# Slipping

Slipping happens when between feet and walking surface is not large enough to prevent your back foot from sliding as it pushes off, or the front foot from sliding when it tries to slow the forward motion of your ). Together, and () provide the forces necessary to support the body and maintain balance. For example, friction prevents crutches from sliding outward when they aren’t held perfectly vertical. Friction is also necessary for , such as walking and running, as we will learn in the Locomotion unit.

# Friction

Friction () is the force that resists surfaces sliding against one another. Rub your palms together, the resistance you feel is friction. Complimentary to , which only points to surfaces, friction only points to surfaces.

Friction can only exist when two objects are attempting to slide past one another, so it is also like . Two surfaces must touch to have friction, so you also can’t get friction without normal force. In fact, frictional force is to normal force.

### Reinforcement Activity

Rub your palms together. Now push your palms together hard and try to slide them at the same time.

Now the normal force is larger causing the frictional force to grow in proportion.

## Static Friction

There are two categories of friction. () acts between two surfaces when they are attempting to slide past one another, but have not yet started sliding.  Static friction is a because it only exists when some other force is pushing an object to attempt to cause it to slide across a surface. Static friction adjusts to maintain with whatever other force is doing the pushing or pulling, but static friction has a maximum value. If the applied force gets larger than the maximum static frictional value, then static friction can’t maintain equilibrium and the object will slide.

## Kinetic Friction

() acts whenever two surfaces are sliding past one another, whether or not some other force is pushing the object to keep it sliding. If there is not another force pushing the object to keep is sliding, then kinetic friction will eventually stop the sliding object, but we will learn more about that later. is larger than . The following graph of force vs. time demonstrates the process of breaking free of static friction when pulling on an object. The graph was created by measuring the force that students applied to a box sitting on a table by pulling on a string tied to the box.

Choose the friction simulation from the simulation set to see how static and kinetic friction behave.

## Friction Coefficient

We now know that force is to and that there are two types of friction, static and kinetic. The final concept that affects friction is the roughness, or alternatively the smoothness, of the two surfaces. The () is a unitless number that rates the roughness and is typically determined experimentally. The static frictional force is larger than the kinetic frictional forces because is larger than . Take a look at the table of static and kinetic friction coefficients found below. You can find more values in this massive table of static friction coefficients.

Table of static and kinetic friction coefficients for various surface pairs[4]
$\textbf{System}$ $\textbf{Static friction,}\boldsymbol{\mu_{\textbf{s}}}$ $\textbf{Kinetic friction,}\boldsymbol{\mu_{\textbf{k}}}$
Rubber on dry concrete 1.0 0.7
Rubber on wet concrete 0.7 0.5
Wood on wood 0.5 0.3
Waxed wood on wet snow 0.14 0.1
Metal on wood 0.5 0.3
Steel on steel (dry) 0.6 0.3
Steel on steel (oiled) 0.05 0.03
Teflon on steel 0.04 0.04
Bone lubricated by synovial fluid 0.016 0.015
Shoes on wood 0.9 0.7
Shoes on ice 0.1 0.05
Ice on ice 0.1 0.03
Steel on ice 0.4 0.02

Notice that two surfaces are always listed in the table; you must have two surfaces to define a .  When someone asks a question like, “what is the of ice?” they usually mean between ice and ice, but its best to avoid asking such questions and just always reference two surfaces.

## Calculating Friction Forces

We can sum up everything we have learned about in two equations that relate the friction forces to the for two surfaces and the acting on the surfaces:

Max static friction before release:

(1)

Kinetic friction once moving:

(2)

### Everyday Example: Firefighter Physical Ability Test

Firefighter candidates must complete a physical ability test (PAT) that includes dragging a dummy across the floor. The PAT for the city of Lincoln Nebraska specifies that candidates must drag a human form dummy weighing 170 lbs for 25 feet, around a barrel, and then back across the starting point for a total distance of 50 feet in six minutes or less. The candidates may only drag the dummy using the pull harness attached to the dummy and cannot carry the dummy[5].

The test is held on a polished concrete floor. The static between cotton clothing and polished concrete is 0.5. If a candidate pulls vertically up on the harness with a force of 70 lbs what horizontal pull force must the candidate apply in order to get the dummy moving?

The dummy starts out in so we know the net force must be zero in both the veritical and horizontal directions. First, let’s analyze the vertical direction: if the candidate pulls vertically up on the harness with a force of 70 lbs then the floor must provide a of 100 lbs  to support the dummy.

Now let’s analyze the horizontal direction: static friction will match whatever horizontal pull the candidate provides, but in the opposite direction, so that the dummy stays in until the pull exceeds the max static friction force. That’s the force the candidate needs to apply to get the dummy moving, so let’s find that. We have the and we already found the so we are ready:

After the dummy starts moving, kinetic friction kicks in so we can use to calculate the kinetic frictional force. The is force is less than the max static frictional force, so it will require less force to keep the dummy moving than it did to get it started.

### Reinforcement Exercises

The equations given for static and kinetic friction are that describe the behavior of the forces of friction. While these formulas are very useful for practical purposes, they do not have the status of or . In fact, there are cases for which these equations are not even good . For instance, neither formula is accurate for surfaces that are well lubricated or sliding at high speeds. Unless specified, we will not be concerned with these exceptions.[6]