What's going on here? Let's look at the data for the teflon the blue data. I fit a linear function to the first 4 data points and you can see it is very linear. The slope of this line gives a coefficient of static friction with a value of 0. However, as I add more and more mass to the friction box, the normal force keeps increasing but the friction force doesn't increase as much. The same thing happens for friction box with felt on the bottom. This shows that the "standard" friction model is just that - a model.
Models were meant to be broken. Really, what is friction? You could say that when two surfaces come near each other call them surface A and surface B , the atoms in surface B get close enough to interact with surface A. The more atoms that are interacting in the two surfaces, the greater the total frictional force. How do you get more atoms to interact from the two surfaces? Well, if you push the surfaces together you can get more atoms from A to be close enough to the atoms from B to interact.
Yes, I am simplifying this a bit. However, the point is that contact area does indeed matter. I am talking about contact area, not surface area. Suppose you put a rubber ball on a glass plate. As you push down on the rubber ball, it will deform such that more of the ball will come in "contact" with the glass. Here is a diagram of this. Greater contact area means greater frictional force. If the contact area is proportional to the normal force, then this looks just like Amontons' Law with the frictional force proportional to the normal force.
Of course this model "breaks" when the contact area can no longer increase. As I add more and more mass onto the friction box, there is less and less available contact area to expand into.
In a sense, the contact area becomes saturated. I suppose that if I kept piling on the weight, the friction force would eventually level out and stop increasing. This really isn't a big deal. The Amontons' Law isn't a law at all ok - it depends on your definition of Law. It's just a model.
Let me give an example. Gravitational Model. Near the surface of the Earth, we can calculate the gravitational force on an object using the following model.
The g vector is the local gravitational field. On Earth, it points "down" and has a magnitude around 9. We often call this gravitational force the weight and it's a very useful model. Even though this model is useful, we still know it's wrong. The above gravitational model says that it doesn't matter how high above the surface of the Earth you are, the weight is the same. Of course that's not true, but it's approximately true when close to the surface. This says that the gravitational force decreases as the two interacting objects get further away from each other.
If you put in the mass of the Earth and the radius of the Earth you get a weight that looks just like the mg version. So, at some point the two versions of gravity agree. The same is true for friction. The introductory physics version of friction works for some stuff and a more complicated version of friction works for other cases.
Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free.
Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles. The magnitude of the frictional force has two forms: one for static situations static friction , the other for when there is motion kinetic friction.
Static friction is a responsive force that increases to be equal and opposite to whatever force is exerted, up to its maximum limit. Once the applied force exceeds f s max , the object will move. As seen in Table 1, the coefficients of kinetic friction are less than their static counterparts. The equations given earlier include the dependence of friction on materials and the normal force. The direction of friction is always opposite that of motion, parallel to the surface between objects, and perpendicular to the normal force.
If the coefficient of static friction is 0. Once there is motion, friction is less and the coefficient of kinetic friction might be 0. If the floor is lubricated, both coefficients are considerably less than they would be without lubrication. Coefficient of friction is a unit less quantity with a magnitude usually between 0 and 1. The coefficient of the friction depends on the two surfaces that are in contact. Find a small plastic object such as a food container and slide it on a kitchen table by giving it a gentle tap.
Now spray water on the table, simulating a light shower of rain. What happens now when you give the object the same-sized tap? Now add a few drops of vegetable or olive oil on the surface of the water and give the same tap. What happens now? This latter situation is particularly important for drivers to note, especially after a light rain shower. Many people have experienced the slipperiness of walking on ice. However, many parts of the body, especially the joints, have much smaller coefficients of friction—often three or four times less than ice.
A joint is formed by the ends of two bones, which are connected by thick tissues. The knee joint is formed by the lower leg bone the tibia and the thighbone the femur. The hip is a ball at the end of the femur and socket part of the pelvis joint. The ends of the bones in the joint are covered by cartilage, which provides a smooth, almost glassy surface.
The joints also produce a fluid synovial fluid that reduces friction and wear. A damaged or arthritic joint can be replaced by an artificial joint Figure 2. These replacements can be made of metals stainless steel or titanium or plastic polyethylene , also with very small coefficients of friction.
Figure 2. Artificial knee replacement is a procedure that has been performed for more than 20 years. In this figure, we see the post-op x rays of the right knee joint replacement. Other natural lubricants include saliva produced in our mouths to aid in the swallowing process, and the slippery mucus found between organs in the body, allowing them to move freely past each other during heartbeats, during breathing, and when a person moves.
For example, when ultrasonic imaging is carried out, the gel that couples the transducer to the skin also serves to to lubricate the surface between the transducer and the skin—thereby reducing the coefficient of friction between the two surfaces.
This allows the transducer to mover freely over the skin. A skier with a mass of 62 kg is sliding down a snowy slope. Find the coefficient of kinetic friction for the skier if friction is known to be The magnitude of kinetic friction was given in to be See the skier and free-body diagram in Figure 3.
The motion of the skier and friction are parallel to the slope and so it is most convenient to project all forces onto a coordinate system where one axis is parallel to the slope and the other is perpendicular axes shown to left of skier. This result is a little smaller than the coefficient listed in Table 5. All objects will slide down a slope with constant acceleration under these circumstances. An object will slide down an inclined plane at a constant velocity if the net force on the object is zero.
We can use this fact to measure the coefficient of kinetic friction between two objects. These forces act in opposite directions, so when they have equal magnitude, the acceleration is zero. Writing these out:. Put a coin on a book and tilt it until the coin slides at a constant velocity down the book. You might need to tap the book lightly to get the coin to move. We have discussed that when an object rests on a horizontal surface, there is a normal force supporting it equal in magnitude to its weight.
Furthermore, simple friction is always proportional to the normal force. The simpler aspects of friction dealt with so far are its macroscopic large-scale characteristics. Great strides have been made in the atomic-scale explanation of friction during the past several decades. Researchers are finding that the atomic nature of friction seems to have several fundamental characteristics. These characteristics not only explain some of the simpler aspects of friction—they also hold the potential for the development of nearly friction-free environments that could save hundreds of billions of dollars in energy which is currently being converted unnecessarily to heat.
Figure 4 illustrates one macroscopic characteristic of friction that is explained by microscopic small-scale research. We have noted that friction is proportional to the normal force, but not to the area in contact, a somewhat counterintuitive notion.
When two rough surfaces are in contact, the actual contact area is a tiny fraction of the total area since only high spots touch. When a greater normal force is exerted, the actual contact area increases, and it is found that the friction is proportional to this area. Figure 4. Two rough surfaces in contact have a much smaller area of actual contact than their total area. When there is a greater normal force as a result of a greater applied force, the area of actual contact increases as does friction.
But the atomic-scale view promises to explain far more than the simpler features of friction. The mechanism for how heat is generated is now being determined. In other words, why do surfaces get warmer when rubbed? Essentially, atoms are linked with one another to form lattices. When surfaces rub, the surface atoms adhere and cause atomic lattices to vibrate—essentially creating sound waves that penetrate the material.
The sound waves diminish with distance and their energy is converted into heat. Chemical reactions that are related to frictional wear can also occur between atoms and molecules on the surfaces. Figure 5 shows how the tip of a probe drawn across another material is deformed by atomic-scale friction. The force needed to drag the tip can be measured and is found to be related to shear stress, which will be discussed later in this chapter.
The variation in shear stress is remarkable more than a factor of 10 12 and difficult to predict theoretically, but shear stress is yielding a fundamental understanding of a large-scale phenomenon known since ancient times—friction.
Figure 5. The tip of a probe is deformed sideways by frictional force as the probe is dragged across a surface. Measurements of how the force varies for different materials are yielding fundamental insights into the atomic nature of friction. Explore the forces at work when you try to push a filing cabinet.
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