Sunday, April 29, 2012

Ignore The Skidmarks

Thirty years ago and I still recall a problem on a physics final exam at UW-Madison. It went something like this:
A tire is rolling at a constant speed along a pavement. A brake is suddenly applied, bringing the tire to a screeching halt. If the initial temperature of the tire is To, what is the final temperature of the tire? You may ignore heat exchange between the tire and road. 
The solution required a couple more pieces of info like the tire's velocity and mass, as well as the heat capacity of the tire.  I omitted those details. I remembered the problem because it was such a nice example of the first and second laws of thermodynamics.

First--all of the kinetic energy (called angular momentum) of the rolling tire changes into thermal energy (heat) as the tire skids to a halt. Nothing is "lost." The rubber in the tire heats up accordingly.*

Second--entropy increases for the energy transformation, meaning that all the well-ordered motion of the rolling tire transforms into the chaotic thermal vibrations of the warmer tire. The second law says that the reverse will not occur. In other words, a rolling tire can suddenly stop and heat up, but heating a tire will never make it roll.
James Joule spent part of his honeymoon in Switzerland measuring temperature differences between the tops and bottoms of waterfalls. His hypothesis was that the water should be warmer after the kinetic energy of the falling water is converted into heat. There were no forthcoming reports of frictional experiments with his bride.


  1. It would seem that the coefficient of friction would apply to many scenarios - some you measure and some that propriety forbids that we would measure.

  2. I thought you were talking about my underwear.

    Working many accident cases I have interviewed skid mark experts, usually engineers and some of the more interesting engineer experts I've interviewed or worked w/. Mechanical engineers are always interesting. Eletrical engineer sometimes are interesting as well as fire spread experts who are sometimes engineers but not always. The most fun guy was an electrical engineer who was a highly functioning alcoholic. We worked a huge fire case together started by an electrical malfunction. This guy would drink till he couldn't fucking see. I would take him to his hotel @ night, pick him up @ 8am and he would be just fine. He liked working w/ me because I could keep up w/ him in the evening, but not every night, and I would get him schmematics from companies that nobody else could get w/o a subpoena. That guinea charm.