First year physics was a long time ago.

August 26th, 2007, 11:21 pm PDT by Greg

So, I rode up to SFU this afternoon. This is something I try to do once a week, but realistically get around to less than that. I tried riding to work for a while, but I’m not really very useful for an hour or so after the ride, so that didn’t really work.

I had ridden up two weeks ago after a long hiatus. If anybody had been there to hear me after I got past the SFU sign, they would have heard something like this:

pantpantgasp… “gonna die”
pantpantgasp… “gonna die”

This week went better. I said “gonna die” way less often than every three breaths.

Anyway, as I was grinding up the hill, I started to wonder how many calories I was burning. Even ignoring the forward motion, I was gaining a lot of height. Gaining height means gaining gravitational potential energy. Energy is conserved, and there was no other energy source around, so I had to be putting out the energy in return.

According to Google Earth, the Security booth at SFU is about 200 m above Curtis and Duthie. I weigh about 80 kg (which is part of the problem). So, my gain of gravitational potential energy was

E = mgh = 80 kg × 9.8 m/s2 × 200 m
= 156800 kg m2/s2 = 156800 J = 37451 cal.

So, that doesn’t sound right. I don’t think I need to eat 65 Big Macs to recover from the ride.

I seem to remember that there’s some confusion between calories and kilocalories when people talk about food. So maybe it’s 37 “calories”? If all I earned from the ride was half a nigiri, then I’m not exercising any more.

So, what the hell am I doing wrong there? I know I’m ignoring the forward motion but, as anybody that rides up the hill will tell you, forward isn’t the hard part.

7 Responses to “First year physics was a long time ago.”

  1. Curtis Says:

    You weigh 80kg + bike, and you lose a lot of energy to friction, I guess?

  2. Kat Says:

    Don’t you HAVE to account for the forward motion because that’s where the friction comes from? Wait until Eastwood gets home. I’m sure he’ll know…

  3. Greg Says:

    I don’t think so. Imagine climbing a 200 m rope: that’s basically what I calculated.

    That’s going to suck pretty hard (and burn way more than 37 calories), and there’s no forward motion to worry about.

  4. Brian Says:

    Yeah, I always hated when my professors told me if I carried a 200lb block around in a circle I would have done no work. They said the same thing if I spent a week working on a single problem but didn’t get the answer. This is why I am a recovering physicist–so don’t assume my answer has any authoritative weight to it.

    So, what you’ve calculated is the work you’ve done against gravity. And, you’re right, a food Calorie (capital C) is 1000 SI calories (lowercase c). Gravitational potential energy is conserved, so, if you turn around at the top of the hill and coast back down, do you put back on those 37 Calories? No, you’ve converted gravitational potential energy to kinetic energy.

    And that’s where the rest of your workout comes from. You’re taking a bike that would be perfectly happy sitting still, and you’re propelling it along the road, increasing its (and your) kinetic energy. You’re applying force to the pedals, which imparts force to the wheels, which exert force on the ground, which pushes back, propelling the bike forward.

    There’s also friction in the system, which usually gets swept under the rug in most physics classrooms. Let’s just say if your brakes are rubbing, they’re introducing more friction to the system, making it harder to push those wheels around. Incidentally, when you stop your bike, you’re converting kinetic energy to thermal energy through friction, and your brake pads and wheels heat up.

    So, to figure out the calories in your workout, you need to integrate the amount of force your wheels exert on the ground over the distance you travel. There are special hubs you can get for your bike (PowerTap comes to mind) which measure your power output (work/time), which you can integrate over time to compute the work you’ve done in your workout.

  5. Kat Says:

    See! So you DO have to factor in forward motion in the form of distance traveled! HAH!

    You rock Brian!!!! Must be your lifestyle (rock and roll) 😛

  6. Ted Kirkpatrick Says:

    1. Let’s all use the SI units correctly. The proper measure of human exertion is neither calories nor Calories, nor nigiri, nor Big Macs, but beers.

    2. In addition to bicycling, how many calories do you spend blogging? Perhaps if you take the bus, thereby arriving at work faster than if you biked, giving you more time to blog, you’d actually earn more beers!

    Thanks to Brian for his analysis. Like Greg, I’d wondered what I might be gaining from crawling up the Hill.

    (Who didn’t bike to work today, but tries to during the regular week…)

  7. Gordon Says:

    I remember a display at the PNE one year. There was a bicycle on friction rollers which people would expend energy to see how much food they could eat extra because of that workout. People would peddle hard for 10 or 15 minutes and the person in charge of the display would inform them that they could now go eat a low single digit number of greesy french fries (usualy between 0.5 and 3).

    Without factoring in the inefficiency of the human body and the energy expended making bodily power available to the muscles you can end up with very small amounts of energy resulting from equations.

    I wonder if anyone has measured the amount of gasoline it takes to go up the hill.