# Frictional force formula

• Friction Isn't Always What You Think It Is
• Static and Kinetic Friction
• 6.2 Friction
• Friction Force in Physics: Definition, Formulas
• ## Friction Isn't Always What You Think It Is

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.

Take-Home Experiment 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. 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. Example 1. Skiing Exercise 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 Strategy The magnitude of kinetic friction was given in to be See the skier and free-body diagram in Figure 3. 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.

Discussion 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. Take-Home Experiment 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.

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. Making Connections: Submicroscopic Explanations of Friction 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 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. Create an applied force and see the resulting friction force and total force acting on the cabinet.

Charts show the forces, position, velocity, and acceleration vs. Draw a free-body diagram of all the forces including gravitational and normal forces. Click to download. Run using Java. Section Summary Friction is a contact force between systems that opposes the motion or attempted motion between them.

Simple friction is proportional to the normal force N pushing the systems together. A normal force is always perpendicular to the contact surface between systems. Friction depends on both of the materials involved. Conceptual Questions Define normal force. What is its relationship to friction when friction behaves simply?

The glue on a piece of tape can exert forces. Can these forces be a type of simple friction? Explain, considering especially that tape can stick to vertical walls and even to ceilings. When you learn to drive, you discover that you need to let up slightly on the brake pedal as you come to a stop or the car will stop with a jerk.

Explain this in terms of the relationship between static and kinetic friction. When you push a piece of chalk across a chalkboard, it sometimes screeches because it rapidly alternates between slipping and sticking to the board.

Describe this process in more detail, in particular explaining how it is related to the fact that kinetic friction is less than static friction. The same slip-grab process occurs when tires screech on pavement. A physics major is cooking breakfast when he notices that the frictional force between his steel spatula and his Teflon frying pan is only 0.

Knowing the coefficient of kinetic friction between the two materials, he quickly calculates the normal force. What is it? What is the maximum force of friction under such conditions?

The frictional forces in joints are relatively small in all circumstances except when the joints deteriorate, such as from injury or arthritis.

Increased frictional forces can cause further damage and pain. Suppose you have a kg wooden crate resting on a wood floor. A team of eight dogs pulls a sled with waxed wood runners on wet snow mush!

The dogs have average masses of Consider the Remember that friction always acts in the direction opposite that of motion or attempted motion between surfaces in contact.

Figure 6. Note that this acceleration is independent of mass. Calculate the deceleration of a snow boarder going up a 5. The result of question 9 may be useful, but be careful to consider the fact that the snow boarder is going uphill.

This resistance is a force of friction. Friction opposes relative motion between systems in contact but also allows us to move, a concept that becomes obvious if you try to walk on ice.

Friction is a common yet complex force, and its behavior still not completely understood. Still, it is possible to understand the circumstances in which it behaves. Static and Kinetic Friction The basic definition of friction is relatively simple to state. Friction Friction is a force that opposes relative motion between systems in contact. There are several forms of friction. One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems and is always in a direction that opposes motion or attempted motion of the systems relative to each other.

If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, friction slows a hockey puck sliding on ice. When objects are stationary, static friction can act between them; the static friction is usually greater than the kinetic friction between two objects. Static and Kinetic Friction If two systems are in contact and stationary relative to one another, then the friction between them is called static friction.

Imagine, for example, trying to slide a heavy crate across a concrete floor—you might push very hard on the crate and not move it at all. This means that the static friction responds to what you do—it increases to be equal to and in the opposite direction of your push. If you finally push hard enough, the crate seems to slip suddenly and starts to move.

Now static friction gives way to kinetic friction. Once in motion, it is easier to keep it in motion than it was to get it started, indicating that the kinetic frictional force is less than the static frictional force. If you add mass to the crate, say by placing a box on top of it, you need to push even harder to get it started and also to keep it moving. Furthermore, if you oiled the concrete you would find it easier to get the crate started and keep it going as you might expect. Figure is a crude pictorial representation of how friction occurs at the interface between two objects.

Close-up inspection of these surfaces shows them to be rough. Thus, when you push to get an object moving in this case, a crate , you must raise the object until it can skip along with just the tips of the surface hitting, breaking off the points, or both. A considerable force can be resisted by friction with no apparent motion. The harder the surfaces are pushed together such as if another box is placed on the crate , the more force is needed to move them.

Part of the friction is due to adhesive forces between the surface molecules of the two objects, which explains the dependence of friction on the nature of the substances.

For example, rubber-soled shoes slip less than those with leather soles. Adhesion varies with substances in contact and is a complicated aspect of surface physics. Once an object is moving, there are fewer points of contact fewer molecules adhering , so less force is required to keep the object moving. At small but nonzero speeds, friction is nearly independent of speed.

Figure 6. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. For the object to move, it must rise to where the peaks of the top surface can skip along the bottom surface. Thus, a force is required just to set the object in motion.

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.

What follows is an approximate empirical experimentally determined model only. These equations for static and kinetic friction are not vector equations. Magnitude of Static Friction The magnitude of static friction.

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.

### Static and Kinetic Friction

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 polyethylenealso 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. 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. Example 1. Skiing Exercise 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 Strategy The magnitude of kinetic friction was given in to be See the skier and free-body diagram in Figure 3. 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.

Discussion 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. Take-Home Experiment 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.

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.

Making Connections: Submicroscopic Explanations of Friction 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.

## 6.2 Friction

For example, rubber-soled shoes slip less than those with leather soles. Adhesion varies with substances in contact and is a complicated aspect of surface physics. Once an object is moving, there are fewer points of contact fewer molecules adheringso less force is required to keep the object moving. At small but nonzero speeds, friction is nearly independent of speed. Figure 6. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view.

For the object to move, it must rise to where the peaks of the top surface can skip along powermta logs bottom surface. Thus, a force is required just to set the object in motion. 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.

What follows is an approximate empirical experimentally determined model only. These equations for static and kinetic friction are not vector equations.

I tried this experiment both with a felt-bottomed box on wood and a teflon box on metal. For each mass, I slowly lifted the incline until the box slipped and then recorded the angle. I repeated the experiment for the same mass 5 or 6 times so that I could get an average angle and a standard deviation in the angle measurement.

Here is a plot of friction force vs. The error bars are calculated using the crank three times method from the standard deviation in angle measurements. 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.

You could say that when two surfaces come near each other call them surface A and surface Bthe 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.

## Friction Force in Physics: Definition, Formulas

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.

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• 07.09.2021 at 03:06