Introduction

Friction is always present when two surfaces in contact are moving one relative to the other. There is the potential for friction even when two surfaces, in contact with each other, are not moving one with respect to the other. This potential for friction becomes friction when there is a net force trying to move the contacting surfaces relative to each other. Friction is a macroscopic effect of microscopic imperfections of the surfaces.

 The figure at the left represents the magnification of the details between the surface of the cylinder and the surface of the piston in an engine. The irregularities at the microscopic level of the two surfaces generates the friction between them. In reality, the physical contact between the cylinder and the piston is through several rings and the friction occurs between rings and cylinder. The magnifier could represent the view of the ring and cylinder rather than piston and cylinder. Also, oil lubrication place a film between the two surfaces that change the contact from ring to cylinder to ring-oil to oil-cylinder. Fluid viscosity is another manifestation of friction, see the chapter on fluids. From the point of view of mechanics, frictions manifest through the frictional forces. In this section, the words friction and frictional forces are use in solving applications without distinction. Friction is divided in two kinds, static friction and kinetic friction.

### Static Friction

Suppose that a box is at rest over the floor. What are the forces acting on the box?

 As shown in the first figure (left), there are only two forces acting on the box, the weight of the box, pulling the box down, and the normal force, reaction of the surface to the box's weight. The weight and the normal force are opposite to each other but they have the same magnitude. In this case, there are not forces in the horizontal direction; consequently, there is not acceleration either. Since the velocity of the box is zero and no horizontal forces are acting over the box, there is not frictional forces between the surfaces. If there were a frictional force acting on the box, this force will be the only one in the horizontal direction; notice that the woman is not touching the box jet. Thus, this frictional force would be an unbalance force and the box would be accelerating by itself! In this second figure (left), the woman starts pushing the box. Thus, in addition to the weight and normal force, there is the horizontal force applied by the woman. Certainly, the force applied by the external agent pushing on an object (the woman) is not  perfectly horizontal in most cases but for the purpose of this analysis there is not difference. In terms of the magnitude, the applied force can be as small as desired; for example, the woman just touching the box, or very large depending on the strength of the woman. For the purpose of this discussion, let us assume that the force applied by the woman is horizontal and starts small gradually increasing in magnitude without a change in direction. Even when the force is just applied, if this is the only horizontal force, the box should start accelerating in the horizontal direction no matter how small this force is. The reality is that the box does not accelerate by just touching it (may be, it could happen if the floor is iced). What prevent the box for moving? The answer is: the static frictional force, . What is the direction of the static frictional force? Opposite to the direction of the applied external force horizontal component; opposite to the force applied by the woman on the drawing, . What is the magnitude of the static frictional force? The same as the magnitude of the applied force; force applied by the woman, . How large can the static friction get? The static friction will increase in magnitude, matching the magnitude of the force applied by the woman, until it reaches a limit, . If the woman applies a force larger than this limit, the box will start accelerating. Now the box will be moving. As soon as the box moves, the friction is not called static friction anymore but rather is called kinetic friction. The word kinetic means motion.

The following result presented about static friction or static frictional force are the result of experimental observations.

 Static Friction, Magnitude: The static frictional force match the magnitude of the external frictional force up to a limit, . Experimentally, the maximum static friction is given by where is the coefficient of static friction and is the normal force acting on the object. Therefore, the magnitude of the static frictional force match the magnitude of the external force up to a limit accordingly with the following relations: Direction: The direction of the static frictional force is always opposite to the direction of the component of the applied external force parallel to the inter surface between the two objects . If there is not a net applied external force, the static frictional force is zero. The static frictional force is parallel to the inter surface between the two object in contact. If the applied force is not parallel to this inter surfaces, then the static frictional force direction is opposite to the parallel component to the inter surface between the objects.

The coefficient of static friction is not a property of the object itself (such as volume or mass) but rather depends of the two surfaces in contact with each other. As it can be seeing in the previous expressions, this coefficient is a proportionality coefficient between two forces, ; therefore, this coefficient is dimensionless. This coefficient is given in tables or need to be measured experimentally.

### Kinetic Friction

After the object starts moving, the friction between the surfaces is called kinetic friction. The kinetic friction will be always present when two surfaces are moving with respect to each other. Even if there is not an external applied force acting on the object, there will be kinetic friction when the object is moving relative to the contact surface. Eventually, the kinetic friction will decelerate the object until it stop moving.

 Kinetic Friction, Magnitude: The magnitude of the kinetic friction has a fixed value given by: Here, is the coefficient of kinetic friction. Just as the coefficient of static friction, the coefficient of kinetic friction depends on the surfaces in contact. Also this coefficient is dimensionless. is the normal force acting on the object. Direction: The direction of the kinetic frictional force is always opposite to the direction of motion and independent of the direction of any possible applied external force. The direction of the kinetic friction is opposite to the direction of the velocity, where is the unit vector in the direction of the velocity.

Notice that in the previous expressions for the static and kinetic frictions there are not dependence on the area of the surfaces. This statement is true as long as the surfaces do not loss contact with each other.

Considering that the front cover, the binding, and the back binding of the book are of the same material. When sliding the book over the table (try with one of your books), the greater friction is when the book is over

 a) the back cover b) the binding c) the front cover N d) the same for the three cases e) None of the above.

If you are having problems understanding the solutions for this example, try to work the experiment using one of your books. Notice that the binding surface has an area about 1/5 of the area for one of the cover. Do you feel 5 times different the effect of friction, when comparing one surface with the other?

In motions where there is not sliding of an object over the other, the friction present is static friction rather than kinetic friction; examples of static friction are: A person walking; and, between the tires and the road for a moving car. On the other side, examples of kinetic friction are: A person sliding over the floor; and, a car sliding with locked wheels while breaking.

### Selected Coefficients of Friction (Approximated Values)

 Materials Coefficient of Static Friction, Coefficient of Kinetic Friction, Aluminum on Steel 0.61 0.47 Copper on Steel 0.53 0.36 Glass on Glass 0.94 0.4 Ice on Ice 0.1 0.03 Rubber on Concrete 1.0 0.8 Steel on Steel 0.74 0.57 Steel on Teflon 0.04 0.04 Wood on Wood 0.5 0.3

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com