# Friction

### Types of Friction

Up until this point, we've been ignoring one of the most useful and most troublesome forces we deal with every day... a force that has tremendous application in transportation, machinery, and all parts of mechanics, yet we spend tremendous amounts of money each day fighting it. This force, friction, is a force that opposes motion.

Question:A box is pushed toward the right across a classroom floor. The force of friction on the box is directed toward the

- left
- right
- ceiling
- floor

Answer:(1) left. Friction opposes motion.

There are two main types of friction. **Kinetic friction** is a frictional force that opposes motion for an object which is sliding along another surface. **Static friction**, on the other hand, acts on an object that isn't sliding. If you push on your textbook, but not so hard that it slides along your desk, static friction is opposing your applied force on the book, leaving the book in static equilibrium.

The magnitude of the frictional force depends upon two factors:

- The nature of the surfaces in contact.
- The normal force acting on the object (F
_{N}).

### Coefficient of Friction

The ratio of the frictional force and the normal force provides us with the coefficient of friction (µ), a proportionality constant that is specific to the two materials in contact. You can look up the coefficient of friction for various surfaces from a variety of references. Make sure you choose the appropriate coefficient... use the static coefficient (µ_{s}) for objects which are not sliding, and the kinetic coefficient (µ_{k}) for objects which are sliding.

Which coefficient would you use for a sled sliding down a snowy hill? The kinetic coefficient of friction, of course. How about a refrigerator on your linoleum floor that is at rest and you want to start in motion? That would be the static coefficient of friction. Let's try a harder one... A car drives with its tires rolling freely. Is the friction between the tires and the road static or kinetic? Static. The tires are in constant contact with the road, much like walking. If the car was skidding, however, and the tires were locked, we would look at kinetic friction. Let's take a look at a sample problem:

The normal force always acts perpendicular to a surface, and comes from the interaction between atoms that act to maintain its shape. In many cases, it can be thought of as the elastic force trying to keep a flat surface flat (instead of bowed). We'll use the normal force to help us calculate the magnitude of the frictional force.

The force of friction, depending only upon the nature of the surfaces in contact (µ) and the magnitude of the normal force (F_{N}), therefore, can be determined using the formula:

### Problem Solving

Solving problems involving friction requires us to apply the same basic principles we've been talking about throughout the dynamics unit... drawing a free body diagram, applying Newton's 2nd Law along the x- and/or y-axes, and solving for our unknowns. The only new skill is drawing the frictional force on the free body diagram, and using the relationship between the force of friction and the normal force () to help us solve for our unknowns.

Let's take a look at a sample problem:

Let's take a look at a more involved problem, tying together free body diagrams, Newton's 2nd Law, and the coefficient of friction:

These same steps can be used in many different ways in many different problems, but the same basic problem solving methodology still works... draw a free body diagram, apply Newton's 2nd Law, utilize the friction formula if necessary, and solve!