I should stop complaining about air resistance, but I can't help myself! I am teaching this semester from Kibble & Berkshire, and in Chapter 3 there are problems about air resistance that use speeds of around 100 meters per second and an atmospheric drag law that is proportional to velocity to the first power. I don't think there is any physical system that could have these properties: If you are small enough to have viscosity matter, you can never go 100 meters per second. Well, I guess molecules can go that fast, but (a) that isn't what the authors have in mind, and (b) molecules aren't really well described by continuum mechanics!
My friends who work in education of the young (the 'fuzz included) like to quote studies that show students answering without comment or concern questions like "Farmer Jake has 13 sheep and walks them 21 miles. How old is Farmer Jake?" There are many mixed-up reasons for this problem; some relate to rote learning; some relate to the artificial dichotomy set up between reading and math; some relate to the decontextualized ways we teach math; some relate to the testing environment that saturates schools; and so on. I feel all these things!
Imagine we want to see students using their common sense and their judgement with every question they consider and answer. I think that would be good. How do we foster this kind of thinking and exercise of common sense? I think we have to let the students call "bullshit".
Here's an example: "Johnny has twelve toy cars. He gives eight to Frances. How many does he have left?" Obviously we should accept the answer "four". But we should also accept the answer "No way! Who would give more than half of his toy cars to someone else?" If we don't accept that answer, we are saying to the students "calculate without thinking". That might be okay for quantum physicists (though I disagree), but it isn't okay for the rest of us.
On the airplane home from Spitzer Science Center and LIGO I made the mistake of watching the new Total Recall (2012
remake). (I also made the good decision to watch Men in Black 3 but that is not relevant to this post.) Central to the story is a tunnel through the Earth through which a train called
The Fall goes from Britain to Australia in 17 minutes. Important to the plot is a
gravity reversal on the journey in the core of the Earth, where the riders on The Fall are briefly weightless, and their chairs rotate from one orientation to the opposite so they are reoriented for arrival.
As everyone in first-year physics (well, for Physics Majors anyway) ought to calculate, the no-air-resistance, free-fall time for this journey (indeed on any straight chord through the Earth) is about 45 minutes (yes, identical to the time to go half-way around the Earth ballistically). That means that if riders were weightless for the entire journey the crossing would take 45 minutes.
The fact that The Fall does the journey faster than that would mean not one gravity reversal but three gravity reversals, because you would have to start the journey accelerating faster than gravity, and end the same. So the whole thing, which was obviously so highly thought out and worked out for the story, was just straight-up wrong.
I think if we ever do dig a chord-like tunnel through the Earth (the Chunnel is getting close to the relevant scale), we probably should run the trips at 45 minutes, because I think for pretty deep reasons this will be very close to minimum-effort travel times. In thinking about this, I have also thought about the relevant engineering gains and safety losses incurred if the Chunnel were operated evacuated of air or at low pressure. There were also idiotic things in the movie related to the implied air pressure, temperature, and air flow in the tunnel outside The Fall but these are more subtle. I digress.
Actually, the excellent MIB3 was even more physically unrealistic than Total Recall (bad time travel and so on), but the tone of the movie made it absolutely clear that you were expected to cut them physics slack.
Problem: The LHC delivers 8 TeV per particle in bunches of 1011 particles. What is the kinetic energy and momentum of a bunch, in SI units and then as compared to (a) a small-caliber bullet and (b) a Major-League baseball pitch?
I get that the bunch has far more kinetic energy than either a bullet or a baseball pitch, but far less momentum. A LHC particle bunch would burn you badly, but it wouldn't knock you down! Of course there are some 109 bunches per second, so you don't want to be hanging out in the beam line when it's running.
I am on a committee at NYU (related to NYU's Morse Academic Program) in which we were given copies of this article on scientific teaching (PDF) by Handelsman et al. The article has many sentences that include the word
should, which is a little annoying, but the worst thing about it is that it advocates, repeatedly, basing our teaching methods on scientifically demonstrable successes, measured with metrics. I don't object to being scientifically accountable, and I, for one, use the research-supported techniques of active learning, participatory classroom activities, and peer instruction. However, the article goes on about metrics without giving a single clear example. Why? Because they don't want to undermine their point by bringing up controversial testing strategies. However, we can't be metric-driven if we don't have metrics! So let's all just stop talking about the philosophy of being
scientific and find some metrics that we can agree on. I, for one, haven't found anything I like. After all, the goal of physics education is not to create students who perform better on isolated, decontextualized exams like the Force Concept Inventory!
I have been pleased to get a few
aha moments out of my undergrads this semester in the small, advanced NYU E&M II class I am teaching. The best was when we looked at the Poynting vector in a highly symmetrical ribbon-like circuit with a perfectly cylindrical resistor and we could see the power flowing from the battery to the resistor in the pure field geometry. That's nice! The point of the class is radiation, primarily, so we are about to start really doing that to death.
In her K/1 class (ages five to seven), the 'fuzz was doing "the weather" when an argument broke out between those who thought the clouds "move the Sun around" and those who thought the clouds "block out the Sun". She let the discussion proceed, encouraging contributions. In the end, the "move the Sun around" group got the consensus. What to do? You can correct them all, and then they learn that scientific truths are handed down by more knowledgeable authorities ("How do you know the Universe is expanding?" "I read it in a book."). Or you can let it lie, in which case they go home thinking they know something that in fact is wrong. Or (best, but extremely time-consuming), you can go through the process of having them turn their pseudo-scientific explanations into predictions about other phenomena, or have them extrapolate their model into other domains, and then see why or where it breaks. That's (to my mind) the only solution you could possibly call science, but it would require an absolutely radical replacement of the current curriculum and structure of school. The 'fuzz didn't have the right (it was someone else's classroom) to blow the schedule, and she didn't want to be a priestess, so she let it lie and moved on to the next activity.