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
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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.
A filtered education March 3, 2014Posted by mareserinitatis in education, homeschooling, math, older son, physics, science, societal commentary, teaching, younger son.
Tags: light, older son, physics, science, science education, teaching, younger son
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The older son is a lot of fun. Despite his statements that he has no desire to go into science, he seems to get and make a lot of science jokes. I know he’s not a scientist, but I feel comfortable that he’s scientifically literate. As he was homeschooled, I’m feeling pretty proud of myself.
I’m more anxious about the younger son, though. This weekend, he brought home his science homework, which focused on optics. The kids were studying filters, and one of the questions asked about what kind of light would you see if you shined a flashlight through a blue filter and then a red one. I asked him what he saw, and he said nothing. Unfortunately, he was told that he saw nothing because the flashlights just weren’t bright enough, but that what he should have seen was purple.
I’m pretty sure that if I had ever been bombarded with gamma rays in the past, I would’ve turned into She-Hulk at that very moment and started smashing things. Fortunately (or unfortunately, if being She-Hulk happens to be a goal of yours), that didn’t happen.
I find it infuriating that, throughout my years of homeschooling older son and teaching younger son math, I have constantly been questioned about my ability to teach them. The implication has always been that I may have a degree, but they are experts on teaching. In fact, this particular teacher attempted to take me to task earlier this year about the younger son’s math curriculum…the same teacher who apparently doesn’t understand that light and pigments work completely differently.
After I managed to calm down, I explained that light filters are like sieves, except that they only let one size of particle pass through: nothing bigger can pass through the holes, but nothing smaller can, either. After this explanation, the younger son was able to correctly explain that the reason he saw no light from his flashlight is that the two filters together had blocked all the light.
I’m going to be watching very carefully to see what kinds of scores he’s getting on his answers and whether the teacher realizes she made a mistake. This was very disappointing. There was a new science curriculum introduced this year, one which I was very excited about. The focus was supposed to be on hands-on, problem-based learning, which is great for science. Despite that, it seems that younger son’s science education may be lacking. What good does it do to have a top of the line science education curriculum (or math…or anything else) when our teachers don’t understand what they’re teaching? And how is it that these same teachers can justify questioning the ability to teach material that some of us understand far better than they do?
99 bottles of…oops January 28, 2014Posted by mareserinitatis in education, physics, science.
Tags: boy scouts, pascal's law, physics, science, Scientists, teaching, video
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Yesterday, I was helping guide some cub scouts (specifically webelos) through their scientist achievement. One of the things we had to discuss was Pascal’s law. Unfortunately, the instruction set on this was pretty limited: read and discuss. That, to me, means they likely wouldn’t understand it at all, so I felt like a demo was in order.
I decided to demonstrate the pressure change in a beer bottle. The concept is simple: fill an empty bottle with a non-compressible fluid (so water works, air won’t) and tap on the open end with a rubber mallet or even your hand. Of course, you want to do this over a bucket because the sudden change in pressure causes the bottle to break at the weakest point, usually the seam along the bottom, and spill it’s contents.
I did this demo for the first time in front of the kids. (I had ONE bottle of beer. No, I didn’t imbibe in front of them…I used it to bake bread.) It worked like a charm. If I didn’t trust physics so much, I wouldn’t have been okay trying it cold like that.
If you don’t have a beer bottle handy and would like to see this demo, there’s a good video on YouTube:
There are four lights! January 27, 2014Posted by mareserinitatis in physics, science.
Tags: lenses, optics, physics
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It’s hard being a physicist. Pretty much every place you look, you’re seeing some cool physical phenomenon that just screams, “Newton (or some other dead guy) discovered me!” If you’re lucky, the screaming isn’t followed by an apple hitting you on the head. Unless you’re a Klingon who is reciting love poetry; then that might be lucky.
Anyway, one such event occurred when I was looking into my coffee mug, which happened to be filled with hot water and a touch of coconut oil for flavor (and medium-chain triglycerides). Some bubbles were sitting there on the surface, breaking up the layer of oil, and behaving like a lens. There was an interesting image on the bottom of the cup, which you can see below.
As you can see, underneath each bubble, there appears to be something that almost looks like a four on a six-sided die. It took me a second to figure out what was going on. Then I realized that, directly above me, were four lights. If I shift my angle, you can see them quite clearly in the reflection, though the one on the bottom left is partially blocked by my phone.
This was surprising to me because this lamp is newly installed. Our previous lamp in this room had only one light. It took me a bit to realize that this was why I was so surprised to see an image in the bottom of my cup: it really was something new.
To get to the other side… September 30, 2013Posted by mareserinitatis in education, engineering, geology, older son, physics, teaching, younger son.
Tags: humor, jokes, physics, students, teaching
Those of you who are friends with me on Facebook may remember that I compiled a whole series of physics jokes. I was posting them daily for about two months. Some people loved them. I think a bunch of people also unfriended me because of it.
When I did this, I had an ulterior motive in mind: I wanted to tell them to my classes. I’ve found that students tend to listen better to teachers they think are likable. Unfortunately, I just don’t have the warm, fuzzy personality that many of my friends (particularly those in geology) have. I come across, sometimes, as a mean, nasty type.
And so the jokes…
They really do work. Students will loosen up and talk. They relax a bit. They smile. And most important, they don’t think I’m out to get them. Those endorphins do wonders.
The problem I’m having now is that so many of my jokes are physics related…and I’m teaching freshmen. While they all know about atoms and noble gases and protons, electrons, and neutrons, many of my jokes cover more esoteric topics. They give me blank stares when I talk about Heisenberg or Schroedinger or neutrinos…
There’s a part of me that would like to teach older students simply so that I have a more receptive audience. Or maybe my problem is that I’m teaching engineers and not physicists. Or maybe too many of them are from farms (see above comic).
But you, my dear reader, are a more receptive audience, right? And my kids…my kids know what neutrinos are…kind of. Maybe they’re just laughing at me because I sound funny when I talk about physics.
Incidentally, the punchline to the joke in the title, if you’re wondering, is, “Why did the tachyon cross the road?”
Friday fun: The best videos I’ve seen this week September 20, 2013Posted by mareserinitatis in Friday Fun, physics, science.
Tags: a capella science, Bill Nye, dancing, nina davuluri, physics, video
In hearing about all the racism that surfaced regarding Nina Davuluri, I heard someone mention she’d done a Bollywood dance for her performance. I had to check it out, and I have to admit that I’m very impressed. Her kneeling spins are something else.
I wasn’t nearly as impressed with Bill Nye’s cha cha on Dancing with the Stars, but you have to admit it’s kind of cute (if a bit stereotyped).
And speaking of science and music (but not dance), I also came across this wonderful remake of Queen’s Bohemian Rhapsody called Bohemian Gravity. I think this one is my favorite this week…it combines some pretty amazing talent with really amazing physics.
Making your mom proud (if she’s a physicist) August 19, 2013Posted by mareserinitatis in gifted, homeschooling, older son, physics, science.
Tags: homeschooling, older son, physics, science
One of the classes that the older boy is doing this year is physics. Rather than give him something very math intensive, I instead chose to have him study from Paul Hewitt’s Conceptual Physics text. It’s a book I came across after I’d already had a couple years of physics, and I regret not having had that book first. It does a wonderful job of explaining how physics works and what the concepts mean without drowning the reader in math.
When I picked up the older son after his study session the other day, he began talking about how imbalances in forces are what cause objects to accelerate. For instance, a car will move forward when the force created by the engine to move the car forward exceeds the forces of friction, gravity (if it’s on a hill), etc. After listening, I asked the question, “What happens then if the forces become balanced?”
I fully expected him to say that the object would stop moving. I really did. This is what the vast majority of students in my physics labs assumed when asked that question. Their assumption is that the forces must always be out of balance if the object is moving.
It would really depend on if the object were moving or still to begin with. If it was moving, it would continue to do so, and if it wasn’t moving, it would continue to stay still.
My response was to yell, “Yes!!!!!” at the top of my lungs and pump my fist. I’ve been proud of my son many times over the past few years, but few things make me beam as much as displaying a clear understanding of Newtonian mechanics.
Friday Fun: What is your favorite wavelength? August 2, 2013Posted by mareserinitatis in electromagnetics, Friday Fun, physics.
Tags: colors, friday fun, light, physics, spectrum, waves
I want to know everyone’s favorite color…by their wavelength. If you need help, here you go:
My personal favorite is right around 400 nm. And it’s entirely for aesthetic reasons.
So what is yours and why?
(Yeah, I know…everyone is going to pick some non-optical frequency. And yes, you have to stick to photons. Maybe we can do sonic waves another week…)
Math is useless July 5, 2013Posted by mareserinitatis in math, physics, Uncategorized, younger son.
Tags: chemistry, fireworks, math, physics, younger son
A lot of kids later become adults who think that math is a useless field of study. Why would I need to know that?! I’ve come across a lot of math books that are trying really hard to express how one can use math in order to motivate the learner by connecting it to an application as well as make it more interesting. Connect math to the ‘real world’ is not something that comes easily to most people.
Independence Day motivated a lot of discussion with the younger son about fireworks. While driving to our pyrotechnic fix last night, the younger son started asking what he would need to study in order to make fireworks. Mike and I both said, “Chemistry.” We both were assuming you need to know a lot about which chemicals to add to make particular colors. I guess it didn’t help that I’d seen this image earlier in the day:
We were both surprised when the younger boy said, “And I’d need to know math, too!” We agreed. And then he continued:
You can calculate how much of each chemical you need, how high it will go (a bigger explosion should be farther away), how fast it will go, how long it will take to before the explosion happens, how hot it will get…
He elaborated on each point and ended up spending somewhere between five and ten minutes telling us all the ways one could use math in making fireworks. I was completely stunned. There is this huge difficulty in getting a lot of people to understand that you can quantify and predict (through physics) so many things we take for granted. Yet, here is a kid who hasn’t even reached an age in the double digits who seems to understand that all of these things can have some sort of number associated with them and that they behave in ways that can be predicted by mathematical equations. Mike and I both sat there with our mouths hanging open, shocked at what we were hearing.
However, as soon as the fireworks came out of the box, the little kid in all of us came out and just wanted to go blow things up.
Rihanna has it wrong! June 27, 2013Posted by mareserinitatis in physics, science.
Tags: music, physics, refraction
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I heard Rihanna’s song “Diamonds” for the first time yesterday. (I know…I live under a rock…though, unfortunately, not that kind of rock or I’d be rich.) I rather liked the song except for the line that keeps popping up: “Shine bright like a diamond.” Something about the way it sounds doesn’t quite fit the rest of the song for me, or maybe it was to repetitive. But what really bugged me is that, every time I heard it, all I could think was, “Diamonds don’t shine! They refract!” I suppose refraction doesn’t sell as much pop music, though. I will suggest, however, if any of you are aces at making music remixes, that the song would benefit from more accurate physics. (Maybe she should take some notes from Britney Spears?)
Anyway, I hate it when science gets in the way of enjoying music. When it’s not wrong, though, it can sometimes make the music more enjoyable.