Posts Tagged ‘Charles-Augustin de Coulomb’

The Frictional Force Formula

Thursday, April 14th, 2016

    Last time we introduced the force of friction, another force in our ongoing discussion about changing forms of energy, and we learned that it’s often a counterproductive force which design engineers and engineering experts such as myself must work to minimize in order to optimize functionality of devices we’re designing.   Today we’ll introduce the frictional force formula, which computes the amount of friction present when two surfaces meet.

    To demonstrate frictional force, we’ve been working with the example of a shattered mug’s broken ceramic pieces and watching their progress as they slide across a concrete floor.   They eventually come to a stop not too far from the point where the mug shattered, because friction causes them to stop.   The mass of the ceramic pieces in combination with the downward pull of gravity causes the broken bits to “bear down” on the floor, thereby maximizing contact and creating friction.

    At first glance the floor and mugs’ surfaces may appear slippery smooth, but when viewed under magnification we see that both actually contain many peaks and valleys.   The peaks of one surface project into the valleys of the other and it’s fight, fight, fight for the ceramic pieces to continue their progress across the floor.   The strength of the frictional force acting upon the pieces is a factor of their individual weights coupled with the roughness of the two surfaces coming into contact — the shattered pieces and the floor.   If friction didn’t exist and no other impediments were in the way, the pieces might travel to the next state before stopping!

 Frictional Force Resists Motion

 Frictional Force Resists Motion


    Last time we introduced Charles-Augustin de Coulomb, a scientist whose work with friction led to the later development of a formula to calculate it.   It’s presented here, and frictional force is denoted as FF,

FF = μ × m × g

where, m is the mass of an object making contact with another surface and g is the gravitational acceleration constant, which is due to the force of Earth’s gravity.   The Greek letter μ, pronounced “mew,” represents the coefficient of friction, a number.   Numerical values for μ were determined by laboratory testing and are recorded in engineering books for many combinations of materials, including rubber on concrete, leather on steel, wood on aluminum, and our own example of ceramic on concrete.

    Next time we’ll plug the numbers that apply to our ceramic-on-concrete example into the friction formula and calculate the frictional force at play.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog



Coulomb’s Frictional Force

Monday, April 4th, 2016

    Humans have been battling the force of friction since the first cave man built the wheel.   Chances are his primitive tools produced a pretty crude wheel that first go-around and the wheel’s surfaces were anything but smooth, making its usefulness less than optimal.   As an engineering expert, I encounter these same dynamics when designing modern devices.   What held true for the cave man holds true for modern man, friction is often a counterproductive force which design engineers must work to minimize.   Today we’ll learn about frictional force and see how it impacts our example broken coffee mug’s scattering pieces, and we’ll introduce the man behind friction’s discovery, Charles-Augustin de Coulomb.

Coulomb's Work on Friction

Charles-Augustin de Coulomb


    Last time we learned that the work required to shatter our mug was transformed into the kinetic energy which propelled its broken pieces across a rough concrete floor.   The broken pieces’ energetic transformation will continue as the propelling force of kinetic energy held within them is transmuted back into the work that will bring each one to an eventual stop a distance from the point of impact.   This last source of work is due to the force of friction.

    In 1785 Charles-Augustin de Coulomb, a French physicist, discovered that friction results when two surfaces make contact with one another, and that friction is of two types, static or dynamic.   Although Leonardo Da Vinci had studied friction hundreds of years before him, it is Coulomb who is attributed with doing the ground work that later enabled scientists to derive the formula to calculate the effects of friction.   Our example scenario illustrates dynamic friction, that is to say, the friction is caused by one of the surfaces being in motion, namely the mug’s ceramic pieces which skid across a stationary concrete floor.

    While in motion, each of the mug’s broken pieces has its own unique velocity and mass and therefore a unique amount of kinetic energy.   The weight of each piece acts as a vertical force pushing the piece down “into” the floor, this due to the influence of Earth’s gravitational pull, that is, the force of gravity.

    Friction is created by a combination of factors, including the ceramic pieces’ weights and the surface roughness of both the pieces themselves and the concrete floor they skid across.   At first glance the floor and ceramic mug’s surfaces may appear slippery smooth, but when viewed under magnification it’s a whole different story.

    Next time we’ll examine the situation under magnification and we’ll introduce the formula used to calculate friction along with a rather odd sounding variable, mu.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog