Physics Across the Country

Okay, perhaps that's a misleading title. This weekend, I didn't notice Physics all over the country (although I know it's there), but I noticed Physics at a Cross Country meet at Kamehameha this Saturday. For anyone who has run at Kamehameha, or seen the Kamehameha campus and can imagine running a few miles there, you know that it's full of hills. And for anyone who has even tried to walk up a hill, you know... IT'S HARD!!!!!

During warmup for our race, our team walked the course so that we would know where to go as we ran. As we were walking up the first hill, I asked myself, "I wonder how much work we have to do to get up this hill." Then I remembered a hill we had run the year before, when the course was different. That hill was insanely steep! And it went high! Going up that hill resulted in a great change in potential energy (delta mgh). I've included an approximate sky view diagram of the hills, however this representation doesn't do their steepness justice. If I only had a camera! Later on, I considered the work involved in going up those two hills. Knowing that these hills did not have angles from horizontal complementary to each other (I doubt that the friction of the road on our shoes would have allowed that), I started plugging numbers into my calculator, and discovered that the steeper hill actually required less work to rise the same vertical distance. That was certainly a surprise, especially since going up the steep hill leaves you feel like collapsing, whereas the less steep hill only leaves your lungs burning. I wonder how the powers compare. Guess I'll have to time myself on those two hills and perform more calculations. However, I'm too lazy. I'd rather do something that requires less work. And homework doesn't count! :-)