mspringer | August 12, 2008Sunday night I was thinking about what to write for Monday morning and settled on the moment of inertia of the tires on a vehicle. If I may say so, it's a pretty good illustration for an interesting topic. Friction was a possible hitch for my proposed experiment, but I figured that cars were specifically designed to minimize friction, and both cars and tires are pretty heavy. Surely friction can be ignored safely. I wrote up the post in about half an hour and went to bed feeling pleased with myself.
Well. I know from experience that physics Ph.D. holders are not infallible even when…
mspringer | August 11, 2008If you live on flat terrain like I do, you might not get a chance to experiment with your car coasting down hills in neutral. It's kind of dangerous even if you can. But let's say you're on the top of your driveway and beginning from a stop you coast down to the street below. If the total drop is 10 feet, that gravitational potential energy will be converted to kinetic energy and you'll end up going something like 17 miles per hour. To do the calculation yourself, just set the potential energy at the top equal to the kinetic energy at the bottom, and solve for the velocity:
The mass…
mspringer | August 10, 2008I trust you're having a relaxing Sunday? Mathematical physics can be relaxing too, especially when you just look at it. We're just going to look at this one. In fact, this is a literal mathematical instantiation of Sunday relaxation.
If you fix a wire or a rope at two points and let it hang naturally, it forms a shape called a catenary.
It looks a lot like a parabola, and it turns out that in fact as long as the suspension points aren't too close together compared to the length of the rope, it's a very good approximation. For this particular graph the error from a purely parabolic…
mspringer | August 9, 2008This is K2. 11 people died this month trying to climb it.
At 28,251 ft (8,611 meters), K2 is the second highest mountain on this planet, and is technically a much more difficult climb than Everest. I've never climbed anything higher than a few hundred feet. Even a passenger jet slashing through the darkness will not reach much higher. To me the appeal of climbing is manifest in photographs like that one. The stern and austere beauty of these peaks is the closest even the most adventurous people can get to something like Buzz Aldrin's magnificent desolation.
In some respects K2 is more…
mspringer | August 8, 2008The Intro Physics II final exam was this week. The signs were all there.
1. It was a summer class. Therefore a fairly high proportion of the students were taking it again after having failed it previously.
2. The class switched professors two weeks before the final. The first professor is a skilled scientist but, well, not necessarily as gifted in passing his skills to his students.
3. The second professor made the final exam from scratch.
I just finished grading three problems worth of the final exam (the other two TAs are taking care of the rest), and I think the exam can be safely…
mspringer | August 7, 2008In 1909, Ernest Rutherford (actually his grad students) shot subatomic particles at gold atoms to try to probe the insides of those atoms. To his surprise, he found that instead of being one continuous glob, atoms actually had most of their mass concentrated in a small nucleus at the center of the atom. This quickly developed into the idea that the atom was like a tiny solar system: massive heavy thing at the center, orbited by electrons. Like this, except replace the planets with electrons and erase all that messy stuff like asteroids and the Kupier belt.
Now the parts of an atom are far…
mspringer | August 6, 2008There's an interesting question in the comments of the last solar sail post:
I have a question that's been bugging me about solar sails for ages: what about the fact that light pressure falls off over distance? Every time I see the idea discussed, this is never mentioned...
He's right. As the sail gets farther from the sun, the intensity of the light reaching the sail diminishes. By the same token, the sun's gravitational force is diminishing as well. To keep going, the radiation pressure has to be greater than the force from the sun's gravity.
Where I0 is the power output of the sun (3.…
mspringer | August 6, 2008Not long ago I wrote about one of the conceptual problems between intro mechanics and intro E&M from the freshman physics standpoint: developing a sense of the size of units between the two subjects. For instance, accelerating a spacecraft to escape velocity is no easy feat, but accelerating an electron to escape velocity only requires a tiny fraction of a volt. Let's do a similar calculation with power radiated from an accelerating point source.
As we know, a particle with an electric charge produces an electric field. A moving charged particle also generates a magnetic field. And…
mspringer | August 5, 2008I spent a few hours on the interstate this weekend, and I heard a Kid Rock song on the radio called "All Summer Long". If your tastes are anything like mine you'd probably rather not hear it. The song describes Kid's life as an 18-year-old, when "it was summertime in northern Michigan". Basically he does several irresponsible things in the chorus, topping the list off with the assertion that these things were done while "singing Sweet Home Alabama all summer long".
Come on, Kid. You were closer to thirteen-letter-expletive Quebec than you were to Alabama. Your lyrical choice lacks a…
mspringer | August 4, 2008There's a long list of things that scientists do that are unpopular. The creation/evolution argument rages on, the stem cell fight still provokes legislative skirmishes, genetic research raises discrimination concerns, neuroscience questions the very sense of self, and that's just the tip of the research iceberg. In broader science culture, there's nuclear energy, Yucca mountain, wind turbine locations, navy sonar, ballistic missile defense, wildlife habitat preservation, the space program, oil exploration, public funding...
But as far as I can tell, there's only one research subject that…
mspringer | August 4, 2008A few days ago Phil Plait at Bad Astronomy wrote a beautifully clear post about why there are no green stars. If I can summarize, it's because anything that's been heated up enough to emit green light is also hot enough to emit red, yellow, and some blue as well. The combination appears to us as a brilliant white. The equation that tells you just how much light is being dumped out by an object at a given temperature is called Planck's law, after the legendary Max Planck. The radiance per frequency emitted by a blackbody (most hot things you meet in daily life are blackbodies to a good…
mspringer | August 3, 2008The Sine Function. Calm and dignified, it sits among the royal court of the Elementary Functions, presiding with undulating grace over the trigonometric functions, partnered with the Exponential Function, and showing forth his power over the realms of physics and mathematics.
On one of the less subtle TV networks, this installment might be called When Good Functions Go Bad.
The sine function is ubiquitous in physics. Figuring out vector components, solving differential equations in E&M and quantum mechanics, decomposing Fourier series, you name it. It's about as well-behaved as…
mspringer | August 2, 2008Weekend posting here is usually pretty light, but it's only the second day here so I think a little extra is a nice way to kick things off. How about a little bit of solar sailing, since it fits pretty well with what I'm teaching in my intro class?
We all know light carries energy. Go outside on a sunny day and you can feel the energy being absorbed by your skin. You feel it as heat, but visible light energy allows you to see and ultraviolet light will induce chemical changes which will finally result in your body making itself a bit more tan. What's less apparent is that light also…
mspringer | August 1, 2008Welcome to the new home of Built on Facts, now happily hosted at ScienceBlogs. For those of you who've been readers of this site for a while, I'm honored that you like my scribblings and I hope you enjoy this new location even better!
For those of you who are curious about this new physics site here on ScienceBlogs, you can get a good idea of the flavor of the writing here by perusing the archives at the old site. In short, I usually write about physics in a style that fills the gap between pop-physics writing and actual physics textbooks. In other words, people who know nothing about…