Mechanics in an Elevator

Though the title of this article is less catchy than the Aerosmith classic rock tune that it alludes to, an elevator is, nonetheless, an excellent place to solidify one's understanding of mechanics.

I rode up an elevator from the ground level to the eighth floor of a condo building long ago with my daughter, who was three at the time, to visit her great-grandmother.  As we approached our destination, and the elevator began to slow down, my daughter asked, "Daddy, are we going down?"

"Amazing," I thought, "kids can sense acceleration, and have already developed the same false preconceptions about it that they bring to their introductory mechanics courses."

It makes sense that people, and all animals for that matter, can sense acceleration, as we live in a dynamic world, and acceleration, which is the rate of change of velocity, may be thought of as the forecaster for motion.  If one can detect one's own acceleration, then one can accurately predict one's future position (provided one knows one's own current position and velocity with accuracy).

Newton's Second Law (Life as a Mass on an Inclined Plane)

The motion of a mass on an inclined plane is perhaps the most classic introductory mechanics problem.  Over the years, as a student, and then later as a physics teacher, I have analyzed more than my fair share of these kinds of scenarios.  I must admit, as an engineer, I have yet to encounter a problem of this type in the field – I have never been asked to design a block or inclined plane, nor have I been asked to verify whether Newton’s 3+ Century-old laws still apply to it.

Do I think all of the time that physics students spend examining masses on inclined planes is wasted?  Of course not – the simple scenario clearly illustrates the most important law of mechanics (Newton’s Second Law), and is a necessary stepping stone towards analyzing more complex situations.  

There is, I believe, a secondary usefulness to examining such systems that extends beyond the practical realm.  Let us take a close look at a mass as it slides up or down a banked surface; I contend that it serves as a powerful metaphor for life.

I know what you are thinking: this guy has drawn one too many free body diagrams.  Correct.