Never ask a woman her weight…but her kinetic energy is fine August 2, 2014Posted by mareserinitatis in math, physics, running, science.
Tags: blerch, gravitation, kinetic energy, mass, physics, runners, running, science, velocity
add a comment
Today, I had one of the most awesome runs I’ve ever had. In particular, I sustained a much faster pace than I have over a 3 mile distance.
I couldn’t help but wonder, however, about the factor weight plays in one’s speed. As much as I try not to worry about weight and focus on being healthy, there’s this part of me that thinks it would be cool to lose a bit of weight because then I would go SO MUCH FASTER. Or at least that’s what I tell myself. However, I wondered if maybe I was exaggerating a bit, so I decided to check it out.
While it’s a bit of an oversimplification (that doesn’t take into account muscle tone, lung capacity, hydration, electrolyte levels, altitude adjustment, and the 18 bazillion other things that can affect a runner, even as stupid as that kink that’s still in your neck from last Thursday’s swim (okay, that only affects the triathletes here)), a quick check is to use the kinetic energy equation.
First, of course, we have to assume a perfectly spherical runner. Or a Blerch:
(As an aside, if you don’t know what the Blerch is, you must check out the Oatmeal’s wonderful cartoon on running. We all have a Blerch deep inside of us.) Either way, perfectly spherical things are happy for physicists because of all the lovely simplifications we can use in learning about them. So, if you’re a perfectly spherical runner, remember that physicists will love you.
Anyway, our hypothetical runner will have a mass (m), which is, of course, directly proportional to weight. (Weight, of course, is also referred to as gravitational attraction, so the more you have of it, the more attractive you are, at least from the perspective of the planetary body you’re closest to. Also, it may start to be more attracted to you if your velocity starts to approach the speed of light. Maybe this is why many humans also find runners attractive? Not sure.) The unit of mass is the kilogram. The runner will also have to maintain an average
speed velocity (v), and of course your pace is inversely proportional to your velocity. Your velocity is probably measured in miles per hour by your local race, but since we’re being scientific, we could also use SI units of meters/second. That being said, if you double your speed in one unit, it will also double in the other. There’s nothing fancy that happens because you’re using one unit or the other.
The kinetic energy of our runner, assuming an average velocity, can be written as
(1) KE=½ mv2
If we have the kinetic energy and mass, but want to find out the velocity, we first divide both sides of the equation by the mass and then take the square root of both sides. This leaves us with the following result:
(2) v=√(2 KE/m)
Let’s take an example. If we have a runner who has a velocity of 5 mph (or 2.2352 m/s) and a weight of 140 lbs. (or 63.5 kg). If we use SI units to compute this runner’s velocity, it turns out her initial kinetic energy (KEi) is 158.63 J.
On the other hand, we don’t really need to know how much initial kinetic energy the runner has, in terms of numbers. We can just define it as the quantity KEi. It turns out that physicists are kind of lazy about using numbers, so we’ll try to go without them because, in my opinion, it sort of confuses things. (You’ll see why later.)
How this this help us? Well, if you want to take a drastic example, let’s assume a runner loses half of her body weight.
First, let’s establish that her initial kinetic energy is defined also by an initial mass mi and velocity vi. (These would be the same as the 5 mph and 140 lbs. above.) This means her initial kinetic energy can be written as
(3) KEi=½ mivi2
and her initial velocity would therefore be
(4) vi=√(2 KEi/mi).
If her weight drops by half, we can write this as her initial weight divided by 2:
If we put (5) into our velocity equation (2) as our new mass and keep the same initial kinetic energy, we get
(6) vnew=√(2 KEi/m)=√(2 KEi/(mi/2))=√2*(2 KEi/(mi))=√2√(2 KEi/(mi))
You can see that the last part in six is basically the square root of two times our initial velocity from (3). That means that by losing half her weight, our runner would run about 1.4 times as fast, or 40% faster.
Now what if she only loses 10% of her weight? It turns out that (5) would become
so our new velocity would be the initial velocity times the square root of 1.1, which is about 1.05. Losing 10% of her weight only makes her 5% faster.
After spending time looking at this, I decided that going on a massive diet definitely isn’t going to help me speed up significantly. (In fact, if I manage to go from my current weight to my ideal, I would maybe get a gain of a bit over 1/2 mph.) It’s the fact that the mass doesn’t play as strong a role as velocity does because velocity gets squared and mass doesn’t. If you want to go faster, you are better off practicing running faster.
So please pass the ice cream! I need it for my fartlek recovery.
Dear runners, about my dogs… July 11, 2012Posted by mareserinitatis in pets.
Tags: dog, dogs, etiquette, Gigadog, runners
It would be much easier to walk the dogs individually, but it’s awfully difficult to find the time, especially with the hot weather. The only time I really have to take them out before the heat sets in is about 6 a.m. So I get everyone leashed up, and we look like this.
Keep in mind…that’s an 1/8 of a ton of dog I’m holding onto.
Today, Rainier left a brown, smelly gift on someone’s lawn. Cleaning this up is not easy while trying to hold onto the dogs. Therefore, I get them to sit down nicely on the sidewalk, and they are pretty good about staying there while I take care of their business.
Except today…because of someone who wasn’t thinking. After this incident, I feel it necessary to convey some etiquette to clueless joggers about dogs. I hope they listen.
If you see a dog seated on the sidewalk, please make a point to take advantage of the 8 feet of boulevard to your left. Only an idiot or small child runs up to a dog they don’t know. Do NOT try to run directly past them. I am not attempting to ‘own’ the sidewalk. I am telling you this to keep you (and me!) safe. If nothing else, try to remember that running on grass is better for your knees, so you can at least give your knees a break.
1 – Running up to a dog you don’t know is stupid. Not all dogs are friendly to strangers. If you run up to a dog you don’t know, they could very well turn around and bite you as they may think you’re attacking them. I hope not…but some dogs are that way.
2 – Running sets off a chase instinct in many dogs. If they didn’t have an inclination to go after you before, they very well may after they see you running away.
3 – A dog who is friendly may also be excitable, and you running up to the dog is likely to result in that dog jumping on you. I can tell you that having 100 lbs. of excitable fluff jump onto you can be an unpleasant experience.
4 – Running up behind a dog is stupid because, even if those dogs are super friendly with people (like mine are), you may spook them (like you did today), and they may take off running (like they did today). This may result in the person who didn’t see you because she is attempting to pick up poop either having her arm yanked out of the socket or nearly pulled over. All I can say is that I am glad Rainier really doesn’t move fast because he was a great anchor when Gigadog decided to check out these interlopers.
Now that I have clearly established reasons why you were not doing the brightest thing today, I can assure that I will continue to take my dogs to sit on the boulevard and let you pass. I realize not all people like dogs, and I make every effort to keep mine from accosting strangers who have no interest. I would ask that you do the same for me, however, when I am not in a position to see you coming.
Seven-month running update: The Fargo Marathon! May 19, 2012Posted by mareserinitatis in Fargo, older son, personal.
Tags: asthma, exercise, Fargo marathon, health, runners, running
1 comment so far
Seven months ago, I decided I was going to see if I could run the full 10k at the Fargo Marathon. I’ll jump to the important part first: I ran the whole 10k and never fell back to walking. In fact, I must’ve had some major runner’s high because when we got to the ramp going down into the Fargodome, I took off at the fastest sprint I could manage. In retrospect, that was not the brightest idea (especially since I’d had to use my asthma inhaler during the run), but I was incredibly excited and couldn’t help myself. Aside from that, I could squeak past 3-4 more people.
The older boy and I met my friend Kari and her husband at the starting line. They were gone pretty quickly (except that Kari’s pedometer attempted to bail on her, so she had to come back briefly and retrieve it). There were a lot of fun things along the course, including an Elvis impersonator and this guy, who cleverly located himself at about the 5 mile marker:
Earlier in the week, they were saying it was going to be unseasonably hot. This morning, it was rather cool but there were thunderstorms. Fortunately, they finished up just as we were leaving for the race, so it was cool and a bit damp outside. The only major issue was the last half mile or so where we were out of the protection of trees and dealing with some gusty wind.
I managed to improve my time from last year by 22 minutes. I also went from one of the last 10 finishers to having about 200 people behind me. (I also started in the middle of the pack and so had nearly half of the participants in the race pass me.) So, I definitely improved. I’m already excited about doing it again next year. First, however, I have a triathlon in mid-August…so I need to start swimming and riding bike.
The runners November 28, 2011Posted by mareserinitatis in feminism, societal commentary.
Tags: runners, work, working environment
From the title, you might think I’m going to be talking about jogging. Not so much. Nor will I be talking about Logan’s Run. Nope…I’m going to be talking about a type of person who annoys me.
I was reminded recently of a trip to Washington, DC. I was there for a conference, and a friend who lived nearby decided to visit. We weren’t sure where to go to dinner, so we met someplace and then grabbed a cab. The driver gave a suggestion, and we went for it.
The restaurant was a very upscale ethnic place near Embassy Row. After my friend and I were seated, I noticed something very strange about the wait staff. I thought it was just me, but then, when our dinner was presented, it became obvious: they weren’t acknowledging my existence at all. All questions were directed to my friend, and when I answered, they would wait for him to repeat what I had just said. They wouldn’t look at me, they wouldn’t speak to me, they wouldn’t hear when I spoke.
The food was fantastic, but I left feeling a bit demoralized. I’m sure my friend was sympathetic…but I think he was amused more than anything. I can’t help but wonder what they would’ve done had I gone to the restaurant with another woman. Would they have ignored both of us?
It’s easy to blow that kind of thing off when it’s a place you’ll only visit once or a fluke. It’s harder to deal with that sort of thing when it’s someone in a professional setting.
Admittedly, I’ve not run into anything as overt as the experience at the restaurant, but I have run into a couple men over the years who simply have no clue how to interact with women colleagues. It’s bad enough having a conversation with someone who stares at your chest…but it’s not much better when they refuse to look anywhere near you. You wonder if they even hear you.
And then there are the times when you try to talk to them, and you get the feeling they’re running from you. Literally. You ask them a question, and the best response you get is a terse, one-word answer. Maybe two, if they’re feeling dangerous. As soon as they’ve muttered their answer while looking the other direction, they turn to leave. They are done with the conversation, whether or not you are.
So these kinds of men are runners. They run away from women. It’s strange because the ones I’ve known have been married, so it’s not like they’re not around women at all. They simply have no idea how to act around a woman who is not a family member or friend…and apparently it’s never occurred to them to treat a female colleague like the rest of their colleagues.