39 Slipping

Slipping happens when between feet and walking surface is not large enough to prevent your feet from sliding as the back foot pushes off and/or the front foot tries to slow the forward motion of your . Together, and (F_f) provie 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 unit on locomotion.

Friction between the crutches and the floor prevents the young boy’s crutches from sliding outward even when they aren’t held straight vertical. This 1942 photo by Fritz Henle was captioned “Nurse training. Using the picture book as bait, the physical therapist encourages a young victim of infantile paralysis [Polio] to learn to use his catches (crutches).”  Polio was effectively eradicated from the United States by the polio vaccine, originally developed by Jonus Salk  “who never patented the vaccine or earned any money from his discovery, preferring it be distributed as widely as possible.” There are two types of vaccine that can prevent polio: inactivated poliovirus vaccine (IPV) and oral poliovirus vaccine (OPV). Only IPV has been used in the United States since 2000 and 99% of children who get all the recommended doses of vaccine will be protected from polio.



Friction (F_f) 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.

The figure shows a crate on a flat surface, and a magnified view of a bottom corner of the crate and the supporting surface. The magnified view shows that there is roughness in the two surfaces in contact with each other. A black arrow points toward the right, away from the crate, and it is labeled as the direction of motion or attempted motion. A red arrow pointing toward the left is located near the bottom left corner of the crate, at the interface between that corner and the supporting surface. The red arrow is labeled as f, representing friction between the two surfaces in contact with each other.
Frictional forces always oppose motion or attempted motion between objects in contact. Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks 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. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles.

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. (F_{f,s}) 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

(F_{f,k}) 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 . Choose the friction simulation from the simulation set to see how static and kinetic friction behave.

Reinforcement Activity

Place a heavy box or book or other object on a desk, table, or the floor. Push the object with your hand, but not hard enough to make it slide. At this point is reacting to your push and exerting a force to perfectly balance your push. The balance between static friction and your push keeps the object in and it doesn’t move.

Now push the object hard enough that it starts to slide. Notice that starts with a jerk. The jerky motion occurs because static friction is larger than kinetic friction. After you “break” static friction and the object starts to move and kinetic friction kicks.  Kinetic friction is smaller than static friction so the object jerks forward before you have time to react and decrease your push force to match up with the smaller kinetic friction.

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 (\mu) 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 \mu_s is larger than \mu_k. 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 \mu.  When someone asks a question like, “what is the \mu 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)   \begin{equation*} F^{max}_{f,s} = \mu_{s}F_{N} \end{equation*}

Kinetic friction once moving:

(2)   \begin{equation*} F_{f,k} = \mu_{k}F_{N} \end{equation*}

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:

    \begin{equation*} F^{max}_{f,s} = \mu_sF_N =0.5\cdot100\, \bold{lbs} = 50\, \bold{lbs} \end{equation*}

After the dummy starts moving, kinetic friction kicks in so we can use \mu_k = 0.4 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.

    \begin{equation*} F_{f,k} = \mu_kF_N =0.4\cdot100\, \bold{lbs} = 40\, \bold{lbs} \end{equation*}

Reinforcement Exercises

A child with a weight of 178 N (40 lbs) clings to a “fire pole” slide on a playground, as demonstrated in the photo below.

What frictional force is need to support the child?

If the coefficient of friction between skin and steel is 0.8, with what force must the child squeeze the pole to remain in place? [Hint: The normal force between the skin and the pole is due to the child squeezing the pole.]

A person clings to a playground fire pole. “Firepole” by Donkeysforever, via Wikimedia Commons is in the Public domain

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]


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