## Thursday, October 25, 2012

### Life is Like a Non-conservative Force

"Mama always said, life was like a box of chocolates..."  Had Mama been a physicist, she may have instead used non-conservative forces as an analogy to depict life's winding roads.  Let us first explore the meaning of a non-conservative force, and then attempt to draw parallels between it and life.

In physics, it is important to understand the distinction between conservative and non-conservative forces.  For one thing, it comes in handy when trying to solve problems using a work/energy approach, which countless mechanics students are no doubt busily doing as I write.

The conservation of energy principle is merely a statement of the first law of thermodynamics, which, for mechanics, translates to: "The change in the total mechanical energy of a system between states 1 and 2 is equal to the total work done on the system by non-conservative forces between states 1 and 2."  The term 'state' refers to a particular position and velocity of the system's components (time does elapse in between states, but the particular amount is not significant for the analysis).

In equation form, these words look like this:

Here, E represents the total mechanical energy, and consists of the sum of kinetic energy (associated with motion) and potential energy (which is stored).  The work done by conservative forces is accounted for using potential energy expressions, whereas that done by non-conservative forces cannot be.  We cannot simply look at two states of a system and know the total work done by non-conservative forces in between them; but we can do this for conservative forces, because their net work is path independent.

Path independence occurs when the change in energy between two states is the same no matter what route is taken between them.﻿  Examples of conservative forces are electrostatic and gravitational, while friction is a non-conservative force.  The gravitational potential energy stored in a roller coaster at one state versus another does not depend upon the path it took - the work done by gravity, and the corresponding change in the potential energy stored in the body, may be assessed by comparing the altitude of the body at each state.  For friction, on the other hand, the path does matter.  If the coaster travels a much longer path, a much greater magnitude of work will be done by friction.

In this way, life is like a non-conservative force.  If life could be measured simply using potential energy functions, it could be reduced to a start and an end without examining the path.  It would be only about the destination, without any attention to the journey.  But life is about the journey more than it is about the destination.

Friction turns out to be a great non-conservative force for our analogy, because it is a force of opposition.  Life is very much a perpetual battle.  Most people will agree that they are best defined by the hurdles they have overcome - by the opposition they have faced.  In life, we can, and often do choose the path of least resistance, but it turns out that the right path for us is often the harder path.  The friction we face keeps us awake, interested.

A life without resistance is path independent, and in my view, a life where all paths are equivalent is not much of a life.  Because, as much as we are defined by the challenges we face, we are also defined by the choices that we make.  When we choose to pursue a challenging path even though we foresee a struggle, we build character.

"Life is like a non-conservative force... You never know what you're gonna get."