“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Monday, January 04, 2010

Mundane examples of energy

I was walking up the hill to my house and started to think about energy. I thought I'd give a few examples. For starters, my "resting metabolism" is somewhere around 1900 kilocalories per day. This is energy per unit of time, or power. Using Google's terrific calculator, this converts to a more familiar figure for power, 92 watts. So it takes about the same amount of energy to run me for an hour as to light a small room for an hour.

OK, now how about the hill? Using Google Earth I find that I gained 91.1 meters in elevation on the climb. Using the National Geodetic Society's Surface Gravity Predictor I find my local gravitational acceleration to be 9.795 meters/second^2, or as Rhett over at Dot Physics prefers, 9.795 Newtons/kilogram. I know this rounds to 9.80 but it's kind of cool to find and use the more precise number. My mass is an embarrassing 84.82 kilograms, so raising it up that hill requires converting 84.82*9.795*91.1 (mass*gravitational acceleration*height) or 75,690 joules of food energy to do the work to accomplish. This is 18 kilocalories (the type referred to in nutritional discussions as "calories")or a tiny bit over four plain chocolate M&M's. I don't use the energy in the M&M's with 100% efficiency though. In this post I estimated an efficiency of 11% to 14% so I'll figure that I'd need to eat about eight times as much fuel energy or 32 plain chocolate M&M's.

Of course more is burned since I'm lifting my feet up and down, swinging my arms, etc. To estimate this, I'll add a "walking briskly" amount to the climb energy. The linked site says I'll burn about 460 kilocalories/hour in my "brisk walk." I run down the hill and walk up, so I'm going to speculate that the running aspect makes up for the energy gain of going down hill. I do try to keep my heart rate in the so-called training zone so this shouldn't be too far off. This run/walk takes me about 42 minutes, and so should burn about (42/60)*460 or 322 kilocalories. Adding the 18, my exercise burned about 340 kilocalories or 1,420,000 joules. This is also about 395 watt hours, so this amount of energy will light a room (with a 100 watt bulb) for about four hours. It's also the amount of heat energy released by the gasoline in about one and a half shot glasses. My Land Rover LR3 HSE would possess this amount of kinetic energy (not counting the energy of the rotating masses) when traveling at about 73 m.p.h.

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