As I climbed to the third-floor
classroom yesterday, I got to wondering how much energy I was burning. I was predisposed to think of stair-climbing
in term of calories (rather than, say, heart health) because I have put on a
few pounds lately. (Okay--more than a
few.)

This could be quite complicated
as a biology question, but in terms of physics, it can be done--very roughly
but adequately--in five minutes on the back of an envelope. In fact, with some simplification it can be
done in your head.

The first thing to realize is
that height is a kind of energy (potential energy). Consider a car about to roll down a hill in
neutral: when that car steam-rolls you at the bottom, you will have experienced
that potential energy converted into the form of motion (kinetic) energy.

*That means***By the same token, energy is "stored" in an object as it is raised to a height**.*the energy I burn in walking up the stairs is roughly equal to the amount I gain in potential energy in going up two floors*.
A moment's thought will convince
you that potential energy depends on both the

**mass**of the object, and**how high**it is. (An anvil falling on your head will affect you differently than a marble from the same height.) It also depends on the "acceleration of gravity" (symbolized "g"), which describes how quickly a falling object on earth accelerates, and is equal to 9.8m/s^{2}. (This translates: a falling object increases its speed by 9.8 meters per second for each second that it falls.) The actual equation for potential energy (E_{p}) is:**E**

_{p}=mgh
--where "m" is mass in
kilograms, and "h" is height in meters. (E

_{p}is in Joules; a Joule is the amount of energy needed to accelerate a 1kilogram object by 1 meter per second every second.)
I'm guessing the floors of the
school to be 4 meters apart, so 8m total height. Taking g to be nearly 10, and my mass to be
almost exactly 100kg, we have:

**100kgX10m/s2X8m=8000J**

Sounds like I'm burning a lot of
energy on my climb! Now to turn that
into a more familiar unit: a calorie is four-point-something Joules--call it
four even for simplicity. Now I have
burned about 200 calories on my climb. But
wait! in one of the stupider coincidences in science, there are two kinds of
calories**: the regular sort used by physics, and the Calorie (big
"C") used in considering food.

*A Calorie is equal to 1000 calories.*So my climb actually only burned about 2 Calories.
Bummer.

According to the sugar bag in my
pantry, a teaspoon of sugar--not much more than I put in my coffee--has 15
Calories. So every time I walk up to the
third floor, I burn through only a few sips of my morning brew.**

Deep funk.

I suppose the take-home lesson is
one I already knew: you can't exercise yourself into weight loss (unless maybe you're
the athletic type, in which case you probably don't have to); you have to
control your eating. (Yes, there's more
to it, but it's still unavoidable.) Probably
I should stop making hermit cookies, full of deadly brown sugar, molasses and
butter. From the scientific point of
view, it's pretty cool (and scary) how much energy food contains.

*Another definition: a calorie
(small c) is the amount of energy needed to warm one gram of water by one
degree Celsius. Therefore a Calorie can
warm a whole kilogram by the same one degree.

**Okay, so it isn't

**Okay, so it isn't

*really*that simple: since I am assuming our bodies are 100% efficient at converting chemical (food) energy--via muscles, joints, etc.--into potential energy. What if our bodies were only 25% efficient? or 15%? I*still*don't burn that whole cup of coffee!
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