Chapter 13: Friction

Table of Contents

13.1 Introduction to Friction

Friction is a fundamental concept in the field of physics that deals with the resistance encountered by two surfaces when they move relative to each other. It plays an essential role in various aspects of our everyday lives, from walking to driving a car. Understanding the nature of friction and its implications is crucial for designing efficient machines, predicting the behavior of moving objects, and solving a wide range of physics problems. In this chapter, we will explore the key concepts, important equations, and real-life examples related to friction.

Drifting is an example of kinetic friction as the tires slide with respect to the road.

13.2 Types of Friction

There are two main types of friction: static friction and kinetic (dynamic) friction.

13.2.1 Static Friction

Static friction is the force that opposes the initiation of relative motion between two surfaces in contact. That’s a bit of a mouthdul, so let’s break it down. Suppose you are standing in front of a box and you begin pushing. At first, the box doesn’t move. Static friction is prevent the “relative motion” between the box and the floor. Eventully, if you push hard enough, the box begins to slide. At the moment just before the box begins sliding, static friction is at it’s max. This is sometimes called the point of impending motion.

Static friction acts to keep the surfaces at rest with respect to each other. The static frictional force $(f_s)$ can vary in magnitude up to a maximum value given by:

$f_s \le \mu_s N$

where $\mu_s$ is the coefficient of static friction and $N$ is the normal force acting between the surfaces. We will discuss more about friction coefficients later on down below.

13.2.2 Kinetic Friction

Kinetic friction, also known as dynamic or sliding friction, is the force that opposes the relative motion of two surfaces in contact. It acts when the surfaces are already moving relative to each other. The kinetic frictional force $(f_k)$ is given by:

$f_k = \mu_k N$

where $\mu_k$ is the coefficient of kinetic friction, and N is, once again, the normal force acting between the surfaces.

13.3 Factors Affecting Friction

Nature of the surfaces: Rougher surfaces generally have higher coefficients of friction, while smoother surfaces have lower coefficients.
Normal force: The frictional force is directly proportional to the normal force acting between the two surfaces.

It’s important to note that friction is independent of the apparent area of contact between the surfaces and the relative speed of the surfaces (though the latter may affect the coefficient of friction in certain cases).

13.4 What is the Friction Coefficient?

At this point, you’re probably wondering what $\mu_s$ and $\mu_k$ are. To begin with, we refer to these quantities as friction coefficients. They are unitless numbers that can range, theoretically, from just greater than zero all the way to infinity. However, almost all values of $\mu_{s/k}$ end up being between 0 and 1.

The values of $\mu{s/k}$ depend entirely on the materials involved. For example, wood sliding on wood will have a different $\mu_k$ value than wood sliding on glass. Even the type of wood will matter. Some are less resistant to sliding than others. The higher the value of $\mu_{s/k}$ , the greater the friction force resisting the motion.

The following table is produced using publicly available data. Get comfortable with the numbers in the table. No one will ever expect you to memorize any of these values. However, you should develop an intuition for what values are reasonable. For example, note that the highest value in this table in 1.35 ( $\mu_s$ for Aluminum on Aluminum). So, if you were to calculate a value of, say, 2.4 for $\mu_s$ during a lab or on a homework question, you may want to check your work. It’s not necessarily wrong, but it is unlikely to get a value so high if the question is using physically realistic values.

Material 1	Material 2	Surface Conditions	$\mu_s$	$\mu_k$
Aluminum	Aluminum	Clean and Dry	1.05-1.35	1.4
Aluminum	Mild Steel	Clean and Dry	0.61	0.47
Brass	Steel	Clean and Dry	0.51	0.44
Cast Iron	Cast Iron	Clean and Dry	1.1	0.15
Copper	Cast Iron	Clean and Dry	1.05	0.29
Copper	Glass	Clean and Dry	0.68	0.53
Copper	Mild Steel	Clean and Dry	0.53	0.36
Glass	Glass	Clean and Dry	0.9-1.0	0.4
Glass	Glass	Lubricated and Greasy	0.1-0.6	0.09-0.12
Ice	Ice	Clean at $0^oC$	0.1	0.02
Leather	Cast Iron	Clean and Dry	0.6	0.56
Leather	Oak	Parallel to Grain	0.61	0.52
Nickel	Nickel	Clean and Dry	0.7-1.1	0.53
Nickel	Nickel	Lubricated and Greasy	0.28	0.12
Rubber	Dry Asphalt	Clean and Dry	0.9	0.5-0.8

Table 1. Values for static and kinetic friction coefficients for various material combinations in different conditions.

13.5 Important Equations

Static friction: $f_s \le \mu_s N$
Kinetic friction: $f_k = \mu_k N$

13.6 Real-life Examples

Walking: Friction between our feet and the ground allows us to walk without slipping. It provides the necessary force to push us forward. The words “without slipping” are extremely important here. They imply that the type of friction involved is static despite the fact that the person is moving.
Car tires: Friction between the tires and the road allows cars to accelerate, decelerate, and change direction. Without sufficient friction, cars would lose control and skid. Generally, tires do not “slip.” Once again, this implies static friction at work. However, if you were to “spin out,” the tires would be sliding against the asphalt. This would be kinetic friction.
Brakes: When brakes are applied in a vehicle, friction between the brake pads and the brake disc helps to slow down or stop the vehicle. This contact between the brake pads and brake disc is a sliding motion that implies kinetic friction.

Friction is an essential working principle of many tools and innovations.

Chapter Summary

Friction influences motion in a variety of ways. By understanding the key concepts and equations related to friction, we can better predict the behavior of moving objects and design efficient systems that utilize or counteract frictional forces.

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13.1 Introduction to Friction