Energy

By Michael on October 15, 2006 at 1:24 am | In Blog Posts, Physics |

There was a “Wanted Pages” entry in the Slackerpedia Galactica for the word “energy“. I banged out a quick paragraph, more as a placeholder than anything else, but it got me thinking. Energy can be somewhat hard to describe. Wikipedia has a good statement to the effect of “the potential for causing changes”. I have been thinking of some examples that illustrate that. I’ll probably do a video podcast about it eventually but here goes in blog form…

What is harder, going up 5 flights of stairs or going down 5 flights of stairs? Going up, of course. That is a qualitative statement, meaning it addresses the qualities of the situation and describes going up as “harder” than going down. How much harder? This is a question that expects a quantitative answer — what quantity, i.e. a number in some units, describes how much harder going up stairs is than down stairs? The question of units is itself interesting, too. Amongst things like meters (m), seconds (s), and pounds per square in (psi), what is the correct unit to describe how much harder it is going up stairs than down stairs.

In physics the word “work” has a very specific definition: it means the force times the distance that the force moves something. Common units for work (energy) are Joules (J), BTUs, ergs, electron-volts (eV), foot-pounds and calories (among others). Most of us are used to thinking of energy in things like watts (W) and that is close — watts (a unit of power) is energy per second.

To go up the stairs, the force you are opposing is gravity and the distance you are going is 5 flights. The acceleration of gravity (g) on the surface of the Earth is 9.81 m/s^2 and a flight of stairs is about 3 meters. Let’s say you weigh 150 lbs which is 68 kilograms (kg), so the work you need to do is W=Fd=gmd=(9.81 m/s^2)*(68 kg)*(15m)=10,012 J. If we say it took you 30 seconds to go that distance you “put out” more than 300 watts to go up the stairs! The bad news is, this equals only about 2 food Calories. A food Calorie is 4180 Joules so if you want to burn 100 Calories you need to go up 209 flights of stairs! This a a little misleading, though. We exert a lot of energy in other ways when we climb stairs — not all of it goes to overcoming gravity. So you’d have to climb at most 209 flights of stairs and probably many less to burn 100 Calories.

Technically speaking, going down the stairs takes negative energy. Thus, if you step off the roof of a building, you will have some nice kinetic energy going by the time you hit bottom. So in theory it is infinitely harder to go up stairs than down stairs, because going up you expend energy and going down you are given energy. But in practice we know that going down stairs is a little bit harder than just standing there. So it takes about 10,000 Joules of energy more to go up 5 flights of stairs than down, or about 2,000 Joules per flight of stairs.

For comparison, there are 2,942,720 Joules of energy in a Big Mac with cheese, 130,880,000 Joules in a gallon of gas and the Sun puts out 400,000,000,000,000,000,000,000,000 Joules per second!