrete (Wet) Saphire Saphire Silver Silver Sintered Bronze Steel 0.13 Solids Rubber Steel Aluminium Bros Steel Brass 0.19 Steel Cast Iron 0.21 Steel Copper Lead Alloy Steel Graphite 0.1 Steel Phos Bros Steel Zinc (Plated on steel) 0.45 Steel(Mild) Brass 0.44 Steel(Mild) Cast Iron Steel(Mild) Lead Steel(Mild) Phos. Bros Steel(Mild) Phos Bros Steel (Hard) Graphite 0.09 Steel (Hard) Polythened 0.2 Steel (Hard) Polystyrene Steel (Hard) Steel (Hard) Teflon Steel Teflon Teflon Tin Cast Iron 0.32 Tungsten Carbide Tungsten Carbide 0.12 Tungsten Carbide Steel Tungsten Carbide Copper Tungsten Carbide Iron

10 (clean) (Wet) Metals(Clean) Metals (Wet) Brick Concrete Zinc Zinc 0.04 Zinc Cast Iron 0.21