Back-of-envelope physics

[…] that education today has too much memorisation. In fact, that refrain isn’t just used in high school; it’s the knee-jerk reaction of any educated person who is asked to name something that’s wrong about the education system. Some of the best teachers (of physics, and other things) I know think otherwise.

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If you remember debates about education from high school, the most common complaint you would’ve heard is that education today has too much memorisation. In fact, that refrain isn’t just used in high school; it’s the knee-jerk reaction of any educated person who is asked to name something that’s wrong about the education system.

The best teachers (of physics, and other things) I know think otherwise. The thing is, people are forced to memorise things without knowing why they need to remember those equations or numbers or what have you. Here’s a (somewhat arbitrary) for-instance: what’s the ‘ideal set’ of BWH measurements for a woman? I think I can safely say that anybody who remembers the numbers (36-24-36) doesn’t feel awfully burdened by this tax on their memory. Memorisation isn’t hard when you know where you’re going to use what you’ve memorised.

I thought I’d write down a few examples of where remembering numbers or equations can tell you interesting things. First, a simple example that requires nothing more than high-school physics:

I’ve written at length about how IISc’s roads are tree-lined and how this makes any pedestrian a prime target for bird-poop. I was walking to my room from the bus stop the other night, when the birds were especially, erm, active, and saw somebody walking in front of me. Suppose I saw a glob of poop as it left the bird, and wanted to warn the person in front, would I be able to – even assuming ideal circumstances – help them escape?

If the trees are about five human-beings tall, and you remember high-school kinematics, you can calculate (go ahead, do it!) that you have a little more than a second from launch to hit. You should also remember that reaction times for human beings are of the order of half a second. This is assuming that the person you randomly yell at on the road understands exactly what you’re saying and moves in exactly the right way. Seems implausible, doesn’t it? Probably is!

Here’s a somewhat more involved one that might seem arcane: Say you wanted to find out how fast molecules vibrate. To make things specific, say you wanted the time scale of vibration of a H2 molecule. (I say H2 to be on the safe side – Hydrogen’s vibrational mode becomes fully excited at about 4 K.)

What you will need to remember is the equipartition theorem of (statistical) thermodynamics: each degree of freedom adds 1*kT of energy to the molecule. You also have to remember, from quantum mechanics and the harmonic oscillator, that energy is Plank’s constant times the frequency. At room temperature, the H2 molecule has a vibration frequency of about one petaHertz. (Continuing along these lines, can you think of how you would estimate the speed with which atoms in the molecule move in course of these vibrations?)

Here’s a third one: suppose you want to find out how much iron you could quench with a given quantity of water. To make things specific again, say you had water at room temperature, and you’ve just heated iron to red-hot. How much water would you need to quench a bar of iron that weighs about 1 kg? Equivalently, what weight of iron can you quench with a bucket of water? Let’s say I give you that the temperature of the water cannot rise by more than one degree.

You’ll need to know that a normal bucket holds about twenty litres of water. You’d also need to remember that the specific heat of water is about 1 calorie per gram per degree Celsius. There is a law in physics called the Dulong-Petit law (equivalent to the equiparitition theorem) that says that the specific heat for solids is 3R, or about 6 calories per mole per deg Celsius. 1 kg of iron is (you’d have to remember that Fe has an atomic weight of 54) about 20 moles. Also, iron becomes red-hot at a temperature of about 300 deg C. This should tell you, with some mental arithmetic that you’d need about two buckets of water to quench a kilogram of red-hot iron.

In the three examples, there are about a dozen numbers or properties that one would’ve had to remember to do the calculations. My point is that this tax on your memory isn’t necessarily cumbersome. Memorisation is only ‘rote’ if you make it so.

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I must confess that I had to look up Fe’s atomic weight. As penance, here’s yesterday’s Abstruse Goose webcomic about relativity. Do you get it? (How close to the speed of light is the Flash running? The answer’s 0.99… to quite a few 9s)

[Einstein!]

[End. Fini. Kaputski. Einstein!]

11 thoughts on “Back-of-envelope physics”

  1. what if the bird was flying (towards you) when it pooped?? you’ll be showered if you forget relative velocity :)….and you still have only 1 second!!

  2. Ah, that. I was hoping nobody would notice!

    One degree of vibrational freedom adds kT. Whereas one degree of translational or rotational freedom adds 0.5*kT. This of course is a result of the two square terms in vibrational energy, but one each or translation or rotation. I didn’t want to write all this in the post.

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