An interesting article in the New York Times has been making the rounds of the internet lately. It talks about the tiny theoretical increase in weight of a Kindle when its memory is full as opposed to when it’s empty. Since I’ve previously written about the weight of data on a magnetic hard drive, I couldn’t resist taking a look at the equivalent effect for flash memory.

To begin with, we need to know a little about how flash memory works, and to do that, we need to know how transistors work. A transistor is just a tiny electrical switch. It has two contacts, the source and the drain, that are separated by a layer of material with an excess or lack of electrons. Normally this configuration blocks any current from flowing between the source and the drain. But when the right kind of voltage is applied to the separation layer, it removes the excess (or fills the lack) of electrons, allowing current to pass through. (For the record, I know I’m not doing justice to semiconductor physics here.)

As described in a pretty good article on Explain That Stuff!, and several other sources I’ve …

http://scienceblogs.com/dotphysics/2010/06/collisions_kinetic_energy_or_m.php

Took the words right out of my mouth. Or right off my keyboard. Whatever. I’m just happy to see other people are considering the same questions.

But I’ve got a couple of things to add. First of all, kinetic energy can be easily related to momentum using the formula

which tells you directly that an object with the same energy but larger mass will have a larger momentum.

Also, the big question: is it energy or momentum that gives a collision its decapitating power? My thought is that it actually depends on force. Think about this from the point of view of a particle in the neck. This particle doesn’t “know” (as if a particle could “know” anything) how big the sheet of glass hitting it is; it doesn’t “know” how much energy or momentum the glass has. The reason is that energy and momentum are what I’m going to call global properties, basically meaning that the total amount of them possessed by some object comes from contributions from all different pieces of the object. To measure a global property of the …

Like everyone else, I feel a need to analyze the giant water slide in the latest Mythbusters episode. But honestly, there isn’t much left to say. The original video has been around for a while and everybody else who does this kind of analysis has already had the chance to do it. Example 1; example 2 (okay, so I’m only linking to one blog, but there must be more).

I guess I might as well do the obvious calculation, but I’ll use the Mythbusters’ parameters instead of those from the original video (which are unknown). The slide starts with a downward ramp \(\unit{165}{\foot}\) long at a \(\unit{24}{\degree}\) slope, which then curves upward to a \(\unit{30}{\degree}\) launch ramp that terminates \(\unit{12}{\foot}\) above the surface of the lake. They didn’t say how long the launch ramp is, but I can work without that information. I’ll be trying to calculate two quantities mentioned on the show: how far each Mythbuster flies from the end of the ramp, and his maximum speed.

(here’s a full-size version)

There are two parts to this problem:

1. The slide
2. The flight

The first part …

The latest episode of Mythbusters features a myth with a deep physical explanation… no pun intended! Well, maybe. Anyway, the myth is that by diving under the water, you can escape injury from an explosion occurring above the surface. Adam and Jamie tried to solve this puzzle by experiment (what else), and their results seemed to show that the myth might actually be true, but I want to look at it from the theoretical standpoint: why might being underwater protect you from an explosion?

There is actually a not-too-obscure answer to this puzzle, and it has to do with refraction and reflection. These are phenomena that occur when a wave (of any sort — light, sound, or whatever) crosses a boundary between two media in which it has different speeds. Part of the wave bounces back (that’s reflection) and part of it continues through, but in a different direction (that’s refraction). Exactly how much of the wave’s power is reflected and how much is transmitted through, as well as the new direction of the transmitted part, depends on the angle of the incoming wave with respect to the surface, and also on the relative speed of the wave …

Here’s something interesting that came up on Slashdot today: scientists at the Israel Institute of Technology report having created an “acoustic black hole”, a region from which no sound waves can escape, just as a normal black hole is a region from which no light waves can escape.

How did they do it? Well, whenever sound travels through a medium, it does so at a characteristic speed — about \(\unit{343}{\frac{\meter}{\second}}\) in air, for example. That speed is relative to the medium, though, so if you can get the medium to move through your lab at a faster speed, the sound waves won’t be able to propagate fast enough to move against it (relative to the lab). If you had a wind tunnel blowing air to the right at \(\unit{400}{\frac{\meter}{\second}}\), the air would carry along all sound waves traveling through it, even those emitted in the leftward direction. Any sound waves produced at the right end of the tunnel would be stuck there — in effect, it’s a one-dimensional acoustic black hole, with an event horizon at the point (surface, really) where the air accelerates past the speed of sound as it …

An interesting question came up on StackOverflow: does a hard drive weigh more when it’s full than when it’s empty? Or more generally, does the weight of a hard drive change depending on how much (and what) data is stored in it?

First of all, as far as anyone in the IT industry is concerned, the answer is no. Any change in mass that would result from magnetic alignment is far too small to be measured by even the most sensitive scales in the world — we’re talking about a difference of something like \(10^{-14}\) grams.

Now, how did I get that number?

Let’s start from the beginning. Every atom has a property called the magnetic dipole moment, which means it acts like a tiny bar magnet, with a north pole and a south pole. In a ferromagnetic material, the type that’s used to store data in a magnetic hard drive, adjacent atoms tend to align parallel to each other, so that their north poles all point in the same direction. This leads to the formation of magnetic domains, small groups of atoms which are all aligned; each domain acts like one tiny bar magnet …