Physics thinking - a skiing example

Explanation of energy and thermodynamic laws, related to downhill skiing.

Jeff Hulett, April 12, 2021

For physicists, classical (macro) physics is the old school Newtonian physics. Generally much less sexy than the Einstein ushered quantum (micro) physics of the last 100 or so years. However, classical physics is very relevant to our everyday life. Having a working understanding is helpful. The following is an example that helps ground me in classical physics.

The physics of downhill snow skiing -

There are 3 relevant dimensions describing energy output. That is; Potential energy (Ep), Kinetic energy (Ek), and Heat or Friction (Eh). For simplicity, I will describe this in 2 stages. Stage 1 (skiing on a mountain slope) only considers Potential and Kinetic energy, leaving out friction (or heat energy) at this stage. On the hill, a small amount of energy is transferred to heat. Please note: Stage 1 is shown as stages A, B, or C in the hand-sketched graphic at the bottom.

In stage 2, (finishing the ski run at the bottom of the hill) I include heat energy. The vast majority of energy is transferred as heat at the end of the process. Please note: Stage 2 is shown as stage D in the same hand-sketched graphic.

Stage 1

  • Location on the hill - this drives the ratio of kinetic to potential energy. As the skier goes down, the ratio increases. That is

1) 0 <= Ekn / Epn <= oo (infinity)

2) lim (Ek / Ep) —> oo (limit as the skier completes their run)

3) Ekn + Epn = Et

where n = a point in the process of skiing down the hill, p = potential energy, k = kinetic energy, t = total energy.

The ratio reaches infinity once the skier reaches the bottom of the hill (I.e., potential energy is exhausted and all nonheat energy has been transferred to kinetic energy)

  • Steepness of the hill - this drives the total energy available to both kinetic and potential energy transformation. That is, Et = Ekn + Epn, st: hill steepness

I think of time only as a reference point. (notice I don’t use “t” as a subscript, only “n” for location) More specifically, the time variable is actually describing entropic transformation (entropy or 2lotd). That is, moving from lower entropy (top of the hill) to higher entropy (bottom of the hill). Also, this is consistent with the conservation of energy (1lotd) as total energy is fixed. (Albeit, fixed in a contrived skiing example)

Stage 2

Ultimately, the potential energy is transformed into kinetic energy, then, the kinetic energy is transformed to heat energy (aka, work or friction) and released to the atmosphere.

1) Ekn + Epn + Ehn = Et

2) lim (Ek + Ep) —> 0,

3) lim (Eh / Et) —>1

(limit as the skier completes their run)

That is, once you get to the bottom of the hill, the hill flattens and your movement ends. This occurs because your energy is transformed to heat from the friction associated with a flattened hill.

Energy is conserved (1lotd), though, in the skiing context, heat is a lot less useful than being at the top of a hill with skis! Also, heat has the highest entropy in this process, so the 2lotd is realized.

My daughter Jacquelyn had a basketball coach named Marie Williams. Coach Marie was famous for yelling “use it” as motivation, whenever something negative happened. Her point was to create kinetic energy from potential energy. So if you get a bad call from a ref, “use it” as potential energy and transform it into kinetic energy to be successful in the next play. I doubt Coach Marie ever knew she was using physics principles for coaching basketball!

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